Daily Papers

The emergence of Large Language Models (LLMs) has necessitated the adoption of parallel training techniques, involving the deployment of thousands of GPUs to train a single model. Unfortunately, we have found that the efficiency of current parallel training is often suboptimal, largely due to the following two main issues. Firstly, hardware failures are inevitable, leading to interruptions in the training tasks. The inability to quickly identify the faulty components results in a substantial waste of GPU resources. Secondly, since GPUs must wait for parameter synchronization to complete before proceeding to the next round of computation, network congestions can greatly increase the waiting time for GPUs. To address these challenges, this paper introduces a communication-driven solution, namely the C4. The key insights of C4 are two folds. First, in parallel training, collective communication exhibits periodic and homogeneous characteristics, so any anomalies are certainly due to some form of hardware malfunction. By leveraging this feature, C4 can rapidly identify the faulty components, swiftly isolate the anomaly, and restart the task, thereby avoiding resource wastage caused by delays in anomaly detection. Second, the predictable communication model of collective communication, involving few large flows, allows C4 to efficiently execute traffic planning, substantially reducing network congestion. C4 has been extensively implemented across our production systems, cutting error-induced overhead by roughly 30% and enhancing runtime performance by about 15% for certain applications with moderate communication costs.

Training large language models is generally done via optimization methods on clusters containing tens of thousands of accelerators, communicating over a high-bandwidth interconnect. Scaling up these clusters is expensive and can become impractical, imposing limits on the size of models that can be trained. Several recent studies have proposed training methods that are less communication intensive, avoiding the need for a highly connected compute cluster. These state-of-the-art low communication training methods still employ a synchronization step for model parameters, which, when performed over all model replicas, can become costly on a low-bandwidth network. In this work, we propose a novel optimization method, NoLoCo, that does not explicitly synchronize all model parameters during training and, as a result, does not require any collective communication. NoLoCo implicitly synchronizes model weights via a novel variant of the Nesterov momentum optimizer by partially averaging model weights with a randomly selected other one. We provide both a theoretical convergence analysis for our proposed optimizer as well as empirical results from language model training. We benchmark NoLoCo on a wide range of accelerator counts and model sizes, between 125M to 6.8B parameters. Our method requires significantly less communication overhead than fully sharded data parallel training or even widely used low communication training method, DiLoCo. The synchronization step itself is estimated to be one magnitude faster than the all-reduce used in DiLoCo for few hundred accelerators training over the internet. We also do not have any global blocking communication that reduces accelerator idling time. Compared to DiLoCo, we also observe up to 4% faster convergence rate with wide range of model sizes and accelerator counts.

To address key limitations in human-object interaction (HOI) video generation -- specifically the reliance on curated motion data, limited generalization to novel objects/scenarios, and restricted accessibility -- we introduce HunyuanVideo-HOMA, a weakly conditioned multimodal-driven framework. HunyuanVideo-HOMA enhances controllability and reduces dependency on precise inputs through sparse, decoupled motion guidance. It encodes appearance and motion signals into the dual input space of a multimodal diffusion transformer (MMDiT), fusing them within a shared context space to synthesize temporally consistent and physically plausible interactions. To optimize training, we integrate a parameter-space HOI adapter initialized from pretrained MMDiT weights, preserving prior knowledge while enabling efficient adaptation, and a facial cross-attention adapter for anatomically accurate audio-driven lip synchronization. Extensive experiments confirm state-of-the-art performance in interaction naturalness and generalization under weak supervision. Finally, HunyuanVideo-HOMA demonstrates versatility in text-conditioned generation and interactive object manipulation, supported by a user-friendly demo interface. The project page is at https://anonymous.4open.science/w/homa-page-0FBE/.

Reinforcement Learning (RL) has become the most effective post-training approach for improving the capabilities of Large Language Models (LLMs). In practice, because of the high demands on latency and memory, it is particularly challenging to develop an efficient RL framework that reliably manages policy models with hundreds to thousands of billions of parameters. In this paper, we present LlamaRL, a fully distributed, asynchronous RL framework optimized for efficient training of large-scale LLMs with various model sizes (8B, 70B, and 405B parameters) on GPU clusters ranging from a handful to thousands of devices. LlamaRL introduces a streamlined, single-controller architecture built entirely on native PyTorch, enabling modularity, ease of use, and seamless scalability to thousands of GPUs. We also provide a theoretical analysis of LlamaRL's efficiency, including a formal proof that its asynchronous design leads to strict RL speed-up. Empirically during the Llama 3 post-training, by leveraging best practices such as colocated model offloading, asynchronous off-policy training, and distributed direct memory access for weight synchronization, LlamaRL achieves significant efficiency gains -- up to 10.7x speed-up compared to DeepSpeed-Chat-like systems on a 405B-parameter policy model. Furthermore, the efficiency advantage continues to grow with increasing model scale, demonstrating the framework's suitability for future large-scale RL training.

The most popular framework for distributed training of machine learning models is the (synchronous) parameter server (PS). This paradigm consists of n workers, which iteratively compute updates of the model parameters, and a stateful PS, which waits and aggregates all updates to generate a new estimate of model parameters and sends it back to the workers for a new iteration. Transient computation slowdowns or transmission delays can intolerably lengthen the time of each iteration. An efficient way to mitigate this problem is to let the PS wait only for the fastest n-b updates, before generating the new parameters. The slowest b workers are called backup workers. The optimal number b of backup workers depends on the cluster configuration and workload, but also (as we show in this paper) on the hyper-parameters of the learning algorithm and the current stage of the training. We propose DBW, an algorithm that dynamically decides the number of backup workers during the training process to maximize the convergence speed at each iteration. Our experiments show that DBW 1) removes the necessity to tune b by preliminary time-consuming experiments, and 2) makes the training up to a factor 3 faster than the optimal static configuration.

While fine-tuning pretrained models has become common practice, these models often underperform outside their specific domains. Recently developed model merging techniques enable the direct integration of multiple models, each fine-tuned for distinct tasks, into a single model. This strategy promotes multitasking capabilities without requiring retraining on the original datasets. However, existing methods fall short in addressing potential conflicts and complex correlations between tasks, especially in parameter-level adjustments, posing a challenge in effectively balancing parameter competition across various tasks. This paper introduces an innovative technique named PCB-Merging (Parameter Competition Balancing), a lightweight and training-free technique that adjusts the coefficients of each parameter for effective model merging. PCB-Merging employs intra-balancing to gauge parameter significance within individual tasks and inter-balancing to assess parameter similarities across different tasks. Parameters with low importance scores are dropped, and the remaining ones are rescaled to form the final merged model. We assessed our approach in diverse merging scenarios, including cross-task, cross-domain, and cross-training configurations, as well as out-of-domain generalization. The experimental results reveal that our approach achieves substantial performance enhancements across multiple modalities, domains, model sizes, number of tasks, fine-tuning forms, and large language models, outperforming existing model merging methods. The code is publicly available at: https://github.com/duguodong7/pcb-merging.

In distributed deep learning with data parallelism, synchronizing gradients at each training step can cause a huge communication overhead, especially when many nodes work together to train large models. Local gradient methods, such as Local SGD, address this issue by allowing workers to compute locally for H steps without synchronizing with others, hence reducing communication frequency. While H has been viewed as a hyperparameter to trade optimization efficiency for communication cost, recent research indicates that setting a proper H value can lead to generalization improvement. Yet, selecting a proper H is elusive. This work proposes a theory-grounded method for determining H, named the Quadratic Synchronization Rule (QSR), which recommends dynamically setting H in proportion to 1{eta^2} as the learning rate eta decays over time. Extensive ImageNet experiments on ResNet and ViT show that local gradient methods with QSR consistently improve the test accuracy over other synchronization strategies. Compared with the standard data parallel training, QSR enables Local AdamW on ViT-B to cut the training time on 16 or 64 GPUs down from 26.7 to 20.2 hours or from 8.6 to 5.5 hours and, at the same time, achieves 1.16% or 0.84% higher top-1 validation accuracy.

The angular synchronization problem aims to accurately estimate (up to a constant additive phase) a set of unknown angles theta_1, dots, theta_nin[0, 2pi) from m noisy measurements of their offsets theta_i-theta_j ;mod ; 2pi. Applications include, for example, sensor network localization, phase retrieval, and distributed clock synchronization. An extension of the problem to the heterogeneous setting (dubbed k-synchronization) is to estimate k groups of angles simultaneously, given noisy observations (with unknown group assignment) from each group. Existing methods for angular synchronization usually perform poorly in high-noise regimes, which are common in applications. In this paper, we leverage neural networks for the angular synchronization problem, and its heterogeneous extension, by proposing GNNSync, a theoretically-grounded end-to-end trainable framework using directed graph neural networks. In addition, new loss functions are devised to encode synchronization objectives. Experimental results on extensive data sets demonstrate that GNNSync attains competitive, and often superior, performance against a comprehensive set of baselines for the angular synchronization problem and its extension, validating the robustness of GNNSync even at high noise levels.

When considering a model architecture, there are several ways to reduce its memory footprint. Historically, popular approaches included selecting smaller architectures and creating sparse networks through pruning. More recently, randomized parameter-sharing (RPS) methods have gained traction for model compression at start of training. In this paper, we comprehensively assess the trade-off between memory and accuracy across RPS, pruning techniques, and building smaller models. Our findings demonstrate that RPS, which is both data and model-agnostic, consistently outperforms/matches smaller models and all moderately informed pruning strategies, such as MAG, SNIP, SYNFLOW, and GRASP, across the entire compression range. This advantage becomes particularly pronounced in higher compression scenarios. Notably, even when compared to highly informed pruning techniques like Lottery Ticket Rewinding (LTR), RPS exhibits superior performance in high compression settings. This points out inherent capacity advantage that RPS enjoys over sparse models. Theoretically, we establish RPS as a superior technique in terms of memory-efficient representation when compared to pruning for linear models. This paper argues in favor of paradigm shift towards RPS based models. During our rigorous evaluation of RPS, we identified issues in the state-of-the-art RPS technique ROAST, specifically regarding stability (ROAST's sensitivity to initialization hyperparameters, often leading to divergence) and Pareto-continuity (ROAST's inability to recover the accuracy of the original model at zero compression). We provably address both of these issues. We refer to the modified RPS, which incorporates our improvements, as STABLE-RPS.

Parameter-shared pre-trained language models (PLMs) have emerged as a successful approach in resource-constrained environments, enabling substantial reductions in model storage and memory costs without significant performance compromise. However, it is important to note that parameter sharing does not alleviate computational burdens associated with inference, thus impeding its practicality in situations characterized by limited stringent latency requirements or computational resources. Building upon neural ordinary differential equations (ODEs), we introduce a straightforward technique to enhance the inference efficiency of parameter-shared PLMs. Additionally, we propose a simple pre-training technique that leads to fully or partially shared models capable of achieving even greater inference acceleration. The experimental results demonstrate the effectiveness of our methods on both autoregressive and autoencoding PLMs, providing novel insights into more efficient utilization of parameter-shared models in resource-constrained settings.

Achieving high synchronization in the synthesis of realistic, speech-driven talking head videos presents a significant challenge. Traditional Generative Adversarial Networks (GAN) struggle to maintain consistent facial identity, while Neural Radiance Fields (NeRF) methods, although they can address this issue, often produce mismatched lip movements, inadequate facial expressions, and unstable head poses. A lifelike talking head requires synchronized coordination of subject identity, lip movements, facial expressions, and head poses. The absence of these synchronizations is a fundamental flaw, leading to unrealistic and artificial outcomes. To address the critical issue of synchronization, identified as the "devil" in creating realistic talking heads, we introduce SyncTalk. This NeRF-based method effectively maintains subject identity, enhancing synchronization and realism in talking head synthesis. SyncTalk employs a Face-Sync Controller to align lip movements with speech and innovatively uses a 3D facial blendshape model to capture accurate facial expressions. Our Head-Sync Stabilizer optimizes head poses, achieving more natural head movements. The Portrait-Sync Generator restores hair details and blends the generated head with the torso for a seamless visual experience. Extensive experiments and user studies demonstrate that SyncTalk outperforms state-of-the-art methods in synchronization and realism. We recommend watching the supplementary video: https://ziqiaopeng.github.io/synctalk

Transfer learning - i.e., further fine-tuning a pre-trained model on a downstream task - can confer significant advantages, including improved downstream performance, faster convergence, and better sample efficiency. These advantages have led to a proliferation of task-specific fine-tuned models, which typically can only perform a single task and do not benefit from one another. Recently, model merging techniques have emerged as a solution to combine multiple task-specific models into a single multitask model without performing additional training. However, existing merging methods often ignore the interference between parameters of different models, resulting in large performance drops when merging multiple models. In this paper, we demonstrate that prior merging techniques inadvertently lose valuable information due to two major sources of interference: (a) interference due to redundant parameter values and (b) disagreement on the sign of a given parameter's values across models. To address this, we propose our method, TrIm, Elect Sign & Merge (TIES-Merging), which introduces three novel steps when merging models: (1) resetting parameters that only changed a small amount during fine-tuning, (2) resolving sign conflicts, and (3) merging only the parameters that are in alignment with the final agreed-upon sign. We find that TIES-Merging outperforms several existing methods in diverse settings covering a range of modalities, domains, number of tasks, model sizes, architectures, and fine-tuning settings. We further analyze the impact of different types of interference on model parameters, highlight the importance of resolving sign interference. Our code is available at https://github.com/prateeky2806/ties-merging

In many neural networks, different values of the parameters may result in the same loss value. Parameter space symmetries are loss-invariant transformations that change the model parameters. Teleportation applies such transformations to accelerate optimization. However, the exact mechanism behind this algorithm's success is not well understood. In this paper, we show that teleportation not only speeds up optimization in the short-term, but gives overall faster time to convergence. Additionally, teleporting to minima with different curvatures improves generalization, which suggests a connection between the curvature of the minimum and generalization ability. Finally, we show that integrating teleportation into a wide range of optimization algorithms and optimization-based meta-learning improves convergence. Our results showcase the versatility of teleportation and demonstrate the potential of incorporating symmetry in optimization.

Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to understand how covariance structure in data, latent state size, and initialization affect the evolution of parameters throughout learning with gradient descent. We show that focusing on the learning dynamics in the frequency domain affords analytical solutions under mild assumptions, and we establish a link between one-dimensional SSMs and the dynamics of deep linear feed-forward networks. Finally, we analyze how latent state over-parameterization affects convergence time and describe future work in extending our results to the study of deep SSMs with nonlinear connections. This work is a step toward a theory of learning dynamics in deep state space models.

The performance of an algorithm often critically depends on its parameter configuration. While a variety of automated algorithm configuration methods have been proposed to relieve users from the tedious and error-prone task of manually tuning parameters, there is still a lot of untapped potential as the learned configuration is static, i.e., parameter settings remain fixed throughout the run. However, it has been shown that some algorithm parameters are best adjusted dynamically during execution, e.g., to adapt to the current part of the optimization landscape. Thus far, this is most commonly achieved through hand-crafted heuristics. A promising recent alternative is to automatically learn such dynamic parameter adaptation policies from data. In this article, we give the first comprehensive account of this new field of automated dynamic algorithm configuration (DAC), present a series of recent advances, and provide a solid foundation for future research in this field. Specifically, we (i) situate DAC in the broader historical context of AI research; (ii) formalize DAC as a computational problem; (iii) identify the methods used in prior-art to tackle this problem; (iv) conduct empirical case studies for using DAC in evolutionary optimization, AI planning, and machine learning.

Hyperparameter tuning is one of the essential steps to guarantee the convergence of machine learning models. We argue that intuition about the optimal choice of hyperparameters for stochastic gradient descent can be obtained by studying a neural network's phase diagram, in which each phase is characterised by distinctive dynamics of the singular values of weight matrices. Taking inspiration from disordered systems, we start from the observation that the loss landscape of a multilayer neural network with mean squared error can be interpreted as a disordered system in feature space, where the learnt features are mapped to soft spin degrees of freedom, the initial variance of the weight matrices is interpreted as the strength of the disorder, and temperature is given by the ratio of the learning rate and the batch size. As the model is trained, three phases can be identified, in which the dynamics of weight matrices is qualitatively different. Employing a Langevin equation for stochastic gradient descent, previously derived using Dyson Brownian motion, we demonstrate that the three dynamical regimes can be classified effectively, providing practical guidance for the choice of hyperparameters of the optimiser.

State Space Models (SSMs) have emerged as efficient alternatives to Transformers, mitigating their quadratic computational cost. However, the application of Parameter-Efficient Fine-Tuning (PEFT) methods to SSMs remains largely unexplored. In particular, prompt-based methods like Prompt Tuning and Prefix-Tuning, which are widely used in Transformers, do not perform well on SSMs. To address this, we propose state-based methods as a superior alternative to prompt-based methods. This new family of methods naturally stems from the architectural characteristics of SSMs. State-based methods adjust state-related features directly instead of depending on external prompts. Furthermore, we introduce a novel state-based PEFT method: State-offset Tuning. At every timestep, our method directly affects the state at the current step, leading to more effective adaptation. Through extensive experiments across diverse datasets, we demonstrate the effectiveness of our method. Code is available at https://github.com/furiosa-ai/ssm-state-tuning.

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural network parameterizations and normalizations during stochastic optimization, which impedes fast convergence and hurts generalization performance. Addressing this, we propose Geometric Parameterization (GmP), a novel neural network parameterization technique that effectively separates the radial and angular components of weights in the hyperspherical coordinate system. We show theoretically that GmP resolves the aforementioned instability issue. We report empirical results on various models and benchmarks to verify GmP's theoretical advantages of optimization stability, convergence speed and generalization performance.

Training deep neural networks (DNNs) using traditional backpropagation (BP) presents challenges in terms of computational complexity and energy consumption, particularly for on-device learning where computational resources are limited. Various alternatives to BP, including random feedback alignment, forward-forward, and local classifiers, have been explored to address these challenges. These methods have their advantages, but they can encounter difficulties when dealing with intricate visual tasks or demand considerable computational resources. In this paper, we propose a novel Local Learning rule inspired by neural activity Synchronization phenomena (LLS) observed in the brain. LLS utilizes fixed periodic basis vectors to synchronize neuron activity within each layer, enabling efficient training without the need for additional trainable parameters. We demonstrate the effectiveness of LLS and its variations, LLS-M and LLS-MxM, on multiple image classification datasets, achieving accuracy comparable to BP with reduced computational complexity and minimal additional parameters. Furthermore, the performance of LLS on the Visual Wake Word (VWW) dataset highlights its suitability for on-device learning tasks, making it a promising candidate for edge hardware implementations.

This study introduces a novel and interpretable model, DiffVox, for matching vocal effects in music production. DiffVox, short for ``Differentiable Vocal Fx", integrates parametric equalisation, dynamic range control, delay, and reverb with efficient differentiable implementations to enable gradient-based optimisation for parameter estimation. Vocal presets are retrieved from two datasets, comprising 70 tracks from MedleyDB and 365 tracks from a private collection. Analysis of parameter correlations highlights strong relationships between effects and parameters, such as the high-pass and low-shelf filters often behaving together to shape the low end, and the delay time correlates with the intensity of the delayed signals. Principal component analysis reveals connections to McAdams' timbre dimensions, where the most crucial component modulates the perceived spaciousness while the secondary components influence spectral brightness. Statistical testing confirms the non-Gaussian nature of the parameter distribution, highlighting the complexity of the vocal effects space. These initial findings on the parameter distributions set the foundation for future research in vocal effects modelling and automatic mixing. Our source code and datasets are accessible at https://github.com/SonyResearch/diffvox.

The rapid scaling of large language models necessitates more lightweight finetuning methods to reduce the explosive GPU memory overhead when numerous customized models are served simultaneously. Targeting more parameter-efficient low-rank adaptation (LoRA), parameter sharing presents a promising solution. Empirically, our research into high-level sharing principles highlights the indispensable role of differentiation in reversing the detrimental effects of pure sharing. Guided by this finding, we propose Mixture of Shards (MoS), incorporating both inter-layer and intra-layer sharing schemes, and integrating four nearly cost-free differentiation strategies, namely subset selection, pair dissociation, vector sharding, and shard privatization. Briefly, it selects a designated number of shards from global pools with a Mixture-of-Experts (MoE)-like routing mechanism before sequentially concatenating them to low-rank matrices. Hence, it retains all the advantages of LoRA while offering enhanced parameter efficiency, and effectively circumvents the drawbacks of peer parameter-sharing methods. Our empirical experiments demonstrate approximately 8x parameter savings in a standard LoRA setting. The ablation study confirms the significance of each component. Our insights into parameter sharing and MoS method may illuminate future developments of more parameter-efficient finetuning methods.

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their parameters while processing an input. For these models, parameter count and computational requirement form two independent axes along which an increase leads to better performance. In this work we derive and justify scaling laws defined on these two variables which generalize those known for standard language models and describe the performance of a wide range of routing architectures trained via three different techniques. Afterwards we provide two applications of these laws: first deriving an Effective Parameter Count along which all models scale at the same rate, and then using the scaling coefficients to give a quantitative comparison of the three routing techniques considered. Our analysis derives from an extensive evaluation of Routing Networks across five orders of magnitude of size, including models with hundreds of experts and hundreds of billions of parameters.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with scalability and handling rich inputs, such as images. To address these issues, we introduce a technique that converts neural networks from weight space to function space, through a dual parameterization. Our parameterization offers: (i) a way to scale function-space methods to large data sets via sparsification, (ii) retention of prior knowledge when access to past data is limited, and (iii) a mechanism to incorporate new data without retraining. Our experiments demonstrate that we can retain knowledge in continual learning and incorporate new data efficiently. We further show its strengths in uncertainty quantification and guiding exploration in model-based RL. Further information and code is available on the project website.

Diffusion models are trained by learning a sequence of models that reverse each step of noise corruption. Typically, the model parameters are fully shared across multiple timesteps to enhance training efficiency. However, since the denoising tasks differ at each timestep, the gradients computed at different timesteps may conflict, potentially degrading the overall performance of image generation. To solve this issue, this work proposes a Decouple-then-Merge (DeMe) framework, which begins with a pretrained model and finetunes separate models tailored to specific timesteps. We introduce several improved techniques during the finetuning stage to promote effective knowledge sharing while minimizing training interference across timesteps. Finally, after finetuning, these separate models can be merged into a single model in the parameter space, ensuring efficient and practical inference. Experimental results show significant generation quality improvements upon 6 benchmarks including Stable Diffusion on COCO30K, ImageNet1K, PartiPrompts, and DDPM on LSUN Church, LSUN Bedroom, and CIFAR10. Code is available at https://github.com/MqLeet/DeMe{GitHub}.

From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization-desynchronization transition in the Kuramoto model. A new way of thinking is to interpret the deterministic time evolution of a macroscopic variable as an external operation to a thermodynamic system. We then find that the irreversible work determines the equation for the collective dynamics. When analyzing the Kuramoto model, we employ a generalized concept of irreversible work which originates from a non-equilibrium identity associated with steady state thermodynamics.

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets and language models.

Merging various task-specific Transformer-based models trained on different tasks into a single unified model can execute all the tasks concurrently. Previous methods, exemplified by task arithmetic, have been proven to be both effective and scalable. Existing methods have primarily focused on seeking a static optimal solution within the original model parameter space. A notable challenge is mitigating the interference between parameters of different models, which can substantially deteriorate performance. In this paper, we propose to merge most of the parameters while upscaling the MLP of the Transformer layers to a weight-ensembling mixture of experts (MoE) module, which can dynamically integrate shared and task-specific knowledge based on the input, thereby providing a more flexible solution that can adapt to the specific needs of each instance. Our key insight is that by identifying and separating shared knowledge and task-specific knowledge, and then dynamically integrating them, we can mitigate the parameter interference problem to a great extent. We conduct the conventional multi-task model merging experiments and evaluate the generalization and robustness of our method. The results demonstrate the effectiveness of our method and provide a comprehensive understanding of our method. The code is available at https://anonymous.4open.science/r/weight-ensembling_MoE-67C9/

Training large neural networks typically requires sharing gradients between accelerators through specialized high-speed interconnects. Drawing from the signal processing principles of frequency decomposition and energy compaction, we demonstrate that synchronizing full optimizer states and model parameters during training is unnecessary. By decoupling momentum updates and allowing controlled divergence in optimizer states across accelerators, we achieve improved convergence compared to state-of-the-art optimizers. We introduce {De}coupled {Mo}mentum (DeMo), a fused optimizer and data parallel algorithm that reduces inter-accelerator communication requirements by several orders of magnitude. This enables training of large neural networks even with limited network bandwidth and heterogeneous hardware. Our method is topology-agnostic and architecture-independent and supports scalable clock-synchronous distributed training with negligible compute and memory overhead. Empirical results show that models trained with DeMo match or exceed the performance of equivalent models trained with AdamW, while eliminating the need for high-speed interconnects when pre-training large scale foundation models. An open source reference PyTorch implementation is published on GitHub at https://github.com/bloc97/DeMo

This paper investigates the global convergence of stepsized Newton methods for convex functions. We propose several simple stepsize schedules with fast global convergence guarantees, up to O (k^{-3}), nearly matching lower complexity bounds Omega (k^{-3.5}) of second-order methods. For cases with multiple plausible smoothness parameterizations or an unknown smoothness constant, we introduce a stepsize backtracking procedure that ensures convergence as if the optimal smoothness parameters were known.

The parameter space for any fixed architecture of feedforward ReLU neural networks serves as a proxy during training for the associated class of functions - but how faithful is this representation? It is known that many different parameter settings can determine the same function. Moreover, the degree of this redundancy is inhomogeneous: for some networks, the only symmetries are permutation of neurons in a layer and positive scaling of parameters at a neuron, while other networks admit additional hidden symmetries. In this work, we prove that, for any network architecture where no layer is narrower than the input, there exist parameter settings with no hidden symmetries. We also describe a number of mechanisms through which hidden symmetries can arise, and empirically approximate the functional dimension of different network architectures at initialization. These experiments indicate that the probability that a network has no hidden symmetries decreases towards 0 as depth increases, while increasing towards 1 as width and input dimension increase.

Varying dynamics parameters in simulation is a popular Domain Randomization (DR) approach for overcoming the reality gap in Reinforcement Learning (RL). Nevertheless, DR heavily hinges on the choice of the sampling distribution of the dynamics parameters, since high variability is crucial to regularize the agent's behavior but notoriously leads to overly conservative policies when randomizing excessively. In this paper, we propose a novel approach to address sim-to-real transfer, which automatically shapes dynamics distributions during training in simulation without requiring real-world data. We introduce DOmain RAndomization via Entropy MaximizatiON (DORAEMON), a constrained optimization problem that directly maximizes the entropy of the training distribution while retaining generalization capabilities. In achieving this, DORAEMON gradually increases the diversity of sampled dynamics parameters as long as the probability of success of the current policy is sufficiently high. We empirically validate the consistent benefits of DORAEMON in obtaining highly adaptive and generalizable policies, i.e. solving the task at hand across the widest range of dynamics parameters, as opposed to representative baselines from the DR literature. Notably, we also demonstrate the Sim2Real applicability of DORAEMON through its successful zero-shot transfer in a robotic manipulation setup under unknown real-world parameters.

We introduce a general framework for generating diverse visual content, including ambiguous images, panorama images, mesh textures, and Gaussian splat textures, by synchronizing multiple diffusion processes. We present exhaustive investigation into all possible scenarios for synchronizing multiple diffusion processes through a canonical space and analyze their characteristics across applications. In doing so, we reveal a previously unexplored case: averaging the outputs of Tweedie's formula while conducting denoising in multiple instance spaces. This case also provides the best quality with the widest applicability to downstream tasks. We name this case SyncTweedies. In our experiments generating visual content aforementioned, we demonstrate the superior quality of generation by SyncTweedies compared to other synchronization methods, optimization-based and iterative-update-based methods.

Parameter generation has struggled to scale up for a long time, significantly limiting its range of applications. In this study, we introduce Recurrent diffusion for large-scale Parameter Generation, called RPG. We first divide the trained parameters into non-overlapping parts, after which a recurrent model is proposed to learn their relationships. The recurrent model's outputs, as conditions, are then fed into a diffusion model to generate the neural network parameters. Using only a single GPU, recurrent diffusion enables us to generate popular vision and language models such as ConvNeXt-L and LoRA parameters of LLaMA-7B. Meanwhile, across various architectures and tasks, the generated parameters consistently perform comparable results over trained networks. Notably, our approach also shows the potential to generate models for handling unseen tasks, which largely increases the practicality of parameter generation. Our code is available https://github.com/NUS-HPC-AI-Lab/Recurrent-Parameter-Generation{here}.

Fine-tuning pre-trained models with custom data leads to numerous expert models on specific tasks. Merging models into one universal model to empower multi-task ability refraining from data leakage has gained popularity. With the expansion in data and model size, parameter efficient tuning becomes the common practice for obtaining task-specific models efficiently. However, we observe that existing methods designed for full fine-tuning merging fail under efficient tuning. To address the issues, we analyze from low-rank decomposition and reveal that maintaining direction and compensating for gap between singular values are crucial for efficient model merging. Consequently, we propose CoPA-Merging, a training-free parameter efficient merging method with complementary parameter adaptation. Specifically, we (1) prune parameters and construct scaling coefficients from inter-parameter relation to compensate for performance drop from task interference and (2) perform cross-task normalization to enhance unseen task generalization. We establish a benchmark consisting of diverse multimodal tasks, on which we conduct experiments to certificate the outstanding performance and generalizability of our method. Additional study and extensive analyses further showcase the effectiveness.

Long-term forecasting of chaotic systems from short-term observations remains a fundamental and underexplored challenge due to the intrinsic sensitivity to initial conditions and the complex geometry of strange attractors. Existing approaches often rely on long-term training data or focus on short-term sequence correlations, struggling to maintain predictive stability and dynamical coherence over extended horizons. We propose PhyxMamba, a novel framework that integrates a Mamba-based state-space model with physics-informed principles to capture the underlying dynamics of chaotic systems. By reconstructing the attractor manifold from brief observations using time-delay embeddings, PhyxMamba extracts global dynamical features essential for accurate forecasting. Our generative training scheme enables Mamba to replicate the physical process, augmented by multi-token prediction and attractor geometry regularization for physical constraints, enhancing prediction accuracy and preserving key statistical invariants. Extensive evaluations on diverse simulated and real-world chaotic systems demonstrate that PhyxMamba delivers superior long-term forecasting and faithfully captures essential dynamical invariants from short-term data. This framework opens new avenues for reliably predicting chaotic systems under observation-scarce conditions, with broad implications across climate science, neuroscience, epidemiology, and beyond. Our code is open-source at https://github.com/tsinghua-fib-lab/PhyxMamba.

As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit intrinsic correlations over time. Capitalizing on this, we introduce Correlation Mode Decomposition (CMD). This algorithm clusters the parameter space into groups, termed modes, that display synchronized behavior across epochs. This enables CMD to efficiently represent the training dynamics of complex networks, like ResNets and Transformers, using only a few modes. Moreover, test set generalization is enhanced. We introduce an efficient CMD variant, designed to run concurrently with training. Our experiments indicate that CMD surpasses the state-of-the-art method for compactly modeled dynamics on image classification. Our modeling can improve training efficiency and lower communication overhead, as shown by our preliminary experiments in the context of federated learning.

Consistency models (CMs) are a powerful class of diffusion-based generative models optimized for fast sampling. Most existing CMs are trained using discretized timesteps, which introduce additional hyperparameters and are prone to discretization errors. While continuous-time formulations can mitigate these issues, their success has been limited by training instability. To address this, we propose a simplified theoretical framework that unifies previous parameterizations of diffusion models and CMs, identifying the root causes of instability. Based on this analysis, we introduce key improvements in diffusion process parameterization, network architecture, and training objectives. These changes enable us to train continuous-time CMs at an unprecedented scale, reaching 1.5B parameters on ImageNet 512x512. Our proposed training algorithm, using only two sampling steps, achieves FID scores of 2.06 on CIFAR-10, 1.48 on ImageNet 64x64, and 1.88 on ImageNet 512x512, narrowing the gap in FID scores with the best existing diffusion models to within 10%.

In this work, we introduce a single parameter omega, to effectively control granularity in diffusion-based synthesis. This parameter is incorporated during the denoising steps of the diffusion model's reverse process. Our approach does not require model retraining, architectural modifications, or additional computational overhead during inference, yet enables precise control over the level of details in the generated outputs. Moreover, spatial masks or denoising schedules with varying omega values can be applied to achieve region-specific or timestep-specific granularity control. Prior knowledge of image composition from control signals or reference images further facilitates the creation of precise omega masks for granularity control on specific objects. To highlight the parameter's role in controlling subtle detail variations, the technique is named Omegance, combining "omega" and "nuance". Our method demonstrates impressive performance across various image and video synthesis tasks and is adaptable to advanced diffusion models. The code is available at https://github.com/itsmag11/Omegance.

Averaging the parameters of models that have the same architecture and initialization can provide a means of combining their respective capabilities. In this paper, we take the perspective that this "merging" operation can be seen as choosing parameters that approximately maximize the joint likelihood of the posteriors of the models' parameters. Computing a simple average of the models' parameters therefore corresponds to making an isotropic Gaussian approximation to their posteriors. We develop an alternative merging procedure based on the Laplace approximation where we approximate each model's posterior as a Gaussian distribution whose precision matrix corresponds to its Fisher information. We first show that our "Fisher merging" technique provides a performance boost in settings where simple parameter averaging is currently used -- specifically, robust fine-tuning and model ensembling. Then, we compare merging to standard gradient-based transfer learning and demonstrate that merging enables a fundamentally different method for transferring capabilities across models. Specifically, we show that Fisher merging is competitive with gradient-based transfer learning approaches (while being significantly cheaper) in intermediate-task training and domain-adaptive pre-training. We also show that our merging procedure makes it possible to combine models in previously unexplored ways. We release our code to facilitate future research into methods for merging models.

As we scale to more massive machine learning models, the frequent synchronization demands inherent in data-parallel approaches create significant slowdowns, posing a critical challenge to further scaling. Recent work develops an approach (DiLoCo) that relaxes synchronization demands without compromising model quality. However, these works do not carefully analyze how DiLoCo's behavior changes with model size. In this work, we study the scaling law behavior of DiLoCo when training LLMs under a fixed compute budget. We focus on how algorithmic factors, including number of model replicas, hyperparameters, and token budget affect training in ways that can be accurately predicted via scaling laws. We find that DiLoCo scales both predictably and robustly with model size. When well-tuned, DiLoCo scales better than data-parallel training with model size, and can outperform data-parallel training even at small model sizes. Our results showcase a more general set of benefits of DiLoCo than previously documented, including increased optimal batch sizes, improved downstream generalization with scale, and improved evaluation loss for a fixed token budget.

It has long been known in both neuroscience and AI that ``binding'' between neurons leads to a form of competitive learning where representations are compressed in order to represent more abstract concepts in deeper layers of the network. More recently, it was also hypothesized that dynamic (spatiotemporal) representations play an important role in both neuroscience and AI. Building on these ideas, we introduce Artificial Kuramoto Oscillatory Neurons (AKOrN) as a dynamical alternative to threshold units, which can be combined with arbitrary connectivity designs such as fully connected, convolutional, or attentive mechanisms. Our generalized Kuramoto updates bind neurons together through their synchronization dynamics. We show that this idea provides performance improvements across a wide spectrum of tasks such as unsupervised object discovery, adversarial robustness, calibrated uncertainty quantification, and reasoning. We believe that these empirical results show the importance of rethinking our assumptions at the most basic neuronal level of neural representation, and in particular show the importance of dynamical representations.

We propose a delay-agnostic asynchronous coordinate update algorithm (DEGAS) for computing operator fixed points, with applications to asynchronous optimization. DEGAS includes novel asynchronous variants of ADMM and block-coordinate descent as special cases. We prove that DEGAS converges under both bounded and unbounded delays under delay-free parameter conditions. We also validate by theory and experiments that DEGAS adapts well to the actual delays. The effectiveness of DEGAS is demonstrated by numerical experiments on classification problems.

Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of studying multiple interacting areas, and RNN theory needs to be likewise extended. We take a constructive approach towards this problem, leveraging tools from nonlinear control theory and machine learning to characterize when combinations of stable RNNs will themselves be stable. Importantly, we derive conditions which allow for massive feedback connections between interacting RNNs. We parameterize these conditions for easy optimization using gradient-based techniques, and show that stability-constrained "networks of networks" can perform well on challenging sequential-processing benchmark tasks. Altogether, our results provide a principled approach towards understanding distributed, modular function in the brain.

The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such proposal uses muP parameterized networks, where the optimal hyperparameters for small width networks transfer to networks with arbitrarily large width. However, in this scheme, hyperparameters do not transfer across depths. As a remedy, we study residual networks with a residual branch scale of 1/text{depth} in combination with the muP parameterization. We provide experiments demonstrating that residual architectures including convolutional ResNets and Vision Transformers trained with this parameterization exhibit transfer of optimal hyperparameters across width and depth on CIFAR-10 and ImageNet. Furthermore, our empirical findings are supported and motivated by theory. Using recent developments in the dynamical mean field theory (DMFT) description of neural network learning dynamics, we show that this parameterization of ResNets admits a well-defined feature learning joint infinite-width and infinite-depth limit and show convergence of finite-size network dynamics towards this limit.

Selective state space models (SSM), such as Mamba, have gained prominence for their effectiveness in modeling sequential data. Despite their outstanding empirical performance, a comprehensive theoretical understanding of deep selective SSM remains elusive, hindering their further development and adoption for applications that need high fidelity. In this paper, we investigate the dynamical properties of tokens in a pre-trained Mamba model. In particular, we derive the dynamical system governing the continuous-time limit of the Mamba model and characterize the asymptotic behavior of its solutions. In the one-dimensional case, we prove that only one of the following two scenarios happens: either all tokens converge to zero, or all tokens diverge to infinity. We provide criteria based on model parameters to determine when each scenario occurs. For the convergent scenario, we empirically verify that this scenario negatively impacts the model's performance. For the divergent scenario, we prove that different tokens will diverge to infinity at different rates, thereby contributing unequally to the updates during model training. Based on these investigations, we propose two refinements for the model: excluding the convergent scenario and reordering tokens based on their importance scores, both aimed at improving practical performance. Our experimental results validate these refinements, offering insights into enhancing Mamba's effectiveness in real-world applications.

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current decomposition methods -- decomposes neural network parameters into a sum of sparsely used vectors in parameter space. However, the current main method in this framework, Attribution-based Parameter Decomposition (APD), is impractical on account of its computational cost and sensitivity to hyperparameters. In this work, we introduce Stochastic Parameter Decomposition (SPD), a method that is more scalable and robust to hyperparameters than APD, which we demonstrate by decomposing models that are slightly larger and more complex than was possible to decompose with APD. We also show that SPD avoids other issues, such as shrinkage of the learned parameters, and better identifies ground truth mechanisms in toy models. By bridging causal mediation analysis and network decomposition methods, this demonstration opens up new research possibilities in mechanistic interpretability by removing barriers to scaling linear parameter decomposition methods to larger models. We release a library for running SPD and reproducing our experiments at https://github.com/goodfire-ai/spd.

Pose based video sychronization can have applications in multiple domains such as gameplay performance evaluation, choreography or guiding athletes. The subject's actions could be compared and evaluated against those performed by professionals side by side. In this paper, we propose an end to end pipeline for synchronizing videos based on pose. The first step crops the region where the person present in the image followed by pose detection on the cropped image. This is followed by application of Dynamic Time Warping(DTW) on angle/ distance measures between the pose keypoints leading to a scale and shift invariant pose matching pipeline.

Practical identifiability is a critical concern in data-driven modeling of mathematical systems. In this paper, we propose a novel framework for practical identifiability analysis to evaluate parameter identifiability in mathematical models of biological systems. Starting with a rigorous mathematical definition of practical identifiability, we demonstrate its equivalence to the invertibility of the Fisher Information Matrix. Our framework establishes the relationship between practical identifiability and coordinate identifiability, introducing a novel metric that simplifies and accelerates the evaluation of parameter identifiability compared to the profile likelihood method. Additionally, we introduce new regularization terms to address non-identifiable parameters, enabling uncertainty quantification and improving model reliability. To guide experimental design, we present an optimal data collection algorithm that ensures all model parameters are practically identifiable. Applications to Hill functions, neural networks, and dynamic biological models demonstrate the feasibility and efficiency of the proposed computational framework in uncovering critical biological processes and identifying key observable variables.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

We introduce a model-based asynchronous multi-fidelity method for hyperparameter and neural architecture search that combines the strengths of asynchronous Hyperband and Gaussian process-based Bayesian optimization. At the heart of our method is a probabilistic model that can simultaneously reason across hyperparameters and resource levels, and supports decision-making in the presence of pending evaluations. We demonstrate the effectiveness of our method on a wide range of challenging benchmarks, for tabular data, image classification and language modelling, and report substantial speed-ups over current state-of-the-art methods. Our new methods, along with asynchronous baselines, are implemented in a distributed framework which will be open sourced along with this publication.

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

Modern RL-based post-training for large language models (LLMs) co-locate trajectory sampling and policy optimisation on the same GPU cluster, forcing the system to switch between inference and training workloads. This serial context switching violates the single-program-multiple-data (SPMD) assumption underlying today's distributed training systems. We present Echo, the RL system that cleanly decouples these two phases across heterogeneous "inference" and "training" swarms while preserving statistical efficiency. Echo introduces two lightweight synchronization protocols: a sequential pull mode that refreshes policy weights according to API call for minimal bias, and an asynchronous push-pull mode that streams version-tagged rollouts through a replay buffer to maximise hardware utilisation. Training four representative RL workloads with Qwen3-4B, Qwen2.5-7B, Qwen3-30B-A3B-Thinking-2507 and Qwen3-32B on a geographically distributed cluster, Echo matches a fully co-located Verl baseline in convergence speed and final reward while off-loading trajectory generation to commodity edge hardware. These promising results demonstrate that large-scale RL for LLMs could achieve datacentre-grade performance using decentralised, heterogeneous resources.

Lip synchronization, known as the task of aligning lip movements in an existing video with new input audio, is typically framed as a simpler variant of audio-driven facial animation. However, as well as suffering from the usual issues in talking head generation (e.g., temporal consistency), lip synchronization presents significant new challenges such as expression leakage from the input video and facial occlusions, which can severely impact real-world applications like automated dubbing, but are often neglected in existing works. To address these shortcomings, we present KeySync, a two-stage framework that succeeds in solving the issue of temporal consistency, while also incorporating solutions for leakage and occlusions using a carefully designed masking strategy. We show that KeySync achieves state-of-the-art results in lip reconstruction and cross-synchronization, improving visual quality and reducing expression leakage according to LipLeak, our novel leakage metric. Furthermore, we demonstrate the effectiveness of our new masking approach in handling occlusions and validate our architectural choices through several ablation studies. Code and model weights can be found at https://antonibigata.github.io/KeySync.

The objective of this study is to evaluate the potential for History Matching (HM) to tune a climate system with multi-scale dynamics. By considering a toy climate model, namely, the two-scale Lorenz96 model and producing experiments in perfect-model setting, we explore in detail how several built-in choices need to be carefully tested. We also demonstrate the importance of introducing physical expertise in the range of parameters, a priori to running HM. Finally we revisit a classical procedure in climate model tuning, that consists of tuning the slow and fast components separately. By doing so in the Lorenz96 model, we illustrate the non-uniqueness of plausible parameters and highlight the specificity of metrics emerging from the coupling. This paper contributes also to bridging the communities of uncertainty quantification, machine learning and climate modeling, by making connections between the terms used by each community for the same concept and presenting promising collaboration avenues that would benefit climate modeling research.

Reinforcement learning (RL) has become a pivotal technology in the post-training phase of large language models (LLMs). Traditional task-colocated RL frameworks suffer from significant scalability bottlenecks, while task-separated RL frameworks face challenges in complex dataflows and the corresponding resource idling and workload imbalance. Moreover, most existing frameworks are tightly coupled with LLM training or inference engines, making it difficult to support custom-designed engines. To address these challenges, we propose AsyncFlow, an asynchronous streaming RL framework for efficient post-training. Specifically, we introduce a distributed data storage and transfer module that provides a unified data management and fine-grained scheduling capability in a fully streamed manner. This architecture inherently facilitates automated pipeline overlapping among RL tasks and dynamic load balancing. Moreover, we propose a producer-consumer-based asynchronous workflow engineered to minimize computational idleness by strategically deferring parameter update process within staleness thresholds. Finally, the core capability of AsynFlow is architecturally decoupled from underlying training and inference engines and encapsulated by service-oriented user interfaces, offering a modular and customizable user experience. Extensive experiments demonstrate an average of 1.59 throughput improvement compared with state-of-the-art baseline. The presented architecture in this work provides actionable insights for next-generation RL training system designs.

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are however difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended beta-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables for the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.

We study compute efficiency of LLM training when using different parameterizations, i.e., rules for adjusting model and optimizer hyperparameters (HPs) as model size changes. Some parameterizations fail to transfer optimal base HPs (such as learning rate) across changes in model depth, requiring practitioners to either re-tune these HPs as they scale up (expensive), or accept sub-optimal training when re-tuning is prohibitive. Even when they achieve HP transfer, we develop theory to show parameterizations may still exist in the lazy learning regime where layers learn only features close to their linearization, preventing effective use of depth and nonlinearity. Finally, we identify and adopt the parameterization we call CompleteP that achieves both depth-wise HP transfer and non-lazy learning in all layers. CompleteP enables a wider range of model width/depth ratios to remain compute-efficient, unlocking shapes better suited for different hardware settings and operational contexts. Moreover, CompleteP enables 12-34% compute efficiency improvements over the prior state-of-the-art.

The widespread applicability and increasing omnipresence of LLMs have instigated a need to align LLM responses to user and stakeholder preferences. Many preference optimization approaches have been proposed that fine-tune LLM parameters to achieve good alignment. However, such parameter tuning is known to interfere with model performance on many tasks. Moreover, keeping up with shifting user preferences is tricky in such a situation. Decoding-time alignment with reward model guidance solves these issues at the cost of increased inference time. However, most of such methods fail to strike the right balance between exploration and exploitation of reward -- often due to the conflated formulation of these two aspects - to give well-aligned responses. To remedy this we decouple these two aspects and implement them in an evolutionary fashion: exploration is enforced by decoding from mutated instructions and exploitation is represented as the periodic replacement of poorly-rewarded generations with well-rewarded ones. Empirical evidences indicate that this strategy outperforms many preference optimization and decode-time alignment approaches on two widely accepted alignment benchmarks AlpacaEval 2 and MT-Bench. Our implementation will be available at: https://darwin-alignment.github.io.

Parameter regularization or allocation methods are effective in overcoming catastrophic forgetting in lifelong learning. However, they solve all tasks in a sequence uniformly and ignore the differences in the learning difficulty of different tasks. So parameter regularization methods face significant forgetting when learning a new task very different from learned tasks, and parameter allocation methods face unnecessary parameter overhead when learning simple tasks. In this paper, we propose the Parameter Allocation & Regularization (PAR), which adaptively select an appropriate strategy for each task from parameter allocation and regularization based on its learning difficulty. A task is easy for a model that has learned tasks related to it and vice versa. We propose a divergence estimation method based on the Nearest-Prototype distance to measure the task relatedness using only features of the new task. Moreover, we propose a time-efficient relatedness-aware sampling-based architecture search strategy to reduce the parameter overhead for allocation. Experimental results on multiple benchmarks demonstrate that, compared with SOTAs, our method is scalable and significantly reduces the model's redundancy while improving the model's performance. Further qualitative analysis indicates that PAR obtains reasonable task-relatedness.

Local stochastic gradient descent (Local-SGD), also referred to as federated averaging, is an approach to distributed optimization where each device performs more than one SGD update per communication. This work presents an empirical study of {\it asynchronous} Local-SGD for training language models; that is, each worker updates the global parameters as soon as it has finished its SGD steps. We conduct a comprehensive investigation by examining how worker hardware heterogeneity, model size, number of workers, and optimizer could impact the learning performance. We find that with naive implementations, asynchronous Local-SGD takes more iterations to converge than its synchronous counterpart despite updating the (global) model parameters more frequently. We identify momentum acceleration on the global parameters when worker gradients are stale as a key challenge. We propose a novel method that utilizes a delayed Nesterov momentum update and adjusts the workers' local training steps based on their computation speed. This approach, evaluated with models up to 150M parameters on the C4 dataset, matches the performance of synchronous Local-SGD in terms of perplexity per update step, and significantly surpasses it in terms of wall clock time.

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.

In the task of talking face generation, the objective is to generate a face video with lips synchronized to the corresponding audio while preserving visual details and identity information. Current methods face the challenge of learning accurate lip synchronization while avoiding detrimental effects on visual quality, as well as robustly evaluating such synchronization. To tackle these problems, we propose utilizing an audio-visual speech representation expert (AV-HuBERT) for calculating lip synchronization loss during training. Moreover, leveraging AV-HuBERT's features, we introduce three novel lip synchronization evaluation metrics, aiming to provide a comprehensive assessment of lip synchronization performance. Experimental results, along with a detailed ablation study, demonstrate the effectiveness of our approach and the utility of the proposed evaluation metrics.

Recent work has shown that orthonormal matrix updates speed up neural network optimization, improve training stability, and offer better hyperparameter transfer across model sizes. Applying these updates efficiently when model weights and optimizer states are sharded across a large-scale distributed LLM training system remains a major challenge. We introduce Dion (DIstributed OrthoNormalization), a scalable and communication-efficient orthonormalizing optimizer. Dion leverages low-rank approximation and decoupled momentum buffers, eliminating the need for full gradient synchronization while producing numerically equivalent results. It is compatible with simultaneous DDP, FSDP, and TP parallelism, and it computes an orthonormalized update without unsharding a full parameter matrix on any single device. We evaluate Dion on language models from 120M to 3B parameters and find that its benefits improve with increasing model size and batch size.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

During typical gradient-based training of deep neural networks, all of the model's parameters are updated at each iteration. Recent work has shown that it is possible to update only a small subset of the model's parameters during training, which can alleviate storage and communication requirements. In this paper, we show that it is possible to induce a fixed sparse mask on the model's parameters that selects a subset to update over many iterations. Our method constructs the mask out of the k parameters with the largest Fisher information as a simple approximation as to which parameters are most important for the task at hand. In experiments on parameter-efficient transfer learning and distributed training, we show that our approach matches or exceeds the performance of other methods for training with sparse updates while being more efficient in terms of memory usage and communication costs. We release our code publicly to promote further applications of our approach.

Second-order optimization has been developed to accelerate the training of deep neural networks and it is being applied to increasingly larger-scale models. In this study, towards training on further larger scales, we identify a specific parameterization for second-order optimization that promotes feature learning in a stable manner even if the network width increases significantly. Inspired by a maximal update parameterization, we consider a one-step update of the gradient and reveal the appropriate scales of hyperparameters including random initialization, learning rates, and damping terms. Our approach covers two major second-order optimization algorithms, K-FAC and Shampoo, and we demonstrate that our parameterization achieves higher generalization performance in feature learning. In particular, it enables us to transfer the hyperparameters across models with different widths.

This paper presents a practical investigation into fine-tuning model parameters for mathematical reasoning tasks through experimenting with various configurations including randomness control, reasoning depth, and sampling strategies, careful tuning demonstrates substantial improvements in efficiency as well as performance. A holistically optimized framework is introduced for five state-of-the-art models on mathematical reasoning tasks, exhibiting significant performance boosts while maintaining solution correctness. Through systematic parameter optimization across Qwen2.5-72B, Llama-3.1-70B, DeepSeek-V3, Mixtral-8x22B, and Yi-Lightning, consistent efficiency gains are demonstrated with 100% optimization success rate. The methodology achieves an average 29.4% reduction in computational cost and 23.9% improvement in inference speed across all tested models. This framework systematically searches parameter spaces including temperature (0.1-0.5), reasoning steps (4-12), planning periods (1-4), and nucleus sampling (0.85-0.98), determining optimal configurations through testing on mathematical reasoning benchmarks. Critical findings show that lower temperature regimes (0.1-0.4) and reduced reasoning steps (4-6) consistently enhance efficiency without compromising accuracy. DeepSeek-V3 achieves the highest accuracy at 98%, while Mixtral-8x22B delivers the most cost-effective performance at 361.5 tokens per accurate response. Key contributions include: (1) the first comprehensive optimization study for five diverse SOTA models in mathematical reasoning, (2) a standardized production-oriented parameter optimization framework, (3) discovery of universal optimization trends applicable across model architectures, and (4) production-ready configurations with extensive performance characterization.

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

Dynamical generative models that produce samples through an iterative process, such as Flow Matching and denoising diffusion models, have seen widespread use, but there have not been many theoretically-sound methods for improving these models with reward fine-tuning. In this work, we cast reward fine-tuning as stochastic optimal control (SOC). Critically, we prove that a very specific memoryless noise schedule must be enforced during fine-tuning, in order to account for the dependency between the noise variable and the generated samples. We also propose a new algorithm named Adjoint Matching which outperforms existing SOC algorithms, by casting SOC problems as a regression problem. We find that our approach significantly improves over existing methods for reward fine-tuning, achieving better consistency, realism, and generalization to unseen human preference reward models, while retaining sample diversity.

Large language models are typically trained densely: all parameters are updated with respect to all inputs. This requires synchronization of billions of parameters across thousands of GPUs. We introduce a simple but effective method to asynchronously train large, sparse language models on arbitrary text corpora. Our method clusters a corpus into sets of related documents, trains a separate expert language model on each cluster, and combines them in a sparse ensemble for inference. This approach generalizes embarrassingly parallel training by automatically discovering the domains for each expert, and eliminates nearly all the communication overhead of existing sparse language models. Our technique outperforms dense baselines on multiple corpora and few-shot tasks, and our analysis shows that specializing experts to meaningful clusters is key to these gains. Performance also improves with the number of experts and size of training data, suggesting this is a highly efficient and accessible approach to training large language models.

Continual learning (CL) refers to the ability of an intelligent system to sequentially acquire and retain knowledge from a stream of data with as little computational overhead as possible. To this end; regularization, replay, architecture, and parameter isolation approaches were introduced to the literature. Parameter isolation using a sparse network which enables to allocate distinct parts of the neural network to different tasks and also allows to share of parameters between tasks if they are similar. Dynamic Sparse Training (DST) is a prominent way to find these sparse networks and isolate them for each task. This paper is the first empirical study investigating the effect of different DST components under the CL paradigm to fill a critical research gap and shed light on the optimal configuration of DST for CL if it exists. Therefore, we perform a comprehensive study in which we investigate various DST components to find the best topology per task on well-known CIFAR100 and miniImageNet benchmarks in a task-incremental CL setup since our primary focus is to evaluate the performance of various DST criteria, rather than the process of mask selection. We found that, at a low sparsity level, Erdos-Renyi Kernel (ERK) initialization utilizes the backbone more efficiently and allows to effectively learn increments of tasks. At a high sparsity level, however, uniform initialization demonstrates more reliable and robust performance. In terms of growth strategy; performance is dependent on the defined initialization strategy, and the extent of sparsity. Finally, adaptivity within DST components is a promising way for better continual learners.

Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the underlying parameter estimates, for which only a logarithmic rate is achieved. In this work, we (re)introduce and investigate a metric, named Orlicz-Wasserstein distance, in the study of the Bayesian contraction behavior for the parameters. We show that despite the overall slow convergence guarantees for all the parameters, posterior contraction for parameters happens at almost polynomial rates in outlier regions of the parameter space. Our theoretical results provide new insight in understanding the convergence behavior of parameters arising from various settings of hierarchical Bayesian nonparametric models. In addition, we provide an algorithm to compute the metric by leveraging Sinkhorn divergences and validate our findings through a simulation study.

This work introduces DADAO: the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of L-smooth and mu-strongly convex functions distributed over a given network of size n. Our key insight is based on modeling the local gradient updates and gossip communication procedures with separate independent Poisson Point Processes. This allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous, leading to communication acceleration compared to synchronous approaches. Our new method employs primal gradients and does not use a multi-consensus inner loop nor other ad-hoc mechanisms such as Error Feedback, Gradient Tracking, or a Proximal operator. By relating the inverse of the smallest positive eigenvalue of the Laplacian matrix chi_1 and the maximal resistance chi_2leq chi_1 of the graph to a sufficient minimal communication rate between the nodes of the network, we show that our algorithm requires O(nfrac{L{mu}}log(1{epsilon})) local gradients and only O(nchi_1chi_2frac{L{mu}}log(1{epsilon})) communications to reach a precision epsilon, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for both computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method. We also propose a SDP relaxation to find the optimal gossip rate of each edge minimizing the total number of communications for a given graph, resulting in faster convergence compared to standard approaches relying on uniform communication weights. Our source code is released on a public repository.

We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed point solving layer into the denoising network of a diffusion model, transforming the diffusion process into a sequence of closely-related fixed point problems. Combined with a new stochastic training method, this approach significantly reduces model size, reduces memory usage, and accelerates training. Moreover, it enables the development of two new techniques to improve sampling efficiency: reallocating computation across timesteps and reusing fixed point solutions between timesteps. We conduct extensive experiments with state-of-the-art models on ImageNet, FFHQ, CelebA-HQ, and LSUN-Church, demonstrating substantial improvements in performance and efficiency. Compared to the state-of-the-art DiT model, FPDM contains 87% fewer parameters, consumes 60% less memory during training, and improves image generation quality in situations where sampling computation or time is limited. Our code and pretrained models are available at https://lukemelas.github.io/fixed-point-diffusion-models.

We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

Model-based reinforcement learning (MBRL) has been shown to be a powerful framework for data-efficiently learning control of continuous tasks. Recent work in MBRL has mostly focused on using more advanced function approximators and planning schemes, with little development of the general framework. In this paper, we identify a fundamental issue of the standard MBRL framework -- what we call the objective mismatch issue. Objective mismatch arises when one objective is optimized in the hope that a second, often uncorrelated, metric will also be optimized. In the context of MBRL, we characterize the objective mismatch between training the forward dynamics model w.r.t.~the likelihood of the one-step ahead prediction, and the overall goal of improving performance on a downstream control task. For example, this issue can emerge with the realization that dynamics models effective for a specific task do not necessarily need to be globally accurate, and vice versa globally accurate models might not be sufficiently accurate locally to obtain good control performance on a specific task. In our experiments, we study this objective mismatch issue and demonstrate that the likelihood of one-step ahead predictions is not always correlated with control performance. This observation highlights a critical limitation in the MBRL framework which will require further research to be fully understood and addressed. We propose an initial method to mitigate the mismatch issue by re-weighting dynamics model training. Building on it, we conclude with a discussion about other potential directions of research for addressing this issue.

Although existing speech-driven talking face generation methods achieve significant progress, they are far from real-world application due to the avatar-specific training demand and unstable lip movements. To address the above issues, we propose the GSmoothFace, a novel two-stage generalized talking face generation model guided by a fine-grained 3d face model, which can synthesize smooth lip dynamics while preserving the speaker's identity. Our proposed GSmoothFace model mainly consists of the Audio to Expression Prediction (A2EP) module and the Target Adaptive Face Translation (TAFT) module. Specifically, we first develop the A2EP module to predict expression parameters synchronized with the driven speech. It uses a transformer to capture the long-term audio context and learns the parameters from the fine-grained 3D facial vertices, resulting in accurate and smooth lip-synchronization performance. Afterward, the well-designed TAFT module, empowered by Morphology Augmented Face Blending (MAFB), takes the predicted expression parameters and target video as inputs to modify the facial region of the target video without distorting the background content. The TAFT effectively exploits the identity appearance and background context in the target video, which makes it possible to generalize to different speakers without retraining. Both quantitative and qualitative experiments confirm the superiority of our method in terms of realism, lip synchronization, and visual quality. See the project page for code, data, and request pre-trained models: https://zhanghm1995.github.io/GSmoothFace.

Biological brains demonstrate complex neural activity, where the timing and interplay between neurons is critical to how brains process information. Most deep learning architectures simplify neural activity by abstracting away temporal dynamics. In this paper we challenge that paradigm. By incorporating neuron-level processing and synchronization, we can effectively reintroduce neural timing as a foundational element. We present the Continuous Thought Machine (CTM), a model designed to leverage neural dynamics as its core representation. The CTM has two core innovations: (1) neuron-level temporal processing, where each neuron uses unique weight parameters to process a history of incoming signals; and (2) neural synchronization employed as a latent representation. The CTM aims to strike a balance between oversimplified neuron abstractions that improve computational efficiency, and biological realism. It operates at a level of abstraction that effectively captures essential temporal dynamics while remaining computationally tractable for deep learning. We demonstrate the CTM's strong performance and versatility across a range of challenging tasks, including ImageNet-1K classification, solving 2D mazes, sorting, parity computation, question-answering, and RL tasks. Beyond displaying rich internal representations and offering a natural avenue for interpretation owing to its internal process, the CTM is able to perform tasks that require complex sequential reasoning. The CTM can also leverage adaptive compute, where it can stop earlier for simpler tasks, or keep computing when faced with more challenging instances. The goal of this work is to share the CTM and its associated innovations, rather than pushing for new state-of-the-art results. To that end, we believe the CTM represents a significant step toward developing more biologically plausible and powerful artificial intelligence systems.

The task of lip synchronization (lip-sync) seeks to match the lips of human faces with different audio. It has various applications in the film industry as well as for creating virtual avatars and for video conferencing. This is a challenging problem as one needs to simultaneously introduce detailed, realistic lip movements while preserving the identity, pose, emotions, and image quality. Many of the previous methods trying to solve this problem suffer from image quality degradation due to a lack of complete contextual information. In this paper, we present Diff2Lip, an audio-conditioned diffusion-based model which is able to do lip synchronization in-the-wild while preserving these qualities. We train our model on Voxceleb2, a video dataset containing in-the-wild talking face videos. Extensive studies show that our method outperforms popular methods like Wav2Lip and PC-AVS in Fr\'echet inception distance (FID) metric and Mean Opinion Scores (MOS) of the users. We show results on both reconstruction (same audio-video inputs) as well as cross (different audio-video inputs) settings on Voxceleb2 and LRW datasets. Video results and code can be accessed from our project page ( https://soumik-kanad.github.io/diff2lip ).

Training of large language models (LLMs) is typically distributed across a large number of accelerators to reduce training time. Since internal states and parameter gradients need to be exchanged at each and every single gradient step, all devices need to be co-located using low-latency high-bandwidth communication links to support the required high volume of exchanged bits. Recently, distributed algorithms like DiLoCo have relaxed such co-location constraint: accelerators can be grouped into ``workers'', where synchronizations between workers only occur infrequently. This in turn means that workers can afford being connected by lower bandwidth communication links without affecting learning quality. However, in these methods, communication across workers still requires the same peak bandwidth as before, as the synchronizations require all parameters to be exchanged across all workers. In this paper, we improve DiLoCo in three ways. First, we synchronize only subsets of parameters in sequence, rather than all at once, which greatly reduces peak bandwidth. Second, we allow workers to continue training while synchronizing, which decreases wall clock time. Third, we quantize the data exchanged by workers, which further reduces bandwidth across workers. By properly combining these modifications, we show experimentally that we can distribute training of billion-scale parameters and reach similar quality as before, but reducing required bandwidth by two orders of magnitude.

Dynamic Algorithm Configuration (DAC) aims to dynamically control a target algorithm's hyperparameters in order to improve its performance. Several theoretical and empirical results have demonstrated the benefits of dynamically controlling hyperparameters in domains like evolutionary computation, AI Planning or deep learning. Replicating these results, as well as studying new methods for DAC, however, is difficult since existing benchmarks are often specialized and incompatible with the same interfaces. To facilitate benchmarking and thus research on DAC, we propose DACBench, a benchmark library that seeks to collect and standardize existing DAC benchmarks from different AI domains, as well as provide a template for new ones. For the design of DACBench, we focused on important desiderata, such as (i) flexibility, (ii) reproducibility, (iii) extensibility and (iv) automatic documentation and visualization. To show the potential, broad applicability and challenges of DAC, we explore how a set of six initial benchmarks compare in several dimensions of difficulty.

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic solutions and their good mathematical properties. Despite their success, an important drawback of diffusion models is their sensitivity to the choice of variance schedule, which controls the dynamics of the diffusion process. Fine-tuning this schedule for specific applications is crucial but time-costly and does not guarantee an optimal result. We propose a novel approach for learning the schedule as part of the training process. Our method supports probabilistic conditioning on data, provides high-quality solutions, and is flexible, proving able to adapt to different applications with minimum overhead. This approach is tested in two unrelated inverse problems: super-resolution microscopy and quantitative phase imaging, yielding comparable or superior results to previous methods and fine-tuned diffusion models. We conclude that fine-tuning the schedule by experimentation should be avoided because it can be learned during training in a stable way that yields better results.

Adapting pre-trained models with broad capabilities has become standard practice for learning a wide range of downstream tasks. The typical approach of fine-tuning different models for each task is performant, but incurs a substantial memory cost. To efficiently learn multiple downstream tasks we introduce Task Adaptive Parameter Sharing (TAPS), a general method for tuning a base model to a new task by adaptively modifying a small, task-specific subset of layers. This enables multi-task learning while minimizing resources used and competition between tasks. TAPS solves a joint optimization problem which determines which layers to share with the base model and the value of the task-specific weights. Further, a sparsity penalty on the number of active layers encourages weight sharing with the base model. Compared to other methods, TAPS retains high accuracy on downstream tasks while introducing few task-specific parameters. Moreover, TAPS is agnostic to the model architecture and requires only minor changes to the training scheme. We evaluate our method on a suite of fine-tuning tasks and architectures (ResNet, DenseNet, ViT) and show that it achieves state-of-the-art performance while being simple to implement.

Recent advancements in speech-driven 3D talking head generation have made significant progress in lip synchronization. However, existing models still struggle to capture the perceptual alignment between varying speech characteristics and corresponding lip movements. In this work, we claim that three criteria -- Temporal Synchronization, Lip Readability, and Expressiveness -- are crucial for achieving perceptually accurate lip movements. Motivated by our hypothesis that a desirable representation space exists to meet these three criteria, we introduce a speech-mesh synchronized representation that captures intricate correspondences between speech signals and 3D face meshes. We found that our learned representation exhibits desirable characteristics, and we plug it into existing models as a perceptual loss to better align lip movements to the given speech. In addition, we utilize this representation as a perceptual metric and introduce two other physically grounded lip synchronization metrics to assess how well the generated 3D talking heads align with these three criteria. Experiments show that training 3D talking head generation models with our perceptual loss significantly improve all three aspects of perceptually accurate lip synchronization. Codes and datasets are available at https://perceptual-3d-talking-head.github.io/.

Model merging aims to cheaply combine individual task-specific models into a single multitask model. In this work, we view past merging methods as leveraging different notions of a ''task subspace'' in which models are matched before being merged. We connect the task subspace of a given model to its loss landscape and formalize how this approach to model merging can be seen as solving a linear system of equations. While past work has generally been limited to linear systems that have a closed-form solution, we consider using the conjugate gradient method to find a solution. We show that using the conjugate gradient method can outperform closed-form solutions, enables merging via linear systems that are otherwise intractable to solve, and flexibly allows choosing from a wide variety of initializations and estimates for the ''task subspace''. We ultimately demonstrate that our merging framework called ''Matching Models in their Task Subspace'' (MaTS) achieves state-of-the-art results in multitask and intermediate-task model merging. We release all of the code and checkpoints used in our work at https://github.com/r-three/mats.

Hyperparameter (HP) tuning in deep learning is an expensive process, prohibitively so for neural networks (NNs) with billions of parameters. We show that, in the recently discovered Maximal Update Parametrization (muP), many optimal HPs remain stable even as model size changes. This leads to a new HP tuning paradigm we call muTransfer: parametrize the target model in muP, tune the HP indirectly on a smaller model, and zero-shot transfer them to the full-sized model, i.e., without directly tuning the latter at all. We verify muTransfer on Transformer and ResNet. For example, 1) by transferring pretraining HPs from a model of 13M parameters, we outperform published numbers of BERT-large (350M parameters), with a total tuning cost equivalent to pretraining BERT-large once; 2) by transferring from 40M parameters, we outperform published numbers of the 6.7B GPT-3 model, with tuning cost only 7% of total pretraining cost. A Pytorch implementation of our technique can be found at github.com/microsoft/mup and installable via `pip install mup`.

Talking face generation aims to create realistic videos with accurate lip synchronization and high visual quality, using given audio and reference video while preserving identity and visual characteristics. In this paper, we start by identifying several issues with existing synchronization learning methods. These involve unstable training, lip synchronization, and visual quality issues caused by lip-sync loss, SyncNet, and lip leaking from the identity reference. To address these issues, we first tackle the lip leaking problem by introducing a silent-lip generator, which changes the lips of the identity reference to alleviate leakage. We then introduce stabilized synchronization loss and AVSyncNet to overcome problems caused by lip-sync loss and SyncNet. Experiments show that our model outperforms state-of-the-art methods in both visual quality and lip synchronization. Comprehensive ablation studies further validate our individual contributions and their cohesive effects.

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

Organizations typically train large models individually. This is costly and time-consuming, particularly for large-scale foundation models. Such vertical production is known to be suboptimal. Inspired by this economic insight, we ask whether it is possible to leverage others' expertise by trading the constituent parts in models, i.e., sets of weights, as if they were market commodities. While recent advances in aligning and interpolating models suggest that doing so may be possible, a number of fundamental questions must be answered to create viable parameter markets. In this work, we address these basic questions, propose a framework containing the infrastructure necessary for market operations to take place, study strategies for exchanging parameters, and offer means for agents to monetize parameters. Excitingly, compared to agents who train siloed models from scratch, we show that it is possible to mutually gain by using the market, even in competitive settings. This suggests that the notion of parameter markets may be a useful paradigm for improving large-scale model training in the future.

We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the amount of changes is arbitrary, lower complexity bounds and corresponding optimal algorithms are known, and the consensus acceleration is not possible. However, in practice the magnitude of network changes may be limited. We derive lower communication complexity bounds for several regimes of velocity of networks changes. Moreover, we show how to obtain accelerated communication rates for a certain class of time-varying graphs using a specific consensus algorithm.

Parameter-efficient tuning (PET) methods can effectively drive extremely large pre-trained language models (PLMs) by only training minimal parameters. Different PET methods utilize different manually designed modules. In a small PLM, there are usually noticeable performance differences among PET methods. Nevertheless, when a PLM's scale grows up to tens of billions of parameters, all PET methods achieve almost the same performance and even perform on par with the full-parameter fine-tuning method. Hence, we hypothesize that model scaling can mitigate the design differences (the module structures and the number of trainable parameters) among PET methods. To study this hypothesis, we introduce a more flexible PET method - arbitrary PET (APET) method - to be compatible with arbitrary module structures and any number of trainable parameters. Then, we experiment on 11 NLP tasks of 5 types and 2 representative PLMs. From our investigations, we find that the model scaling (1) mitigates the effects of the arbitrary module structure on the performance of tuning methods, and (2) enables the tuning methods to optimize fewer parameters to achieve the full-parameter fine-tuning performance. Intriguingly, we also observe that all tuning methods require almost the same number of trainable parameters to drive PLMs. We discuss this phenomenon and the above two findings collectively from optimization perspectives to fathom the mechanisms behind them. These conclusions not only demonstrate the positive impact of model scaling on tuning methods but disclose its mechanisms, which help us design more effective and efficient tuning methods on larger-scale PLMs.

Deep neural networks have become increasingly of interest in dynamical system prediction, but out-of-distribution generalization and long-term stability still remains challenging. In this work, we treat the domain parameters of dynamical systems as factors of variation of the data generating process. By leveraging ideas from supervised disentanglement and causal factorization, we aim to separate the domain parameters from the dynamics in the latent space of generative models. In our experiments we model dynamics both in phase space and in video sequences and conduct rigorous OOD evaluations. Results indicate that disentangled VAEs adapt better to domain parameters spaces that were not present in the training data. At the same time, disentanglement can improve the long-term and out-of-distribution predictions of state-of-the-art models in video sequences.

State-of-the-art space science missions increasingly rely on automation due to spacecraft complexity and the costs of human oversight. The high volume of data, including scientific and telemetry data, makes manual inspection challenging. Machine learning offers significant potential to meet these demands. The Euclid space telescope, in its survey phase since February 2024, exemplifies this shift. Euclid's success depends on accurate monitoring and interpretation of housekeeping telemetry and science-derived data. Thousands of telemetry parameters, monitored as time series, may or may not impact the quality of scientific data. These parameters have complex interdependencies, often due to physical relationships (e.g., proximity of temperature sensors). Optimising science operations requires careful anomaly detection and identification of hidden parameter states. Moreover, understanding the interactions between known anomalies and physical quantities is crucial yet complex, as related parameters may display anomalies with varied timing and intensity. We address these challenges by analysing temperature anomalies in Euclid's telemetry from February to August 2024, focusing on eleven temperature parameters and 35 covariates. We use a predictive XGBoost model to forecast temperatures based on historical values, detecting anomalies as deviations from predictions. A second XGBoost model predicts anomalies from covariates, capturing their relationships to temperature anomalies. We identify the top three anomalies per parameter and analyse their interactions with covariates using SHAP (Shapley Additive Explanations), enabling rapid, automated analysis of complex parameter relationships. Our method demonstrates how machine learning can enhance telemetry monitoring, offering scalable solutions for other missions with similar data challenges.

The Model Context Protocol (MCP) has recently emerged as a standardized interface for connecting language models with external tools and data. As the ecosystem rapidly expands, the lack of a structured, comprehensive view of existing MCP artifacts presents challenges for research. To bridge this gap, we introduce MCPCorpus, a large-scale dataset containing around 14K MCP servers and 300 MCP clients. Each artifact is annotated with 20+ normalized attributes capturing its identity, interface configuration, GitHub activity, and metadata. MCPCorpus provides a reproducible snapshot of the real-world MCP ecosystem, enabling studies of adoption trends, ecosystem health, and implementation diversity. To keep pace with the rapid evolution of the MCP ecosystem, we provide utility tools for automated data synchronization, normalization, and inspection. Furthermore, to support efficient exploration and exploitation, we release a lightweight web-based search interface. MCPCorpus is publicly available at: https://github.com/Snakinya/MCPCorpus.

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics and limits learning to the hard-to-model term, which is called parametrization or closure and captures the effect of fine- onto large-scale dynamics. Leveraging neural operators, we are the first to learn grid-independent, non-local, and flexible parametrizations. Our multiscale neural operator is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

Deep reinforcement learning (RL) methods generally engage in exploratory behavior through noise injection in the action space. An alternative is to add noise directly to the agent's parameters, which can lead to more consistent exploration and a richer set of behaviors. Methods such as evolutionary strategies use parameter perturbations, but discard all temporal structure in the process and require significantly more samples. Combining parameter noise with traditional RL methods allows to combine the best of both worlds. We demonstrate that both off- and on-policy methods benefit from this approach through experimental comparison of DQN, DDPG, and TRPO on high-dimensional discrete action environments as well as continuous control tasks. Our results show that RL with parameter noise learns more efficiently than traditional RL with action space noise and evolutionary strategies individually.

This work explores the in-context learning capabilities of State Space Models (SSMs) and presents, to the best of our knowledge, the first theoretical explanation of a possible underlying mechanism. We introduce a novel weight construction for SSMs, enabling them to predict the next state of any dynamical system after observing previous states without parameter fine-tuning. This is accomplished by extending the HiPPO framework to demonstrate that continuous SSMs can approximate the derivative of any input signal. Specifically, we find an explicit weight construction for continuous SSMs and provide an asymptotic error bound on the derivative approximation. The discretization of this continuous SSM subsequently yields a discrete SSM that predicts the next state. Finally, we demonstrate the effectiveness of our parameterization empirically. This work should be an initial step toward understanding how sequence models based on SSMs learn in context.

State-of-the-art parameter-efficient fine-tuning methods rely on introducing adapter modules between the layers of a pretrained language model. However, such modules are trained separately for each task and thus do not enable sharing information across tasks. In this paper, we show that we can learn adapter parameters for all layers and tasks by generating them using shared hypernetworks, which condition on task, adapter position, and layer id in a transformer model. This parameter-efficient multi-task learning framework allows us to achieve the best of both worlds by sharing knowledge across tasks via hypernetworks while enabling the model to adapt to each individual task through task-specific adapters. Experiments on the well-known GLUE benchmark show improved performance in multi-task learning while adding only 0.29% parameters per task. We additionally demonstrate substantial performance improvements in few-shot domain generalization across a variety of tasks. Our code is publicly available in https://github.com/rabeehk/hyperformer.

A fundamental dilemma in generative modeling persists: iterative diffusion models achieve outstanding fidelity, but at a significant computational cost, while efficient few-step alternatives are constrained by a hard quality ceiling. This conflict between generation steps and output quality arises from restrictive training objectives that focus exclusively on either infinitesimal dynamics (PF-ODEs) or direct endpoint prediction. We address this challenge by introducing an exact, continuous-time dynamics equation that analytically defines state transitions across any finite time interval. This leads to a novel generative paradigm, Transition Models (TiM), which adapt to arbitrary-step transitions, seamlessly traversing the generative trajectory from single leaps to fine-grained refinement with more steps. Despite having only 865M parameters, TiM achieves state-of-the-art performance, surpassing leading models such as SD3.5 (8B parameters) and FLUX.1 (12B parameters) across all evaluated step counts. Importantly, unlike previous few-step generators, TiM demonstrates monotonic quality improvement as the sampling budget increases. Additionally, when employing our native-resolution strategy, TiM delivers exceptional fidelity at resolutions up to 4096x4096.

Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs), which enables deterministic inference and exact likelihood evaluation. However, the likelihood estimation results by diffusion ODEs are still far from those of the state-of-the-art likelihood-based generative models. In this work, we propose several improved techniques for maximum likelihood estimation for diffusion ODEs, including both training and evaluation perspectives. For training, we propose velocity parameterization and explore variance reduction techniques for faster convergence. We also derive an error-bounded high-order flow matching objective for finetuning, which improves the ODE likelihood and smooths its trajectory. For evaluation, we propose a novel training-free truncated-normal dequantization to fill the training-evaluation gap commonly existing in diffusion ODEs. Building upon these techniques, we achieve state-of-the-art likelihood estimation results on image datasets (2.56 on CIFAR-10, 3.43/3.69 on ImageNet-32) without variational dequantization or data augmentation.

Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings, can be approximated by straight trajectories with constant velocity. However, we observe that modeling with constant velocity and using reflow procedures have limitations in accurately learning straight trajectories between pairs, resulting in suboptimal performance in few-step generation. To address these limitations, we introduce Constant Acceleration Flow (CAF), a novel framework based on a simple constant acceleration equation. CAF introduces acceleration as an additional learnable variable, allowing for more expressive and accurate estimation of the ODE flow. Moreover, we propose two techniques to further improve estimation accuracy: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity. Our comprehensive studies on toy datasets, CIFAR-10, and ImageNet 64x64 demonstrate that CAF outperforms state-of-the-art baselines for one-step generation. We also show that CAF dramatically improves few-step coupling preservation and inversion over Rectified flow. Code is available at https://github.com/mlvlab/CAF{https://github.com/mlvlab/CAF}.

Recent work has highlighted the complex influence training hyperparameters, e.g., the number of training epochs, can have on the prunability of machine learning models. Perhaps surprisingly, a systematic approach to predict precisely how adjusting a specific hyperparameter will affect prunability remains elusive. To address this gap, we introduce a phenomenological model grounded in the statistical mechanics of learning. Our approach uses temperature-like and load-like parameters to model the impact of neural network (NN) training hyperparameters on pruning performance. A key empirical result we identify is a sharp transition phenomenon: depending on the value of a load-like parameter in the pruned model, increasing the value of a temperature-like parameter in the pre-pruned model may either enhance or impair subsequent pruning performance. Based on this transition, we build a three-regime model by taxonomizing the global structure of the pruned NN loss landscape. Our model reveals that the dichotomous effect of high temperature is associated with transitions between distinct types of global structures in the post-pruned model. Based on our results, we present three case-studies: 1) determining whether to increase or decrease a hyperparameter for improved pruning; 2) selecting the best model to prune from a family of models; and 3) tuning the hyperparameter of the Sharpness Aware Minimization method for better pruning performance.

This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear measurements. First, we consider the symmetric setting with the symmetric parameterization where M^* in R^{n times n} is a positive semi-definite unknown matrix of rank r ll n, and one uses a symmetric parameterization XX^top to learn M^*. Here X in R^{n times k} with k > r is the factor matrix. We give a novel Omega (1/T^2) lower bound of randomly initialized GD for the over-parameterized case (k >r) where T is the number of iterations. This is in stark contrast to the exact-parameterization scenario (k=r) where the convergence rate is exp (-Omega (T)). Next, we study asymmetric setting where M^* in R^{n_1 times n_2} is the unknown matrix of rank r ll min{n_1,n_2}, and one uses an asymmetric parameterization FG^top to learn M^* where F in R^{n_1 times k} and G in R^{n_2 times k}. Building on prior work, we give a global exact convergence result of randomly initialized GD for the exact-parameterization case (k=r) with an exp (-Omega(T)) rate. Furthermore, we give the first global exact convergence result for the over-parameterization case (k>r) with an exp(-Omega(alpha^2 T)) rate where alpha is the initialization scale. This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from Omega (1/T^2) to linear convergence. On the other hand, we propose a novel method that only modifies one step of GD and obtains a convergence rate independent of alpha, recovering the rate in the exact-parameterization case.

Post-training has emerged as a crucial paradigm for adapting large-scale pre-trained models to various tasks, whose effects are fully reflected by delta parameters (i.e., the disparity between post-trained and pre-trained parameters). While numerous studies have explored delta parameter properties via operations like pruning, quantization, low-rank approximation, and extrapolation, a unified framework for systematically examining these characteristics has been lacking. In this paper, we propose a novel perspective based on Riemann sum approximation of the loss function to elucidate delta parameter editing operations. Our analysis categorizes existing methods into three classes based on their post-editing performance: competitive, decreased, and improved, explaining how they are expressed by the Riemann sum approximation term and how they alter the model performance. Extensive experiments on both visual and language models, including ViT, LLaMA 3, Qwen 2, and Mistral, corroborate our theoretical findings. Furthermore, we introduce extensions to existing techniques like DARE and BitDelta, highlighting their limitations in leveraging the properties of delta parameters and reorganizing them into general expressions to enhance the applicability and effectiveness of delta parameter editing in post-trained models.

It is commonly believed that scaling language models should commit a significant space or time cost, by increasing the parameters (parameter scaling) or output tokens (inference-time scaling). We introduce the third and more inference-efficient scaling paradigm: increasing the model's parallel computation during both training and inference time. We apply P diverse and learnable transformations to the input, execute forward passes of the model in parallel, and dynamically aggregate the P outputs. This method, namely parallel scaling (ParScale), scales parallel computation by reusing existing parameters and can be applied to any model structure, optimization procedure, data, or task. We theoretically propose a new scaling law and validate it through large-scale pre-training, which shows that a model with P parallel streams is similar to scaling the parameters by O(log P) while showing superior inference efficiency. For example, ParScale can use up to 22times less memory increase and 6times less latency increase compared to parameter scaling that achieves the same performance improvement. It can also recycle an off-the-shelf pre-trained model into a parallelly scaled one by post-training on a small amount of tokens, further reducing the training budget. The new scaling law we discovered potentially facilitates the deployment of more powerful models in low-resource scenarios, and provides an alternative perspective for the role of computation in machine learning.

In this work, we propose a communication-efficient parameterization, FedPara, for federated learning (FL) to overcome the burdens on frequent model uploads and downloads. Our method re-parameterizes weight parameters of layers using low-rank weights followed by the Hadamard product. Compared to the conventional low-rank parameterization, our FedPara method is not restricted to low-rank constraints, and thereby it has a far larger capacity. This property enables to achieve comparable performance while requiring 3 to 10 times lower communication costs than the model with the original layers, which is not achievable by the traditional low-rank methods. The efficiency of our method can be further improved by combining with other efficient FL optimizers. In addition, we extend our method to a personalized FL application, pFedPara, which separates parameters into global and local ones. We show that pFedPara outperforms competing personalized FL methods with more than three times fewer parameters.

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

Molecular dynamics (MD) simulations play a crucial role in scientific research. Yet their computational cost often limits the timescales and system sizes that can be explored. Most data-driven efforts have been focused on reducing the computational cost of accurate interatomic forces required for solving the equations of motion. Despite their success, however, these machine learning interatomic potentials (MLIPs) are still bound to small time-steps. In this work, we introduce TrajCast, a transferable and data-efficient framework based on autoregressive equivariant message passing networks that directly updates atomic positions and velocities lifting the constraints imposed by traditional numerical integration. We benchmark our framework across various systems, including a small molecule, crystalline material, and bulk liquid, demonstrating excellent agreement with reference MD simulations for structural, dynamical, and energetic properties. Depending on the system, TrajCast allows for forecast intervals up to 30times larger than traditional MD time-steps, generating over 15 ns of trajectory data per day for a solid with more than 4,000 atoms. By enabling efficient large-scale simulations over extended timescales, TrajCast can accelerate materials discovery and explore physical phenomena beyond the reach of traditional simulations and experiments. An open-source implementation of TrajCast is accessible under https://github.com/IBM/trajcast.

Various algorithms for continual learning (CL) have been designed with the goal of effectively alleviating the trade-off between stability and plasticity during the CL process. To achieve this goal, tuning appropriate hyperparameters for each algorithm is essential. As an evaluation protocol, it has been common practice to train a CL algorithm using diverse hyperparameter values on a CL scenario constructed with a benchmark dataset. Subsequently, the best performance attained with the optimal hyperparameter value serves as the criterion for evaluating the CL algorithm. In this paper, we contend that this evaluation protocol is not only impractical but also incapable of effectively assessing the CL capability of a CL algorithm. Returning to the fundamental principles of model evaluation in machine learning, we propose an evaluation protocol that involves Hyperparameter Tuning and Evaluation phases. Those phases consist of different datasets but share the same CL scenario. In the Hyperparameter Tuning phase, each algorithm is iteratively trained with different hyperparameter values to find the optimal hyperparameter values. Subsequently, in the Evaluation phase, the optimal hyperparameter values is directly applied for training each algorithm, and their performance in the Evaluation phase serves as the criterion for evaluating them. Through experiments on CIFAR-100 and ImageNet-100 based on the proposed protocol in class-incremental learning, we not only observed that the existing evaluation method fail to properly assess the CL capability of each algorithm but also observe that some recently proposed state-of-the-art algorithms, which reported superior performance, actually exhibit inferior performance compared to the previous algorithm.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Lip-syncing videos with given audio is the foundation for various applications including the creation of virtual presenters or performers. While recent studies explore high-fidelity lip-sync with different techniques, their task-orientated models either require long-term videos for clip-specific training or retain visible artifacts. In this paper, we propose a unified and effective framework ReSyncer, that synchronizes generalized audio-visual facial information. The key design is revisiting and rewiring the Style-based generator to efficiently adopt 3D facial dynamics predicted by a principled style-injected Transformer. By simply re-configuring the information insertion mechanisms within the noise and style space, our framework fuses motion and appearance with unified training. Extensive experiments demonstrate that ReSyncer not only produces high-fidelity lip-synced videos according to audio, but also supports multiple appealing properties that are suitable for creating virtual presenters and performers, including fast personalized fine-tuning, video-driven lip-syncing, the transfer of speaking styles, and even face swapping. Resources can be found at https://guanjz20.github.io/projects/ReSyncer.

Decentralized learning provides a scalable alternative to traditional parameter-server-based training, yet its performance is often hindered by limited peer-to-peer communication. In this paper, we study how communication should be scheduled over time, including determining when and how frequently devices synchronize. Our empirical results show that concentrating communication budgets in the later stages of decentralized training markedly improves global generalization. Surprisingly, we uncover that fully connected communication at the final step, implemented by a single global merging, is sufficient to match the performance of server-based training. We further show that low communication in decentralized learning preserves the mergeability of local models throughout training. Our theoretical contributions, which explains these phenomena, are first to establish that the globally merged model of decentralized SGD can converge faster than centralized mini-batch SGD. Technically, we novelly reinterpret part of the discrepancy among local models, which were previously considered as detrimental noise, as constructive components that accelerate convergence. This work challenges the common belief that decentralized learning generalizes poorly under data heterogeneity and limited communication, while offering new insights into model merging and neural network loss landscapes.

Even when massively overparameterized, deep neural networks show a remarkable ability to generalize. Research on this phenomenon has focused on generalization within distribution, via smooth interpolation. Yet in some settings neural networks also learn to extrapolate to data far beyond the bounds of the original training set, sometimes even allowing for infinite generalization, implying that an algorithm capable of solving the task has been learned. Here we undertake a case study of the learning dynamics of recurrent neural networks (RNNs) trained on the streaming parity task in order to develop an effective theory of algorithm development. The streaming parity task is a simple but nonlinear task defined on sequences up to arbitrary length. We show that, with sufficient finite training experience, RNNs exhibit a phase transition to perfect infinite generalization. Using an effective theory for the representational dynamics, we find an implicit representational merger effect which can be interpreted as the construction of a finite automaton that reproduces the task. Overall, our results disclose one mechanism by which neural networks can generalize infinitely from finite training experience.

The problem of robotic synchronisation and coordination is a long-standing one. Combining autonomous, computerised systems with unpredictable real-world conditions can have consequences ranging from poor performance to collisions and damage. This paper proposes using coupled oscillators to create a drone swarm that is decentralised and self organising. This allows for greater flexibility and adaptiveness than a hard-coded swarm, with more resilience and scalability than a centralised system. Our method allows for a variable number of drones to spontaneously form a swarm and react to changing swarm conditions. Additionally, this method includes provisions to prevent communication interference between drones, and signal processing techniques to ensure a smooth and cohesive swarm.

Large models represent a groundbreaking advancement in multiple application fields, enabling remarkable achievements across various tasks. However, their unprecedented scale comes with significant computational costs. These models, often consisting of billions of parameters, require vast amounts of computational resources for execution. Especially, the expansive scale and computational demands pose considerable challenges when customizing them for particular downstream tasks, particularly over the hardware platforms constrained by computational capabilities. Parameter Efficient Fine-Tuning (PEFT) provides a practical solution by efficiently adapt the large models over the various downstream tasks. In particular, PEFT refers to the process of adjusting the parameters of a pre-trained large models to adapt it to a specific task while minimizing the number of additional parameters introduced or computational resources required. This approach is particularly important when dealing with large language models with high parameter counts, as fine-tuning these models from scratch can be computationally expensive and resource-intensive, posing considerable challenges in the supporting system platform design. In this survey, we present comprehensive studies of various PEFT algorithms, examining their performance and computational overhead. Moreover, we provide an overview of applications developed using different PEFT algorithms and discuss common techniques employed to mitigate computation costs for PEFT. In addition to the algorithmic perspective, we overview various real-world system designs to investigate the implementation costs associated with different PEFT algorithms. This survey serves as an indispensable resource for researchers aiming to understand both the PEFT algorithm and its system implementation, offering detailed insights into recent advancements and practical applications.

Federated Learning is a distributed learning paradigm with two key challenges that differentiate it from traditional distributed optimization: (1) significant variability in terms of the systems characteristics on each device in the network (systems heterogeneity), and (2) non-identically distributed data across the network (statistical heterogeneity). In this work, we introduce a framework, FedProx, to tackle heterogeneity in federated networks. FedProx can be viewed as a generalization and re-parametrization of FedAvg, the current state-of-the-art method for federated learning. While this re-parameterization makes only minor modifications to the method itself, these modifications have important ramifications both in theory and in practice. Theoretically, we provide convergence guarantees for our framework when learning over data from non-identical distributions (statistical heterogeneity), and while adhering to device-level systems constraints by allowing each participating device to perform a variable amount of work (systems heterogeneity). Practically, we demonstrate that FedProx allows for more robust convergence than FedAvg across a suite of realistic federated datasets. In particular, in highly heterogeneous settings, FedProx demonstrates significantly more stable and accurate convergence behavior relative to FedAvg---improving absolute test accuracy by 22% on average.

Learning the underlying dynamics of single cells from snapshot data has gained increasing attention in scientific and machine learning research. The destructive measurement technique and cell proliferation/death result in unpaired and unbalanced data between snapshots, making the learning of the underlying dynamics challenging. In this paper, we propose joint Velocity-Growth Flow Matching (VGFM), a novel paradigm that jointly learns state transition and mass growth of single-cell populations via flow matching. VGFM builds an ideal single-cell dynamics containing velocity of state and growth of mass, driven by a presented two-period dynamic understanding of the static semi-relaxed optimal transport, a mathematical tool that seeks the coupling between unpaired and unbalanced data. To enable practical usage, we approximate the ideal dynamics using neural networks, forming our joint velocity and growth matching framework. A distribution fitting loss is also employed in VGFM to further improve the fitting performance for snapshot data. Extensive experimental results on both synthetic and real datasets demonstrate that VGFM can capture the underlying biological dynamics accounting for mass and state variations over time, outperforming existing approaches for single-cell dynamics modeling.

Message passing graph neural networks (GNNs) would appear to be powerful tools to learn distributed algorithms via gradient descent, but generate catastrophically incorrect predictions when nodes update asynchronously during inference. This failure under asynchrony effectively excludes these architectures from many potential applications, such as learning local communication policies between resource-constrained agents in, e.g., robotic swarms or sensor networks. In this work we explore why this failure occurs in common GNN architectures, and identify "implicitly-defined" GNNs as a class of architectures which is provably robust to partially asynchronous "hogwild" inference, adapting convergence guarantees from work in asynchronous and distributed optimization, e.g., Bertsekas (1982); Niu et al. (2011). We then propose a novel implicitly-defined GNN architecture, which we call an energy GNN. We show that this architecture outperforms other GNNs from this class on a variety of synthetic tasks inspired by multi-agent systems, and achieves competitive performance on real-world datasets.

Despite their remarkable success in complex tasks propelling widespread adoption, large language-model-based agents still face critical deployment challenges due to prohibitive latency and inference costs. While recent work has explored various methods to accelerate inference, existing approaches suffer from significant limitations: they either fail to preserve performance fidelity, require extensive offline training of router modules, or incur excessive operational costs. Moreover, they provide minimal user control over the tradeoff between acceleration and other performance metrics. To address these gaps, we introduce Dynamic Speculative Planning (DSP), an asynchronous online reinforcement learning framework that provides lossless acceleration with substantially reduced costs without requiring additional pre-deployment preparation. DSP explicitly optimizes a joint objective balancing end-to-end latency against dollar cost, allowing practitioners to adjust a single parameter that steers the system toward faster responses, cheaper operation, or any point along this continuum. Experiments on two standard agent benchmarks demonstrate that DSP achieves comparable efficiency to the fastest lossless acceleration method while reducing total cost by 30% and unnecessary cost up to 60%. Our code and data are available through https://github.com/guanyilin428/Dynamic-Speculative-Planning.

We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal effort. The key motivation of our framework is to view any multivariate time series as a cumulative sum of fine-grained trajectory increments, with each increment governed by a novel spin-gas dynamical Ising model. This fine-grained perspective motivates the development of a parsimonious set of operators that summarize multivariate time series in an abstract fashion, serving as the foundation for large-scale automated feature engineering. Numerically, we validate the efficacy of our method on several synthetic and real-world noisy time series datasets.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.

Recent years have seen a growing interest and adoption of LLMs, with muTransfer becoming a key technique for tuning hyperparameters in large-scale training. Meanwhile, Mixture-of-Experts (MoE) has emerged as a leading architecture in extremely large models. However, the intersection of these two advancements has remained unexplored. In this work, we derive a mu-Parameterization (muP) for MoE, providing theoretical guarantees for feature learning across model widths in both the router and experts. We empirically validate our parameterization and further investigate how scaling the number of experts and granularity affects the optimal learning rate.

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that recovers the data distribution from time-dependent data scores. In this work, we observe that the stochastic reverse process of data scores is a martingale, from which concentration bounds and the optional stopping theorem for data scores can be derived. Then, we discover a simple way for calibrating an arbitrary pretrained DPM, with which the score matching loss can be reduced and the lower bounds of model likelihood can consequently be increased. We provide general calibration guidelines under various model parametrizations. Our calibration method is performed only once and the resulting models can be used repeatedly for sampling. We conduct experiments on multiple datasets to empirically validate our proposal. Our code is at https://github.com/thudzj/Calibrated-DPMs.

Despite significant progress in model editing methods, their application in real-world scenarios remains challenging as they often cause large language models (LLMs) to collapse. Among them, ROME is particularly concerning, as it could disrupt LLMs with only a single edit. In this paper, we study the root causes of such collapse. Through extensive analysis, we identify two primary factors that contribute to the collapse: i) inconsistent handling of prefixed and unprefixed keys in the parameter update equation may result in very small denominators, causing excessively large parameter updates; ii) the subject of collapse cases is usually the first token, whose unprefixed key distribution significantly differs from the prefixed key distribution in autoregressive transformers, causing the aforementioned issue to materialize. To validate our findings, we propose a simple yet effective approach: uniformly using prefixed keys during editing phase and adding prefixes during testing phase to ensure the consistency between training and testing. The experimental results show that the proposed solution can prevent model collapse while maintaining the effectiveness of the edits.

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and biochemistry. Each system is paired with precomputed multivariate and univariate time series. Our dataset has comparable scale to existing static time series databases; however, our systems can be re-integrated to produce additional datasets of arbitrary length and granularity. Our dataset is annotated with known mathematical properties of each system, and we perform feature analysis to broadly categorize the diverse dynamics present across the collection. Chaotic systems inherently challenge forecasting models, and across extensive benchmarks we correlate forecasting performance with the degree of chaos present. We also exploit the unique generative properties of our dataset in several proof-of-concept experiments: surrogate transfer learning to improve time series classification, importance sampling to accelerate model training, and benchmarking symbolic regression algorithms.

Test-time scaling has emerged as a prominent research direction in machine learning, enabling models to enhance their expressive capabilities during inference.Transformers, renowned for striking a delicate balance between efficiency and expressiveness, have benefited from test-time scaling techniques that leverage an expanding key-value (KV) cache to significantly improve performance.In this paper, we introduce a novel state-based approach to test-time scaling, which we term state tuning, tailored to the RNN-based RWKV-7 model.By exploiting the unique strengths of RWKV-7, our method achieves state-of-the-art performance on the target task without altering the model's pre-trained weights. Our approach centers on three key innovations. First, we develop an observer framework that allows a smaller model to replicate and learn the state dynamics of the RWKV-7 model. Second, we employ a kernel method to dynamically upscale the state size, enhancing the model's capacity to capture intricate patterns. Third, we integrate Decorrelated Backpropagation (DBP) to optimize the upscaled state matrix, thereby improving convergence and expressivity. By tuning only the state matrix, we demonstrate that a smaller model can outperform larger models on the given task. This method preserves the efficiency of the original RWKV-7 architecture while harnessing the power of test-time scaling to deliver superior results. Our findings underscore the potential of state tuning as an effective strategy for advancing model performance in resource-constrained settings. Our code is https://github.com/TorchRWKV/flash-linear-attention.

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required for accurate integration. In this paper, we introduce an inference process that maps complex systems into a simplified representational space and models large jumps in time. To achieve this, we propose Time-lagged Information Bottleneck (T-IB), a principled objective rooted in information theory, which aims to capture relevant temporal features while discarding high-frequency information to simplify the simulation task and minimize the inference error. Our experiments demonstrate that T-IB learns information-optimal representations for accurately modeling the statistical properties and dynamics of the original process at a selected time lag, outperforming existing time-lagged dimensionality reduction methods.

Continuous-time event sequences play a vital role in real-world domains such as healthcare, finance, online shopping, social networks, and so on. To model such data, temporal point processes (TPPs) have emerged as the most natural and competitive models, making a significant impact in both academic and application communities. Despite the emergence of many powerful models in recent years, there hasn't been a central benchmark for these models and future research endeavors. This lack of standardization impedes researchers and practitioners from comparing methods and reproducing results, potentially slowing down progress in this field. In this paper, we present EasyTPP, the first central repository of research assets (e.g., data, models, evaluation programs, documentations) in the area of event sequence modeling. Our EasyTPP makes several unique contributions to this area: a unified interface of using existing datasets and adding new datasets; a wide range of evaluation programs that are easy to use and extend as well as facilitate reproducible research; implementations of popular neural TPPs, together with a rich library of modules by composing which one could quickly build complex models. All the data and implementation can be found at https://github.com/ant-research/EasyTemporalPointProcess. We will actively maintain this benchmark and welcome contributions from other researchers and practitioners. Our benchmark will help promote reproducible research in this field, thus accelerating research progress as well as making more significant real-world impacts.

Existing checkpointing approaches seem ill-suited for distributed training even though hardware limitations make model parallelism, i.e., sharding model state across multiple accelerators, a requirement for model scaling. Consolidating distributed model state into a single checkpoint unacceptably slows down training, and is impractical at extreme scales. Distributed checkpoints, in contrast, are tightly coupled to the model parallelism and hardware configurations of the training run, and thus unusable on different configurations. To address this problem, we propose Universal Checkpointing, a technique that enables efficient checkpoint creation while providing the flexibility of resuming on arbitrary parallelism strategy and hardware configurations. Universal Checkpointing unlocks unprecedented capabilities for large-scale training such as improved resilience to hardware failures through continued training on remaining healthy hardware, and reduced training time through opportunistic exploitation of elastic capacity. The key insight of Universal Checkpointing is the selection of the optimal representation in each phase of the checkpointing life cycle: distributed representation for saving, and consolidated representation for loading. This is achieved using two key mechanisms. First, the universal checkpoint format, which consists of a consolidated representation of each model parameter and metadata for mapping parameter fragments into training ranks of arbitrary model-parallelism configuration. Second, the universal checkpoint language, a simple but powerful specification language for converting distributed checkpoints into the universal checkpoint format. Our evaluation demonstrates the effectiveness and generality of Universal Checkpointing on state-of-the-art model architectures and a wide range of parallelism techniques.

By merging models, AI systems can combine the distinct strengths of separate language models, achieving a balance between multiple capabilities without requiring substantial retraining. However, the integration process can be intricate due to differences in training methods and fine-tuning, typically necessitating specialized knowledge and repeated refinement. This paper explores model merging techniques across a spectrum of complexity, examining where automated methods like evolutionary strategies stand compared to hyperparameter-driven approaches such as DARE, TIES-Merging and simpler methods like Model Soups. In addition, we introduce Differentiable Adaptive Merging (DAM), an efficient, adaptive merging approach as an alternative to evolutionary merging that optimizes model integration through scaling coefficients, minimizing computational demands. Our findings reveal that even simple averaging methods, like Model Soups, perform competitively when model similarity is high, underscoring each technique's unique strengths and limitations. We open-sourced DAM, including the implementation code and experiment pipeline, on GitHub: https://github.com/arcee-ai/DAM.

As the typical retraining paradigm is unacceptably time- and resource-consuming, researchers are turning to model editing to find an effective way that supports both consecutive and batch scenarios to edit the model behavior directly. Despite all these practical expectations, existing model editing methods fail to realize all of them. Furthermore, the memory demands for such sequential model editing approaches tend to be prohibitive, frequently necessitating an external memory that grows incrementally over time. To cope with these challenges, we propose CoachHooK, a model editing method that simultaneously supports sequential and batch editing. CoachHooK is memory-friendly as it only needs a small amount of it to store several hook layers whose size remains unchanged over time. Experimental results demonstrate the superiority of our method over other batch-supportive model editing methods under both single-round and consecutive batch editing scenarios. Extensive analyses of CoachHooK have been conducted to verify the stability of our method over a number of consecutive steps.

Fine-tuning pre-trained models has become the standard approach to endow them with specialized knowledge, but it poses fundamental challenges. In particular, (i) fine-tuning often leads to catastrophic forgetting, where improvements on a target domain degrade generalization on other tasks, and (ii) merging fine-tuned checkpoints from disparate tasks can lead to significant performance loss. To address these challenges, we introduce LiNeS, Layer-increasing Network Scaling, a post-training editing technique designed to preserve pre-trained generalization while enhancing fine-tuned task performance. LiNeS scales parameter updates linearly based on their layer depth within the network, maintaining shallow layers close to their pre-trained values to preserve general features while allowing deeper layers to retain task-specific representations. In multi-task model merging scenarios, layer-wise scaling of merged parameters reduces negative task interference. LiNeS demonstrates significant improvements in both single-task and multi-task settings across various benchmarks in vision and natural language processing. It mitigates forgetting, enhances out-of-distribution generalization, integrates seamlessly with existing multi-task model merging baselines improving their performance across benchmarks and model sizes, and can boost generalization when merging LLM policies aligned with different rewards via RLHF. Our method is simple to implement, computationally efficient and complementary to many existing techniques. Our source code is available at https://github.com/wang-kee/LiNeS

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

Neural network training is commonly accelerated by using multiple synchronized workers to compute gradient updates in parallel. Asynchronous methods remove synchronization overheads and improve hardware utilization at the cost of introducing gradient delay, which impedes optimization and can lead to lower final model performance. We introduce Adaptive Braking (AB), a modification for momentum-based optimizers that mitigates the effects of gradient delay. AB dynamically scales the gradient based on the alignment of the gradient and the velocity. This can dampen oscillations along high curvature directions of the loss surface, stabilizing and accelerating asynchronous training. We show that applying AB on top of SGD with momentum enables training ResNets on CIFAR-10 and ImageNet-1k with delays D geq 32 update steps with minimal drop in final test accuracy.

One puzzling artifact in machine learning dubbed grokking is where delayed generalization is achieved tenfolds of iterations after near perfect overfitting to the training data. Focusing on the long delay itself on behalf of machine learning practitioners, our goal is to accelerate generalization of a model under grokking phenomenon. By regarding a series of gradients of a parameter over training iterations as a random signal over time, we can spectrally decompose the parameter trajectories under gradient descent into two components: the fast-varying, overfitting-yielding component and the slow-varying, generalization-inducing component. This analysis allows us to accelerate the grokking phenomenon more than times 50 with only a few lines of code that amplifies the slow-varying components of gradients. The experiments show that our algorithm applies to diverse tasks involving images, languages, and graphs, enabling practical availability of this peculiar artifact of sudden generalization. Our code is available at https://github.com/ironjr/grokfast.

The rapid development of AI systems has been greatly influenced by the emergence of foundation models. A common approach for targeted problems involves fine-tuning these pre-trained foundation models for specific target tasks, resulting in a rapid spread of models fine-tuned across a diverse array of tasks. This work focuses on the problem of merging multiple fine-tunings of the same foundation model derived from a spectrum of auxiliary tasks. We introduce a new simple method, Model Breadcrumbs, which consists of a sparsely defined set of weights that carve out a trajectory within the weight space of a pre-trained model, enhancing task performance when traversed. These breadcrumbs are constructed by subtracting the weights from a pre-trained model before and after fine-tuning, followed by a sparsification process that eliminates weight outliers and negligible perturbations. Our experiments demonstrate the effectiveness of Model Breadcrumbs to simultaneously improve performance across multiple tasks. This contribution aligns with the evolving paradigm of updatable machine learning, reminiscent of the collaborative principles underlying open-source software development, fostering a community-driven effort to reliably update machine learning models. Our method is shown to be more efficient and unlike previous proposals does not require hyperparameter tuning for each new task added. Through extensive experimentation involving various models, tasks, and modalities we establish that integrating Model Breadcrumbs offers a simple, efficient, and highly effective approach for constructing multi-task models and facilitating updates to foundation models.

Efficient LLM pre-training requires well-tuned hyperparameters (HPs), including learning rate {\eta} and weight decay {\lambda}. We study scaling laws for HPs: formulas for how to scale HPs as we scale model size N, dataset size D, and batch size B. Recent work suggests the AdamW timescale, B/({\eta}{\lambda}D), should remain constant across training settings, and we verify the implication that optimal {\lambda} scales linearly with B, for a fixed N,D. However, as N,D scale, we show the optimal timescale obeys a precise power law in the tokens-per-parameter ratio, D/N. This law thus provides a method to accurately predict {\lambda}opt in advance of large-scale training. We also study scaling laws for optimal batch size Bopt (the B enabling lowest loss at a given N,D) and critical batch size Bcrit (the B beyond which further data parallelism becomes ineffective). In contrast with prior work, we find both Bopt and Bcrit scale as power laws in D, independent of model size, N. Finally, we analyze how these findings inform the real-world selection of Pareto-optimal N and D under dual training time and compute objectives.

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related state-action distribution--can be found all across the literature. Despite its importance, the state distribution is mostly discussed indirectly and theoretically, rather than being modeled explicitly. The reason being an absence of appropriate density estimation tools. In this work, we investigate applications of a normalizing flow-based model for the aforementioned distributions. In particular, we use a pair of flows coupled through the optimality point of the Donsker-Varadhan representation of the Kullback-Leibler (KL) divergence, for distribution matching based imitation learning. Our algorithm, Coupled Flow Imitation Learning (CFIL), achieves state-of-the-art performance on benchmark tasks with a single expert trajectory and extends naturally to a variety of other settings, including the subsampled and state-only regimes.

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude.

It is well-known that inverse dynamics models can improve tracking performance in robot control. These models need to precisely capture the robot dynamics, which consist of well-understood components, e.g., rigid body dynamics, and effects that remain challenging to capture, e.g., stick-slip friction and mechanical flexibilities. Such effects exhibit hysteresis and partial observability, rendering them, particularly challenging to model. Hence, hybrid models, which combine a physical prior with data-driven approaches are especially well-suited in this setting. We present a novel hybrid model formulation that enables us to identify fully physically consistent inertial parameters of a rigid body dynamics model which is paired with a recurrent neural network architecture, allowing us to capture unmodeled partially observable effects using the network memory. We compare our approach against state-of-the-art inverse dynamics models on a 7 degree of freedom manipulator. Using data sets obtained through an optimal experiment design approach, we study the accuracy of offline torque prediction and generalization capabilities of joint learning methods. In control experiments on the real system, we evaluate the model as a feed-forward term for impedance control and show the feedback gains can be drastically reduced to achieve a given tracking accuracy.

Effective planning in model-based reinforcement learning (MBRL) and model-predictive control (MPC) relies on the accuracy of the learned dynamics model. In many instances of MBRL and MPC, this model is assumed to be stationary and is periodically re-trained from scratch on state transition experience collected from the beginning of environment interactions. This implies that the time required to train the dynamics model - and the pause required between plan executions - grows linearly with the size of the collected experience. We argue that this is too slow for lifelong robot learning and propose HyperCRL, a method that continually learns the encountered dynamics in a sequence of tasks using task-conditional hypernetworks. Our method has three main attributes: first, it includes dynamics learning sessions that do not revisit training data from previous tasks, so it only needs to store the most recent fixed-size portion of the state transition experience; second, it uses fixed-capacity hypernetworks to represent non-stationary and task-aware dynamics; third, it outperforms existing continual learning alternatives that rely on fixed-capacity networks, and does competitively with baselines that remember an ever increasing coreset of past experience. We show that HyperCRL is effective in continual model-based reinforcement learning in robot locomotion and manipulation scenarios, such as tasks involving pushing and door opening. Our project website with videos is at this link https://rvl.cs.toronto.edu/blog/2020/hypercrl

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics and compute their expressive power by the trajectory length measure in latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs. Code and data are available at https://github.com/raminmh/liquid_time_constant_networks

In distributed computing, slower nodes (stragglers) usually become a bottleneck. Gradient Coding (GC), introduced by Tandon et al., is an efficient technique that uses principles of error-correcting codes to distribute gradient computation in the presence of stragglers. In this paper, we consider the distributed computation of a sequence of gradients {g(1),g(2),ldots,g(J)}, where processing of each gradient g(t) starts in round-t and finishes by round-(t+T). Here Tgeq 0 denotes a delay parameter. For the GC scheme, coding is only across computing nodes and this results in a solution where T=0. On the other hand, having T>0 allows for designing schemes which exploit the temporal dimension as well. In this work, we propose two schemes that demonstrate improved performance compared to GC. Our first scheme combines GC with selective repetition of previously unfinished tasks and achieves improved straggler mitigation. In our second scheme, which constitutes our main contribution, we apply GC to a subset of the tasks and repetition for the remainder of the tasks. We then multiplex these two classes of tasks across workers and rounds in an adaptive manner, based on past straggler patterns. Using theoretical analysis, we demonstrate that our second scheme achieves significant reduction in the computational load. In our experiments, we study a practical setting of concurrently training multiple neural networks over an AWS Lambda cluster involving 256 worker nodes, where our framework naturally applies. We demonstrate that the latter scheme can yield a 16\% improvement in runtime over the baseline GC scheme, in the presence of naturally occurring, non-simulated stragglers.

We propose a novel framework to study asynchronous federated learning optimization with delays in gradient updates. Our theoretical framework extends the standard FedAvg aggregation scheme by introducing stochastic aggregation weights to represent the variability of the clients update time, due for example to heterogeneous hardware capabilities. Our formalism applies to the general federated setting where clients have heterogeneous datasets and perform at least one step of stochastic gradient descent (SGD). We demonstrate convergence for such a scheme and provide sufficient conditions for the related minimum to be the optimum of the federated problem. We show that our general framework applies to existing optimization schemes including centralized learning, FedAvg, asynchronous FedAvg, and FedBuff. The theory here provided allows drawing meaningful guidelines for designing a federated learning experiment in heterogeneous conditions. In particular, we develop in this work FedFix, a novel extension of FedAvg enabling efficient asynchronous federated training while preserving the convergence stability of synchronous aggregation. We empirically demonstrate our theory on a series of experiments showing that asynchronous FedAvg leads to fast convergence at the expense of stability, and we finally demonstrate the improvements of FedFix over synchronous and asynchronous FedAvg.

A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.

Recent advances in large language models have led to numerous task-specialized fine-tuned variants, creating a need for efficient model merging techniques that preserve specialized capabilities while avoiding costly retraining. While existing task vector-based merging methods show promise, they typically apply uniform coefficients across all parameters, overlooking varying parameter importance both within and across tasks. We present Sens-Merging, a sensitivity-guided coefficient adjustment method that enhances existing model merging techniques by operating at both task-specific and cross-task levels. Our method analyzes parameter sensitivity within individual tasks and evaluates cross-task transferability to determine optimal merging coefficients. Extensive experiments on Mistral 7B and LLaMA2-7B/13B models demonstrate that Sens-Merging significantly improves performance across general knowledge, mathematical reasoning, and code generation tasks. Notably, when combined with existing merging techniques, our method enables merged models to outperform specialized fine-tuned models, particularly in code generation tasks. Our findings reveal important trade-offs between task-specific and cross-task scalings, providing insights for future model merging strategies.

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

Stochastic gradient MCMC methods, such as stochastic gradient Langevin dynamics (SGLD), employ fast but noisy gradient estimates to enable large-scale posterior sampling. Although we can easily extend SGLD to distributed settings, it suffers from two issues when applied to federated non-IID data. First, the variance of these estimates increases significantly. Second, delaying communication causes the Markov chains to diverge from the true posterior even for very simple models. To alleviate both these problems, we propose conducive gradients, a simple mechanism that combines local likelihood approximations to correct gradient updates. Notably, conducive gradients are easy to compute, and since we only calculate the approximations once, they incur negligible overhead. We apply conducive gradients to distributed stochastic gradient Langevin dynamics (DSGLD) and call the resulting method federated stochastic gradient Langevin dynamics (FSGLD). We demonstrate that our approach can handle delayed communication rounds, converging to the target posterior in cases where DSGLD fails. We also show that FSGLD outperforms DSGLD for non-IID federated data with experiments on metric learning and neural networks.

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as geometric graphs, i.e., graphs with nodes positioned in the Euclidean space given an arbitrarily chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as Galilean invariance. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge of code optimization. Naturally, users need different term types either to have different algebraic properties for them, or to use efficient data structures. To this end, we developed Symbolics.jl, an extendable symbolic system which uses dynamic multiple dispatch to change behavior depending on the domain needs. In this work we detail an underlying abstract term interface which allows for speed without sacrificing generality. We show that by formalizing a generic API on actions independent of implementation, we can retroactively add optimized data structures to our system without changing the pre-existing term rewriters. We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations. Further, we show that such a generic API allows for complementary term-rewriting implementations. We demonstrate the ability to swap between classical term-rewriting simplifiers and e-graph-based term-rewriting simplifiers. We showcase an e-graph ruleset which minimizes the number of CPU cycles during expression evaluation, and demonstrate how it simplifies a real-world reaction-network simulation to halve the runtime. Additionally, we show a reaction-diffusion partial differential equation solver which is able to be automatically converted into symbolic expressions via multiple dispatch tracing, which is subsequently accelerated and parallelized to give a 157x simulation speedup. Together, this presents Symbolics.jl as a next-generation symbolic-numeric computing environment geared towards modeling and simulation.

Diffusion Policies have demonstrated impressive performance in robotic manipulation tasks. However, their long inference time, resulting from an extensive iterative denoising process, and the need to execute an action chunk before the next prediction to maintain consistent actions limit their applicability to latency-critical tasks or simple tasks with a short cycle time. While recent methods explored distillation or alternative policy structures to accelerate inference, these often demand additional training, which can be resource-intensive for large robotic models. In this paper, we introduce a novel approach inspired by the Real-Time Iteration (RTI) Scheme, a method from optimal control that accelerates optimization by leveraging solutions from previous time steps as initial guesses for subsequent iterations. We explore the application of this scheme in diffusion inference and propose a scaling-based method to effectively handle discrete actions, such as grasping, in robotic manipulation. The proposed scheme significantly reduces runtime computational costs without the need for distillation or policy redesign. This enables a seamless integration into many pre-trained diffusion-based models, in particular, to resource-demanding large models. We also provide theoretical conditions for the contractivity which could be useful for estimating the initial denoising step. Quantitative results from extensive simulation experiments show a substantial reduction in inference time, with comparable overall performance compared with Diffusion Policy using full-step denoising. Our project page with additional resources is available at: https://rti-dp.github.io/.

Reservoir computers (RCs) provide a computationally efficient alternative to deep learning while also offering a framework for incorporating brain-inspired computational principles. By using an internal neural network with random, fixed connections-the 'reservoir'-and training only the output weights, RCs simplify the training process but remain sensitive to the choice of hyperparameters that govern activation functions and network architecture. Moreover, typical RC implementations overlook a critical aspect of neuronal dynamics: the balance between excitatory and inhibitory (E-I) signals, which is essential for robust brain function. We show that RCs characteristically perform best in balanced or slightly over-inhibited regimes, outperforming excitation-dominated ones. To reduce the need for precise hyperparameter tuning, we introduce a self-adapting mechanism that locally adjusts E/I balance to achieve target neuronal firing rates, improving performance by up to 130% in tasks like memory capacity and time series prediction compared with globally tuned RCs. Incorporating brain-inspired heterogeneity in target neuronal firing rates further reduces the need for fine-tuning hyperparameters and enables RCs to excel across linear and non-linear tasks. These results support a shift from static optimization to dynamic adaptation in reservoir design, demonstrating how brain-inspired mechanisms improve RC performance and robustness while deepening our understanding of neural computation.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

Learning to remember over long timescales is fundamentally challenging for recurrent neural networks (RNNs). While much prior work has explored why RNNs struggle to learn long timescales and how to mitigate this, we still lack a clear understanding of the dynamics involved when RNNs learn long timescales via gradient descent. Here we build a mathematical theory of the learning dynamics of linear RNNs trained to integrate white noise. We show that when the initial recurrent weights are small, the dynamics of learning are described by a low-dimensional system that tracks a single outlier eigenvalue of the recurrent weights. This reveals the precise manner in which the long timescale associated with white noise integration is learned. We extend our analyses to RNNs learning a damped oscillatory filter, and find rich dynamical equations for the evolution of a conjugate pair of outlier eigenvalues. Taken together, our analyses build a rich mathematical framework for studying dynamical learning problems salient for both machine learning and neuroscience.

Diffusion-based stylization methods typically denoise from a specific partial noise state for image-to-image and video-to-video tasks. This multi-step diffusion process is computationally expensive and hinders real-world application. A promising solution to speed up the process is to obtain few-step consistency models through trajectory distillation. However, current consistency models only force the initial-step alignment between the probability flow ODE (PF-ODE) trajectories of the student and the imperfect teacher models. This training strategy can not ensure the consistency of whole trajectories. To address this issue, we propose single trajectory distillation (STD) starting from a specific partial noise state. We introduce a trajectory bank to store the teacher model's trajectory states, mitigating the time cost during training. Besides, we use an asymmetric adversarial loss to enhance the style and quality of the generated images. Extensive experiments on image and video stylization demonstrate that our method surpasses existing acceleration models in terms of style similarity and aesthetic evaluations. Our code and results will be available on the project page: https://single-trajectory-distillation.github.io.

Diffusion models are a family of generative models that yield record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse denoising process, remains a challenge due to slow convergence rates and high computational costs. In this work, we introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models that is more parameter-efficient, exhibits faster convergence, and demonstrates increased noise robustness. Experimenting with denoising probabilistic diffusion models, our framework operates with approximately a quarter of the parameters and 30% of the Floating Point Operations (FLOPs) compared to standard U-Nets in Denoising Diffusion Probabilistic Models (DDPMs). Furthermore, our model is up to 70% faster in inference than the baseline models when measured in equal conditions while converging to better quality solutions.

Federated learning (FL) has emerged as a promising paradigm for enabling the collaborative training of models without centralized access to the raw data on local devices. In the typical FL paradigm (e.g., FedAvg), model weights are sent to and from the server each round to participating clients. Recently, the use of small pre-trained models has been shown to be effective in federated learning optimization and improving convergence. However, recent state-of-the-art pre-trained models are getting more capable but also have more parameters, known as the "Foundation Models." In conventional FL, sharing the enormous model weights can quickly put a massive communication burden on the system, especially if more capable models are employed. Can we find a solution to enable those strong and readily available pre-trained models in FL to achieve excellent performance while simultaneously reducing the communication burden? To this end, we investigate the use of parameter-efficient fine-tuning in federated learning and thus introduce a new framework: FedPEFT. Specifically, we systemically evaluate the performance of FedPEFT across a variety of client stability, data distribution, and differential privacy settings. By only locally tuning and globally sharing a small portion of the model weights, significant reductions in the total communication overhead can be achieved while maintaining competitive or even better performance in a wide range of federated learning scenarios, providing insight into a new paradigm for practical and effective federated systems.

Practitioners frequently aim to infer an unobserved population trajectory using sample snapshots at multiple time points. For instance, in single-cell sequencing, scientists would like to learn how gene expression evolves over time. But sequencing any cell destroys that cell. So we cannot access any cell's full trajectory, but we can access snapshot samples from many cells. Stochastic differential equations are commonly used to analyze systems with full individual-trajectory access; since here we have only sample snapshots, these methods are inapplicable. The deep learning community has recently explored using Schr\"odinger bridges (SBs) and their extensions to estimate these dynamics. However, these methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic within the SB, which is often just set to be Brownian motion. But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. In particular, we suggest an iterative projection method inspired by Schr\"odinger bridges; we alternate between learning a piecewise SB on the unobserved trajectories and using the learned SB to refine our best guess for the dynamics within the reference class. We demonstrate the advantages of our method via a well-known simulated parametric model from ecology, simulated and real data from systems biology, and real motion-capture data.

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~iLQR - on the learned model to minimize a target cost. This paper conducts a rigorous analysis of a simplified variant of this strategy for general nonlinear systems. We analyze an algorithm which iterates between estimating local linear models of nonlinear system dynamics and performing iLQR-like policy updates. We demonstrate that this algorithm attains sample complexity polynomial in relevant problem parameters, and, by synthesizing locally stabilizing gains, overcomes exponential dependence in problem horizon. Experimental results validate the performance of our algorithm, and compare to natural deep-learning baselines.

We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data generation. Intersecting paths in turn lead to integration trajectories that are more straight than those obtained in the classic rectified flow formulation, where integration paths cannot intersect. This leads to modeling of data distributions with fewer neural function evaluations. We empirically verify this on synthetic 1D and 2D data as well as MNIST, CIFAR-10, and ImageNet-32 data. Our code is available at: https://riccizz.github.io/HRF/.

This work studies training instabilities of behavior cloning with deep neural networks. We observe that minibatch SGD updates to the policy network during training result in sharp oscillations in long-horizon rewards, despite negligibly affecting the behavior cloning loss. We empirically disentangle the statistical and computational causes of these oscillations, and find them to stem from the chaotic propagation of minibatch SGD noise through unstable closed-loop dynamics. While SGD noise is benign in the single-step action prediction objective, it results in catastrophic error accumulation over long horizons, an effect we term gradient variance amplification (GVA). We show that many standard mitigation techniques do not alleviate GVA, but find an exponential moving average (EMA) of iterates to be surprisingly effective at doing so. We illustrate the generality of this phenomenon by showing the existence of GVA and its amelioration by EMA in both continuous control and autoregressive language generation. Finally, we provide theoretical vignettes that highlight the benefits of EMA in alleviating GVA and shed light on the extent to which classical convex models can help in understanding the benefits of iterate averaging in deep learning.

Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian optimization and random search based approaches to automating this laborious and compute intensive task, the fundamental learning theoretic complexity of tuning hyperparameters for deep neural networks is poorly understood. Inspired by this glaring gap, we initiate the formal study of hyperparameter tuning complexity in deep learning through a recently introduced data driven setting. We assume that we have a series of deep learning tasks, and we have to tune hyperparameters to do well on average over the distribution of tasks. A major difficulty is that the utility function as a function of the hyperparameter is very volatile and furthermore, it is given implicitly by an optimization problem over the model parameters. To tackle this challenge, we introduce a new technique to characterize the discontinuities and oscillations of the utility function on any fixed problem instance as we vary the hyperparameter; our analysis relies on subtle concepts including tools from differential/algebraic geometry and constrained optimization. This can be used to show that the learning theoretic complexity of the corresponding family of utility functions is bounded. We instantiate our results and provide sample complexity bounds for concrete applications tuning a hyperparameter that interpolates neural activation functions and setting the kernel parameter in graph neural networks.

We present a dynamic model in which the weights are conditioned on an input sample x and are learned to match those that would be obtained by finetuning a base model on x and its label y. This mapping between an input sample and network weights is approximated by a denoising diffusion model. The diffusion model we employ focuses on modifying a single layer of the base model and is conditioned on the input, activations, and output of this layer. Since the diffusion model is stochastic in nature, multiple initializations generate different networks, forming an ensemble, which leads to further improvements. Our experiments demonstrate the wide applicability of the method for image classification, 3D reconstruction, tabular data, speech separation, and natural language processing. Our code is available at https://github.com/ShaharLutatiPersonal/OCD

Majorities of distillation methods on pre-trained diffusion models or on pre-trained rectified flow, focus on either the distillation outputs or the trajectories between random noises and clean images to speed up sample generations from pre-trained models. In those trajectory-based distillation methods, consistency distillation requires the self-consistent trajectory projection to regulate the trajectory, which might avoid the common ODE approximation error {while still be concerning about sampling efficiencies}. At the same time, rectified flow distillations enforce straight trajectory for fast sampling, although an ODE solver is still required. In this work, we propose a trajectory distillation method, \modelname, that enjoys the benefits of both and enables few-step generations. TraFlow adopts the settings of consistency trajectory models, and further enforces the properties of self-consistency and straightness throughout the entire trajectory. These two properties are pursued by reaching a balance with following three targets: (1) reconstruct the output from pre-trained models; (2) learn the amount of changes by pre-trained models; (3) satisfy the self-consistency over its trajectory. Extensive experimental results have shown the effectiveness of our proposed method.

We explore a data-driven approach for learning to optimize neural networks. We construct a dataset of neural network checkpoints and train a generative model on the parameters. In particular, our model is a conditional diffusion transformer that, given an initial input parameter vector and a prompted loss, error, or return, predicts the distribution over parameter updates that achieve the desired metric. At test time, it can optimize neural networks with unseen parameters for downstream tasks in just one update. We find that our approach successfully generates parameters for a wide range of loss prompts. Moreover, it can sample multimodal parameter solutions and has favorable scaling properties. We apply our method to different neural network architectures and tasks in supervised and reinforcement learning.

We demonstrate that Muon, the simplest instantiation of a second-order optimizer, explicitly expands the Pareto frontier over AdamW on the compute-time tradeoff. We find that Muon is more effective than AdamW in retaining data efficiency at large batch sizes, far beyond the so-called critical batch size, while remaining computationally efficient, thus enabling more economical training. We study the combination of Muon and the maximal update parameterization (muP) for efficient hyperparameter transfer and present a simple telescoping algorithm that accounts for all sources of error in muP while introducing only a modest overhead in resources. We validate our findings through extensive experiments with model sizes up to four billion parameters and ablations on the data distribution and architecture.

AdamW has long been the dominant optimizer in language model pretraining, despite numerous claims that alternative optimizers offer 1.4 to 2x speedup. We posit that two methodological shortcomings have obscured fair comparisons and hindered practical adoption: (i) unequal hyperparameter tuning and (ii) limited or misleading evaluation setups. To address these two issues, we conduct a systematic study of ten deep learning optimizers across four model scales (0.1B-1.2B parameters) and data-to-model ratios (1-8x the Chinchilla optimum). We find that fair and informative comparisons require rigorous hyperparameter tuning and evaluations across a range of model scales and data-to-model ratios, performed at the end of training. First, optimal hyperparameters for one optimizer may be suboptimal for another, making blind hyperparameter transfer unfair. Second, the actual speedup of many proposed optimizers over well-tuned baselines is lower than claimed and decreases with model size to only 1.1x for 1.2B parameter models. Thirdly, comparing intermediate checkpoints before reaching the target training budgets can be misleading, as rankings between two optimizers can flip during training due to learning rate decay. Through our thorough investigation, we find that all the fastest optimizers such as Muon and Soap, use matrices as preconditioners -- multiplying gradients with matrices rather than entry-wise scalars. However, the speedup of matrix-based optimizers is inversely proportional to model scale, decreasing from 1.4x over AdamW for 0.1B parameter models to merely 1.1x for 1.2B parameter models.

Fine-tuning large language models (LMs) for individual tasks yields strong performance but is expensive for deployment and storage. Recent works explore model merging to combine multiple task-specific models into a single multi-task model without additional training. However, existing merging methods often fail for models fine-tuned with low-rank adaptation (LoRA), due to significant performance degradation. In this paper, we show that this issue arises from a previously overlooked interplay between model parameters and data distributions. We propose Orthogonal Subspaces for Robust model Merging (OSRM) to constrain the LoRA subspace *prior* to fine-tuning, ensuring that updates relevant to one task do not adversely shift outputs for others. Our approach can seamlessly integrate with most existing merging algorithms, reducing the unintended interference among tasks. Extensive experiments on eight datasets, tested with three widely used LMs and two large LMs, demonstrate that our method not only boosts merging performance but also preserves single-task accuracy. Furthermore, our approach exhibits greater robustness to the hyperparameters of merging. These results highlight the importance of data-parameter interaction in model merging and offer a plug-and-play solution for merging LoRA models.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

Continual Instruction Tuning (CIT) is adopted to continually instruct Large Models to follow human intent data by data. It is observed that existing gradient update would heavily destroy the performance on previous datasets during CIT process. Instead, Exponential Moving Average (EMA), owns the ability to trace previous parameters, which can aid in decreasing forgetting. Nonetheless, its stable balance weight fails to deal with the ever-changing datasets, leading to the out-of-balance between plasticity and stability. In this paper, we propose a general continual instruction tuning framework to address the challenge. Starting from the trade-off prerequisite and EMA update, we propose the plasticity and stability ideal condition. Based on Taylor expansion in the loss function, we find the optimal balance weight can be automatically determined by the gradients and learned parameters. Therefore, we propose a stable-plasticity balanced coefficient to avoid knowledge interference. Based on the semantic similarity of the instructions, we can determine whether to retrain or expand the training parameters and allocate the most suitable parameters for the testing instances. Extensive experiments across multiple continual instruction tuning benchmarks demonstrate that our approach not only enhances anti-forgetting capabilities but also significantly improves overall continual tuning performance. Our code is available at https://github.com/JingyangQiao/CoIN.

In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting - and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks.

We propose Tied-LoRA, a simple paradigm utilizes weight tying and selective training to further increase parameter efficiency of the Low-rank adaptation (LoRA) method. Our investigations include all feasible combinations parameter training/freezing in conjunction with weight tying to identify the optimal balance between performance and the number of trainable parameters. Through experiments covering a variety of tasks and two base language models, we provide analysis revealing trade-offs between efficiency and performance. Our experiments uncovered a particular Tied-LoRA configuration that stands out by demonstrating comparable performance across several tasks while employing only 13~\% percent of parameters utilized by the standard LoRA method.

Primal-dual safe RL methods commonly perform iterations between the primal update of the policy and the dual update of the Lagrange Multiplier. Such a training paradigm is highly susceptible to the error in cumulative cost estimation since this estimation serves as the key bond connecting the primal and dual update processes. We show that this problem causes significant underestimation of cost when using off-policy methods, leading to the failure to satisfy the safety constraint. To address this issue, we propose conservative policy optimization, which learns a policy in a constraint-satisfying area by considering the uncertainty in cost estimation. This improves constraint satisfaction but also potentially hinders reward maximization. We then introduce local policy convexification to help eliminate such suboptimality by gradually reducing the estimation uncertainty. We provide theoretical interpretations of the joint coupling effect of these two ingredients and further verify them by extensive experiments. Results on benchmark tasks show that our method not only achieves an asymptotic performance comparable to state-of-the-art on-policy methods while using much fewer samples, but also significantly reduces constraint violation during training. Our code is available at https://github.com/ZifanWu/CAL.

Continual Test-Time Adaptation (CTTA) aims to adapt a pretrained model to ever-changing environments during the test time under continuous domain shifts. Most existing CTTA approaches are based on the Mean Teacher (MT) structure, which contains a student and a teacher model, where the student is updated using the pseudo-labels from the teacher model, and the teacher is then updated by exponential moving average strategy. However, these methods update the MT model indiscriminately on all parameters of the model. That is, some critical parameters involving sharing knowledge across different domains may be erased, intensifying error accumulation and catastrophic forgetting. In this paper, we introduce Parameter-Selective Mean Teacher (PSMT) method, which is capable of effectively updating the critical parameters within the MT network under domain shifts. First, we introduce a selective distillation mechanism in the student model, which utilizes past knowledge to regularize novel knowledge, thereby mitigating the impact of error accumulation. Second, to avoid catastrophic forgetting, in the teacher model, we create a mask through Fisher information to selectively update parameters via exponential moving average, with preservation measures applied to crucial parameters. Extensive experimental results verify that PSMT outperforms state-of-the-art methods across multiple benchmark datasets. Our code is available at https://github.com/JiaxuTian/PSMT.

Variational inference using the reparameterization trick has enabled large-scale approximate Bayesian inference in complex probabilistic models, leveraging stochastic optimization to sidestep intractable expectations. The reparameterization trick is applicable when we can simulate a random variable by applying a differentiable deterministic function on an auxiliary random variable whose distribution is fixed. For many distributions of interest (such as the gamma or Dirichlet), simulation of random variables relies on acceptance-rejection sampling. The discontinuity introduced by the accept-reject step means that standard reparameterization tricks are not applicable. We propose a new method that lets us leverage reparameterization gradients even when variables are outputs of a acceptance-rejection sampling algorithm. Our approach enables reparameterization on a larger class of variational distributions. In several studies of real and synthetic data, we show that the variance of the estimator of the gradient is significantly lower than other state-of-the-art methods. This leads to faster convergence of stochastic gradient variational inference.

In order to improve reproducibility, deep reinforcement learning (RL) has been adopting better scientific practices such as standardized evaluation metrics and reporting. However, the process of hyperparameter optimization still varies widely across papers, which makes it challenging to compare RL algorithms fairly. In this paper, we show that hyperparameter choices in RL can significantly affect the agent's final performance and sample efficiency, and that the hyperparameter landscape can strongly depend on the tuning seed which may lead to overfitting. We therefore propose adopting established best practices from AutoML, such as the separation of tuning and testing seeds, as well as principled hyperparameter optimization (HPO) across a broad search space. We support this by comparing multiple state-of-the-art HPO tools on a range of RL algorithms and environments to their hand-tuned counterparts, demonstrating that HPO approaches often have higher performance and lower compute overhead. As a result of our findings, we recommend a set of best practices for the RL community, which should result in stronger empirical results with fewer computational costs, better reproducibility, and thus faster progress. In order to encourage the adoption of these practices, we provide plug-and-play implementations of the tuning algorithms used in this paper at https://github.com/facebookresearch/how-to-autorl.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Convergent Cross Mapping (CCM) is a powerful method for detecting causality in coupled nonlinear dynamical systems, providing a model-free approach to capture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced as an extension of CCM to address indirect causality in three-variable systems by comparing cross-mapping quality between direct cause-effect mapping and indirect mapping through an intermediate conditioning variable. However, PCM remains limited to univariate delay embeddings in its cross-mapping processes. In this work, we extend PCM to the multivariate setting, introducing multiPCM, which leverages multivariate embeddings to more effectively distinguish indirect causal relationships. We further propose a multivariate cross-mapping framework (MXMap) for causal discovery in dynamical systems. This two-phase framework combines (1) pairwise CCM tests to establish an initial causal graph and (2) multiPCM to refine the graph by pruning indirect causal connections. Through experiments on simulated data and the ERA5 Reanalysis weather dataset, we demonstrate the effectiveness of MXMap. Additionally, MXMap is compared against several baseline methods, showing advantages in accuracy and causal graph refinement.

Chaos and unpredictability are traditionally synonymous, yet large-scale machine learning methods recently have demonstrated a surprising ability to forecast chaotic systems well beyond typical predictability horizons. However, recent works disagree on whether specialized methods grounded in dynamical systems theory, such as reservoir computers or neural ordinary differential equations, outperform general-purpose large-scale learning methods such as transformers or recurrent neural networks. These prior studies perform comparisons on few individually-chosen chaotic systems, thereby precluding robust quantification of how statistical modeling choices and dynamical invariants of different chaotic systems jointly determine empirical predictability. Here, we perform the largest to-date comparative study of forecasting methods on the classical problem of forecasting chaos: we benchmark 24 state-of-the-art forecasting methods on a crowdsourced database of 135 low-dimensional systems with 17 forecast metrics. We find that large-scale, domain-agnostic forecasting methods consistently produce predictions that remain accurate up to two dozen Lyapunov times, thereby accessing a new long-horizon forecasting regime well beyond classical methods. We find that, in this regime, accuracy decorrelates with classical invariant measures of predictability like the Lyapunov exponent. However, in data-limited settings outside the long-horizon regime, we find that physics-based hybrid methods retain a comparative advantage due to their strong inductive biases.

Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized models trained separately on individual time series, or foundation models trained on vast time series databases with little underlying dynamical structure. Motivated by dynamical systems theory, we present Panda, Patched Attention for Nonlinear DynAmics. We train Panda on a novel synthetic, extensible dataset of 2 times 10^4 chaotic dynamical systems that we discover using an evolutionary algorithm. Trained purely on simulated data, Panda exhibits emergent properties: zero-shot forecasting of unseen real world chaotic systems, and nonlinear resonance patterns in cross-channel attention heads. Despite having been trained only on low-dimensional ordinary differential equations, Panda spontaneously develops the ability to predict partial differential equations without retraining. We demonstrate a neural scaling law for differential equations, underscoring the potential of pretrained models for probing abstract mathematical domains like nonlinear dynamics.

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential for predicting the temporal evolution of populations across novel samples and unseen environments. Flow-based models allow for learning these dynamics at the population level - they model the evolution of the entire distribution of samples. However, current flow-based models are limited to a single initial population and a set of predefined conditions which describe different dynamics. We argue that multiple processes in natural sciences have to be represented as vector fields on the Wasserstein manifold of probability densities. That is, the change of the population at any moment in time depends on the population itself due to the interactions between samples. In particular, this is crucial for personalized medicine where the development of diseases and their respective treatment response depends on the microenvironment of cells specific to each patient. We propose Meta Flow Matching (MFM), a practical approach to integrating along these vector fields on the Wasserstein manifold by amortizing the flow model over the initial populations. Namely, we embed the population of samples using a Graph Neural Network (GNN) and use these embeddings to train a Flow Matching model. This gives MFM the ability to generalize over the initial distributions unlike previously proposed methods. We demonstrate the ability of MFM to improve prediction of individual treatment responses on a large scale multi-patient single-cell drug screen dataset.

Time-series forecasting is crucial for numerous real-world applications including weather prediction and financial market modeling. While temporal-domain methods remain prevalent, frequency-domain approaches can effectively capture multi-scale periodic patterns, reduce sequence dependencies, and naturally denoise signals. However, existing approaches typically train model components for all frequencies under a unified training objective, often leading to mismatched learning speeds: high-frequency components converge faster and risk overfitting, while low-frequency components underfit due to insufficient training time. To deal with this challenge, we propose BEAT (Balanced frEquency Adaptive Tuning), a novel framework that dynamically monitors the training status for each frequency and adaptively adjusts their gradient updates. By recognizing convergence, overfitting, or underfitting for each frequency, BEAT dynamically reallocates learning priorities, moderating gradients for rapid learners and increasing those for slower ones, alleviating the tension between competing objectives across frequencies and synchronizing the overall learning process. Extensive experiments on seven real-world datasets demonstrate that BEAT consistently outperforms state-of-the-art approaches.

Despite the promising performance of state space models (SSMs) in long sequence modeling, limitations still exist. Advanced SSMs like S5 and S6 (Mamba) in addressing non-uniform sampling, their recursive structures impede efficient SSM computation via convolution. To overcome compatibility limitations in parallel convolutional computation, this paper proposes a novel non-recursive non-uniform sample processing strategy. Theoretical analysis of SSMs through the lens of Event-Triggered Control (ETC) theory reveals the Non-Stable State (NSS) problem, where deviations from sampling point requirements lead to error transmission and accumulation, causing the divergence of the SSM's hidden state. Our analysis further reveals that adjustments of input sequences with early memories can mitigate the NSS problem, achieving Sampling Step Adaptation (SSA). Building on this insight, we introduce a simple yet effective plug-and-play mechanism, State Memory Replay (SMR), which utilizes learnable memories to adjust the current state with multi-step information for generalization at sampling points different from those in the training data. This enables SSMs to stably model varying sampling points. Experiments on long-range modeling tasks in autoregressive language modeling and Long Range Arena demonstrate the general effectiveness of the SMR mechanism for a series of SSM models.

Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship between, loss, or task performance, and scale. All components of this process vary, from the specific equation being fit, to the training setup, to the optimization method. Each of these factors may affect the fitted law, and therefore, the conclusions of a given study. We discuss discrepancies in the conclusions that several prior works reach, on questions such as the optimal token to parameter ratio. We augment this discussion with our own analysis of the critical impact that changes in specific details may effect in a scaling study, and the resulting altered conclusions. Additionally, we survey over 50 papers that study scaling trends: while 45 of these papers quantify these trends using a power law, most under-report crucial details needed to reproduce their findings. To mitigate this, we we propose a checklist for authors to consider while contributing to scaling law research.

Federated learning (FL) allows mutually untrusted clients to collaboratively train a common machine learning model without sharing their private/proprietary training data among each other. FL is unfortunately susceptible to poisoning by malicious clients who aim to hamper the accuracy of the commonly trained model through sending malicious model updates during FL's training process. We argue that the key factor to the success of poisoning attacks against existing FL systems is the large space of model updates available to the clients, allowing malicious clients to search for the most poisonous model updates, e.g., by solving an optimization problem. To address this, we propose Federated Rank Learning (FRL). FRL reduces the space of client updates from model parameter updates (a continuous space of float numbers) in standard FL to the space of parameter rankings (a discrete space of integer values). To be able to train the global model using parameter ranks (instead of parameter weights), FRL leverage ideas from recent supermasks training mechanisms. Specifically, FRL clients rank the parameters of a randomly initialized neural network (provided by the server) based on their local training data. The FRL server uses a voting mechanism to aggregate the parameter rankings submitted by clients in each training epoch to generate the global ranking of the next training epoch. Intuitively, our voting-based aggregation mechanism prevents poisoning clients from making significant adversarial modifications to the global model, as each client will have a single vote! We demonstrate the robustness of FRL to poisoning through analytical proofs and experimentation. We also show FRL's high communication efficiency. Our experiments demonstrate the superiority of FRL in real-world FL settings.

Training language models currently requires pre-determining a fixed compute budget because the typical cosine learning rate schedule depends on the total number of steps. In contrast, the Warmup-Stable-Decay (WSD) schedule uses a constant learning rate to produce a main branch of iterates that can in principle continue indefinitely without a pre-specified compute budget. Then, given any compute budget, one can branch out from the main branch at a proper time with a rapidly decaying learning rate to produce a strong model. Empirically, WSD generates a non-traditional loss curve: the loss remains elevated during the stable phase but sharply declines during the decay phase. Towards explaining this phenomenon, we conjecture that pretraining loss exhibits a river valley landscape, which resembles a deep valley with a river at its bottom. Under this assumption, we show that during the stable phase, the iterate undergoes large oscillations due to the high learning rate, yet it progresses swiftly along the river. During the decay phase, the rapidly dropping learning rate minimizes the iterate's oscillations, moving it closer to the river and revealing true optimization progress. Therefore, the sustained high learning rate phase and fast decaying phase are responsible for progress in the river and the mountain directions respectively, and are both critical. Our analysis predicts phenomenons consistent with empirical observations and shows that this landscape can emerge from pretraining on a simple bi-gram dataset. Inspired by the theory, we introduce WSD-S, a variant of WSD that reuses previous checkpoints' decay phases and keeps only one main branch, where we resume from a decayed checkpoint. WSD-S empirically outperforms WSD and Cyclic-Cosine in obtaining multiple language model checkpoints across various compute budgets in a single run for parameters scaling from 0.1B to 1.2B.

This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the "standard" semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude -- including full LTL model checking, analysis with user-defined analysis strategies, and even statistical model checking -- for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Romeo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Romeo in many cases.

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative trajectories, and results in costly inference for diffusion models. To address these limitations, we introduce Neural Flow Diffusion Models (NFDM), a novel framework that enhances diffusion models by supporting a broader range of forward processes beyond the fixed linear Gaussian. We also propose a novel parameterization technique for learning the forward process. Our framework provides an end-to-end, simulation-free optimization objective, effectively minimizing a variational upper bound on the negative log-likelihood. Experimental results demonstrate NFDM's strong performance, evidenced by state-of-the-art likelihood estimation. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories. This exploration underscores NFDM's versatility and its potential for a wide range of applications.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

Large artificial neural networks have become a mainstay of language, vision, and audio processing and synthesis, yet their initializations and learning rates are often set in an unsophisticated fashion, due to the high cost of hyperparameter sweeps at scale. The mu-Parameterization (muP) offers a potential solution to this challenge, yielding scaling rules for model initialization and learning rates while reportedly enabling zero-shot hyperparameter transfer from small to large models. Despite its evident promise, the muP method is not yet widely adopted, perhaps due to higher implementation complexity, many variations, or complex theoretical background. This work investigates muP empirically, focusing on the ubiquitous transformer architecture, and aims to answer a simple question: does mu-Transfer yield optimal learning rates in practice? Studying models of up to 10B parameters and training budgets of up to 190B tokens, we find mu-Transfer works as intended for the majority of important cases, yet also identify a few cases where it may not.

Time series forecasting is widely used in extensive applications, such as traffic planning and weather forecasting. However, real-world time series usually present intricate temporal variations, making forecasting extremely challenging. Going beyond the mainstream paradigms of plain decomposition and multiperiodicity analysis, we analyze temporal variations in a novel view of multiscale-mixing, which is based on an intuitive but important observation that time series present distinct patterns in different sampling scales. The microscopic and the macroscopic information are reflected in fine and coarse scales respectively, and thereby complex variations can be inherently disentangled. Based on this observation, we propose TimeMixer as a fully MLP-based architecture with Past-Decomposable-Mixing (PDM) and Future-Multipredictor-Mixing (FMM) blocks to take full advantage of disentangled multiscale series in both past extraction and future prediction phases. Concretely, PDM applies the decomposition to multiscale series and further mixes the decomposed seasonal and trend components in fine-to-coarse and coarse-to-fine directions separately, which successively aggregates the microscopic seasonal and macroscopic trend information. FMM further ensembles multiple predictors to utilize complementary forecasting capabilities in multiscale observations. Consequently, TimeMixer is able to achieve consistent state-of-the-art performances in both long-term and short-term forecasting tasks with favorable run-time efficiency.

We provide a concise framework for generalized ensemble theory through a matrix-based approach. By introducing an observation matrix, any discrete probability distribution, including those for non-equilibrium steady states, can be expressed as a generalized Boltzmann distribution, with observables and conjugate variables as the basis and coordinates in a linear space. In this framework, we identify the minimal sufficient statistics required for inferring the Boltzmann distribution. Furthermore, we show that the Hadamard and Vandermonde matrices are suitable observation matrices for spin systems and random walks. In master equation systems, the probability flux observation matrix facilitates the identification of detailed balance violations. Our findings provide a new approach to developing generalized ensemble theory for non-equilibrium steady-state systems.

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the future state distant in time with high accuracy. Although these methods have diverse designs in modeling the coordinates and interacting forces of the system, we show that they actually share a common paradigm that learns the integration of the velocity over the interval between the initial and terminal coordinates. However, their integrand is constant w.r.t. time. Inspired by this observation, we propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas and prove its effectiveness theoretically. Extensive experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.

Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive but accurate numerical routines are replaced by fast and inaccurate methods, trading inference time for solution accuracy. This paper provides techniques to improve the quality of optimized control policies given a fixed computational budget. We achieve the above via a hypersolvers approach, which hybridizes a differential equation solver and a neural network. The performance is evaluated in direct and receding-horizon optimal control tasks in both low and high dimensions, where the proposed approach shows consistent Pareto improvements in solution accuracy and control performance.

We introduce controlgym, a library of thirty-six safety-critical industrial control settings, and ten infinite-dimensional partial differential equation (PDE)-based control problems. Integrated within the OpenAI Gym/Gymnasium (Gym) framework, controlgym allows direct applications of standard reinforcement learning (RL) algorithms like stable-baselines3. Our control environments complement those in Gym with continuous, unbounded action and observation spaces, motivated by real-world control applications. Moreover, the PDE control environments uniquely allow the users to extend the state dimensionality of the system to infinity while preserving the intrinsic dynamics. This feature is crucial for evaluating the scalability of RL algorithms for control. This project serves the learning for dynamics & control (L4DC) community, aiming to explore key questions: the convergence of RL algorithms in learning control policies; the stability and robustness issues of learning-based controllers; and the scalability of RL algorithms to high- and potentially infinite-dimensional systems. We open-source the controlgym project at https://github.com/xiangyuan-zhang/controlgym.

Speech-driven 3D facial animation aims to generate realistic lip movements and facial expressions for 3D head models from arbitrary audio clips. Although existing diffusion-based methods are capable of producing natural motions, their slow generation speed limits their application potential. In this paper, we introduce a novel autoregressive model that achieves real-time generation of highly synchronized lip movements and realistic head poses and eye blinks by learning a mapping from speech to a multi-scale motion codebook. Furthermore, our model can adapt to unseen speaking styles using sample motion sequences, enabling the creation of 3D talking avatars with unique personal styles beyond the identities seen during training. Extensive evaluations and user studies demonstrate that our method outperforms existing approaches in lip synchronization accuracy and perceived quality.

When training deep learning models, the performance depends largely on the selected hyperparameters. However, hyperparameter optimization (HPO) is often one of the most expensive parts of model design. Classical HPO methods treat this as a black-box optimization problem. However, gray-box HPO methods, which incorporate more information about the setup, have emerged as a promising direction for more efficient optimization. For example, using intermediate loss evaluations to terminate bad selections. In this work, we propose an HPO method for neural networks using logged checkpoints of the trained weights to guide future hyperparameter selections. Our method, Forecasting Model Search (FMS), embeds weights into a Gaussian process deep kernel surrogate model, using a permutation-invariant graph metanetwork to be data-efficient with the logged network weights. To facilitate reproducibility and further research, we open-source our code at https://github.com/NVlabs/forecasting-model-search.

Solving time-dependent parametric partial differential equations (PDEs) is challenging, as models must adapt to variations in parameters such as coefficients, forcing terms, and boundary conditions. Data-driven neural solvers either train on data sampled from the PDE parameters distribution in the hope that the model generalizes to new instances or rely on gradient-based adaptation and meta-learning to implicitly encode the dynamics from observations. This often comes with increased inference complexity. Inspired by the in-context learning capabilities of large language models (LLMs), we introduce Zebra, a novel generative auto-regressive transformer designed to solve parametric PDEs without requiring gradient adaptation at inference. By leveraging in-context information during both pre-training and inference, Zebra dynamically adapts to new tasks by conditioning on input sequences that incorporate context trajectories or preceding states. This approach enables Zebra to flexibly handle arbitrarily sized context inputs and supports uncertainty quantification through the sampling of multiple solution trajectories. We evaluate Zebra across a variety of challenging PDE scenarios, demonstrating its adaptability, robustness, and superior performance compared to existing approaches.

This paper proposes an online, provably robust, and scalable Bayesian approach for changepoint detection. The resulting algorithm has key advantages over previous work: it provides provable robustness by leveraging the generalised Bayesian perspective, and also addresses the scalability issues of previous attempts. Specifically, the proposed generalised Bayesian formalism leads to conjugate posteriors whose parameters are available in closed form by leveraging diffusion score matching. The resulting algorithm is exact, can be updated through simple algebra, and is more than 10 times faster than its closest competitor.

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., |Params(M){-}Params(m)|{<}Delta. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed naturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call Stability -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of Stability as defined by our measure will remain valid after potential ``naturally-occurring'' model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes.

We consider minimizing functions for which it is expensive to compute the (possibly stochastic) gradient. Such functions are prevalent in reinforcement learning, imitation learning and adversarial training. Our target optimization framework uses the (expensive) gradient computation to construct surrogate functions in a target space (e.g. the logits output by a linear model for classification) that can be minimized efficiently. This allows for multiple parameter updates to the model, amortizing the cost of gradient computation. In the full-batch setting, we prove that our surrogate is a global upper-bound on the loss, and can be (locally) minimized using a black-box optimization algorithm. We prove that the resulting majorization-minimization algorithm ensures convergence to a stationary point of the loss. Next, we instantiate our framework in the stochastic setting and propose the SSO algorithm, which can be viewed as projected stochastic gradient descent in the target space. This connection enables us to prove theoretical guarantees for SSO when minimizing convex functions. Our framework allows the use of standard stochastic optimization algorithms to construct surrogates which can be minimized by any deterministic optimization method. To evaluate our framework, we consider a suite of supervised learning and imitation learning problems. Our experiments indicate the benefits of target optimization and the effectiveness of SSO.

Adapting large language models (LLMs) to new languages typically involves continual pre-training (CT) followed by supervised fine-tuning (SFT). However, this CT-then-SFT approach struggles with limited data in the context of low-resource languages, failing to balance language modeling and task-solving capabilities. We thus propose model merging as an alternative for low-resource languages, combining models with distinct capabilities into a single model without additional training. We use model merging to develop task-solving LLMs for low-resource languages without SFT data in the target languages. Our experiments based on Llama-2-7B demonstrate that model merging effectively endows LLMs for low-resource languages with task-solving abilities, outperforming CT-then-SFT in scenarios with extremely scarce data. Observing performance saturation in model merging with more training tokens, we further analyze the merging process and introduce a slack variable to the model merging algorithm to mitigate the loss of important parameters, thereby enhancing performance. We hope that model merging can benefit more human languages suffering from data scarcity with its higher data efficiency.

Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems, but also in the training of large language models. In contrast to infinite horizon MDPs optimal policies are not stationary, policies must be learned for every single epoch. In practice all parameters are often trained simultaneously, ignoring the inherent structure suggested by dynamic programming. This paper introduces a combination of dynamic programming and policy gradient called dynamic policy gradient, where the parameters are trained backwards in time. For the tabular softmax parametrisation we carry out the convergence analysis for simultaneous and dynamic policy gradient towards global optima, both in the exact and sampled gradient settings without regularisation. It turns out that the use of dynamic policy gradient training much better exploits the structure of finite-time problems which is reflected in improved convergence bounds.

Chaotic dynamical systems (DS) are ubiquitous in nature and society. Often we are interested in reconstructing such systems from observed time series for prediction or mechanistic insight, where by reconstruction we mean learning geometrical and invariant temporal properties of the system in question (like attractors). However, training reconstruction algorithms like recurrent neural networks (RNNs) on such systems by gradient-descent based techniques faces severe challenges. This is mainly due to exploding gradients caused by the exponential divergence of trajectories in chaotic systems. Moreover, for (scientific) interpretability we wish to have as low dimensional reconstructions as possible, preferably in a model which is mathematically tractable. Here we report that a surprisingly simple modification of teacher forcing leads to provably strictly all-time bounded gradients in training on chaotic systems, and, when paired with a simple architectural rearrangement of a tractable RNN design, piecewise-linear RNNs (PLRNNs), allows for faithful reconstruction in spaces of at most the dimensionality of the observed system. We show on several DS that with these amendments we can reconstruct DS better than current SOTA algorithms, in much lower dimensions. Performance differences were particularly compelling on real world data with which most other methods severely struggled. This work thus led to a simple yet powerful DS reconstruction algorithm which is highly interpretable at the same time.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

We present a novel approach to accelerate stochastic gradient descent (SGD) by utilizing curvature information obtained from Hessian-vector products or finite differences of parameters and gradients, similar to the BFGS algorithm. Our approach involves two preconditioners: a matrix-free preconditioner and a low-rank approximation preconditioner. We update both preconditioners online using a criterion that is robust to stochastic gradient noise and does not require line search or damping. To preserve the corresponding symmetry or invariance, our preconditioners are constrained to certain connected Lie groups. The Lie group's equivariance property simplifies the preconditioner fitting process, while its invariance property eliminates the need for damping, which is commonly required in second-order optimizers. As a result, the learning rate for parameter updating and the step size for preconditioner fitting are naturally normalized, and their default values work well in most scenarios. Our proposed approach offers a promising direction for improving the convergence of SGD with low computational overhead. We demonstrate that Preconditioned SGD (PSGD) outperforms SoTA on Vision, NLP, and RL tasks across multiple modern deep-learning architectures. We have provided code for reproducing toy and large scale experiments in this paper.

Triggered by the realization that AI emulators can rival the performance of traditional numerical weather prediction models running on HPC systems, there is now an increasing number of large AI models that address use cases such as forecasting, downscaling, or nowcasting. While the parallel developments in the AI literature focus on foundation models -- models that can be effectively tuned to address multiple, different use cases -- the developments on the weather and climate side largely focus on single-use cases with particular emphasis on mid-range forecasting. We close this gap by introducing Prithvi WxC, a 2.3 billion parameter foundation model developed using 160 variables from the Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). Prithvi WxC employs an encoder-decoder-based architecture, incorporating concepts from various recent transformer models to effectively capture both regional and global dependencies in the input data. The model has been designed to accommodate large token counts to model weather phenomena in different topologies at fine resolutions. Furthermore, it is trained with a mixed objective that combines the paradigms of masked reconstruction with forecasting. We test the model on a set of challenging downstream tasks namely: Autoregressive rollout forecasting, Downscaling, Gravity wave flux parameterization, and Extreme events estimation. The pretrained model with 2.3 billion parameters, along with the associated fine-tuning workflows, has been publicly released as an open-source contribution via Hugging Face.

This paper presents AlphaOne (alpha1), a universal framework for modulating reasoning progress in large reasoning models (LRMs) at test time. alpha1 first introduces alpha moment, which represents the scaled thinking phase with a universal parameter alpha. Within this scaled pre-alpha moment phase, it dynamically schedules slow thinking transitions by modeling the insertion of reasoning transition tokens as a Bernoulli stochastic process. After the alpha moment, alpha1 deterministically terminates slow thinking with the end-of-thinking token, thereby fostering fast reasoning and efficient answer generation. This approach unifies and generalizes existing monotonic scaling methods by enabling flexible and dense slow-to-fast reasoning modulation. Extensive empirical studies on various challenging benchmarks across mathematical, coding, and scientific domains demonstrate alpha1's superior reasoning capability and efficiency. Project page: https://alphaone-project.github.io/

Much has been said about observability in system theory and control; however, it has been recently that observability in complex networks has seriously attracted the attention of researchers. This paper examines the state-of-the-art and discusses some issues raised due to "complexity" and "stochasticity". These unresolved issues call for a new practical methodology. For stochastic systems, a degree of observability may be defined and the observability problem is not a binary (i.e., yes-no) question anymore. Here, we propose to employ a goal-seeking system to play a supervisory role in the network. Hence, improving the degree of observability would be a valid objective for the supervisory system. Towards this goal, the supervisor dynamically optimizes the observation process by reconfiguring the sensory parts in the network. A cognitive dynamic system is suggested as a proper choice for the supervisory system. In this framework, the network itself is viewed as the environment with which the cognitive dynamic system interacts. Computer experiments confirm the potential of the proposed approach for addressing some of the issues raised in networks due to complexity and stochasticity.

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.

Fine-tuning large pre-trained language models on downstream tasks has become the de-facto learning paradigm in NLP. However, conventional approaches fine-tune all the parameters of the pre-trained model, which becomes prohibitive as the model size and the number of tasks grow. Recent work has proposed a variety of parameter-efficient transfer learning methods that only fine-tune a small number of (extra) parameters to attain strong performance. While effective, the critical ingredients for success and the connections among the various methods are poorly understood. In this paper, we break down the design of state-of-the-art parameter-efficient transfer learning methods and present a unified framework that establishes connections between them. Specifically, we re-frame them as modifications to specific hidden states in pre-trained models, and define a set of design dimensions along which different methods vary, such as the function to compute the modification and the position to apply the modification. Through comprehensive empirical studies across machine translation, text summarization, language understanding, and text classification benchmarks, we utilize the unified view to identify important design choices in previous methods. Furthermore, our unified framework enables the transfer of design elements across different approaches, and as a result we are able to instantiate new parameter-efficient fine-tuning methods that tune less parameters than previous methods while being more effective, achieving comparable results to fine-tuning all parameters on all four tasks.

Differentiable programming techniques are widely used in the community and are responsible for the machine learning renaissance of the past several decades. While these methods are powerful, they have limits. In this short report, we discuss a common chaos based failure mode which appears in a variety of differentiable circumstances, ranging from recurrent neural networks and numerical physics simulation to training learned optimizers. We trace this failure to the spectrum of the Jacobian of the system under study, and provide criteria for when a practitioner might expect this failure to spoil their differentiation based optimization algorithms.

Reinforcement learning (RL) tackles sequential decision-making problems by creating agents that interacts with their environment. However, existing algorithms often view these problem as static, focusing on point estimates for model parameters to maximize expected rewards, neglecting the stochastic dynamics of agent-environment interactions and the critical role of uncertainty quantification. Our research leverages the Kalman filtering paradigm to introduce a novel and scalable sampling algorithm called Langevinized Kalman Temporal-Difference (LKTD) for deep reinforcement learning. This algorithm, grounded in Stochastic Gradient Markov Chain Monte Carlo (SGMCMC), efficiently draws samples from the posterior distribution of deep neural network parameters. Under mild conditions, we prove that the posterior samples generated by the LKTD algorithm converge to a stationary distribution. This convergence not only enables us to quantify uncertainties associated with the value function and model parameters but also allows us to monitor these uncertainties during policy updates throughout the training phase. The LKTD algorithm paves the way for more robust and adaptable reinforcement learning approaches.

Language model training in distributed settings is limited by the communication cost of gradient exchanges. In this short note, we extend recent work from Malladi et al. (2023), using shared randomness to perform distributed fine-tuning with low bandwidth. The method is a natural decentralized extension of memory-efficient Simultaneous Perturbation Stochastic Approximation (SPSA). Each iteration, each machine seeds a Random Number Generator (RNG) to perform local reproducible perturbations on model weights and calculate and exchange scalar projected gradients, which are then used to update each model. By using a (machine, sample) identifier as the random seed, each model can regenerate one another's perturbations. As machines only exchange single-byte projected gradients, this is highly communication efficient. There are also potential privacy benefits, as projected gradients may be calculated on different training data, and models never access the other's data. Our approach not only drastically reduces communication bandwidth requirements but also accommodates dynamic addition or removal of machines during the training process and retains the memory-efficient and inference-only advantages of recent work. We perform proof-of-concept experiments to demonstrate the potential usefulness of this method, building off of rich literature on distributed optimization and memory-efficient training.

Some fractals -- for instance those associated with the Mandelbrot and quadratic Julia sets -- are computed by iterating a function, and identifying the boundary between hyperparameters for which the resulting series diverges or remains bounded. Neural network training similarly involves iterating an update function (e.g. repeated steps of gradient descent), can result in convergent or divergent behavior, and can be extremely sensitive to small changes in hyperparameters. Motivated by these similarities, we experimentally examine the boundary between neural network hyperparameters that lead to stable and divergent training. We find that this boundary is fractal over more than ten decades of scale in all tested configurations.

This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables multiple autonomous agents to collaboratively estimate the smallest eigenvalue of large matrices. Each agent employs a localized neural network, refining its estimates through communication with neighboring agents. Our empirical results confirm the algorithm's convergence towards the true eigenvalue, with estimates clustered closely around the true value. Even in the presence of communication delays or network disruptions, the method demonstrates strong robustness and scalability. Theoretical analysis further validates the accuracy and stability of the proposed approach, while empirical tests highlight its efficiency and precision, surpassing traditional centralized algorithms in large-scale eigenvalue computations.