Daily Papers

Continual Pre-Training (CPT) has become a popular and effective method to apply strong foundation models to specific downstream tasks. In this work, we explore the learning dynamics throughout the CPT process for large language models. We specifically focus on how general and downstream domain performance evolves at each training step, with domain performance measured via validation losses. We have observed that the CPT loss curve fundamentally characterizes the transition from one curve to another hidden curve, and could be described by decoupling the effects of distribution shift and learning rate annealing. We derive a CPT scaling law that combines the two factors, enabling the prediction of loss at any (continual) training steps and across learning rate schedules (LRS) in CPT. Our formulation presents a comprehensive understanding of several critical factors in CPT, including loss potential, peak learning rate, training steps, replay ratio, etc. Moreover, our approach can be adapted to customize training hyper-parameters to different CPT goals such as balancing general and domain-specific performance. Extensive experiments demonstrate that our scaling law holds across various CPT datasets and training hyper-parameters.

Learning dynamics, which describes how the learning of specific training examples influences the model's predictions on other examples, gives us a powerful tool for understanding the behavior of deep learning systems. We study the learning dynamics of large language models during different types of finetuning, by analyzing the step-wise decomposition of how influence accumulates among different potential responses. Our framework allows a uniform interpretation of many interesting observations about the training of popular algorithms for both instruction tuning and preference tuning. In particular, we propose a hypothetical explanation of why specific types of hallucination are strengthened after finetuning, e.g., the model might use phrases or facts in the response for question B to answer question A, or the model might keep repeating similar simple phrases when generating responses. We also extend our framework and highlight a unique "squeezing effect" to explain a previously observed phenomenon in off-policy direct preference optimization (DPO), where running DPO for too long makes even the desired outputs less likely. This framework also provides insights into where the benefits of on-policy DPO and other variants come from. The analysis not only provides a novel perspective of understanding LLM's finetuning but also inspires a simple, effective method to improve alignment performance.

Preference-based reinforcement learning (PbRL) aligns a robot behavior with human preferences via a reward function learned from binary feedback over agent behaviors. We show that dynamics-aware reward functions improve the sample efficiency of PbRL by an order of magnitude. In our experiments we iterate between: (1) learning a dynamics-aware state-action representation (z^{sa}) via a self-supervised temporal consistency task, and (2) bootstrapping the preference-based reward function from (z^{sa}), which results in faster policy learning and better final policy performance. For example, on quadruped-walk, walker-walk, and cheetah-run, with 50 preference labels we achieve the same performance as existing approaches with 500 preference labels, and we recover 83\% and 66\% of ground truth reward policy performance versus only 38\% and 21\%. The performance gains demonstrate the benefits of explicitly learning a dynamics-aware reward model. Repo: https://github.com/apple/ml-reed.

Without relevant human priors, neural networks may learn uninterpretable features. We propose Dynamics of Attention for Focus Transition (DAFT) as a human prior for machine reasoning. DAFT is a novel method that regularizes attention-based reasoning by modelling it as a continuous dynamical system using neural ordinary differential equations. As a proof of concept, we augment a state-of-the-art visual reasoning model with DAFT. Our experiments reveal that applying DAFT yields similar performance to the original model while using fewer reasoning steps, showing that it implicitly learns to skip unnecessary steps. We also propose a new metric, Total Length of Transition (TLT), which represents the effective reasoning step size by quantifying how much a given model's focus drifts while reasoning about a question. We show that adding DAFT results in lower TLT, demonstrating that our method indeed obeys the human prior towards shorter reasoning paths in addition to producing more interpretable attention maps. Our code is available at https://github.com/kakao/DAFT.

Current deep learning models for dynamics forecasting struggle with generalization. They can only forecast in a specific domain and fail when applied to systems with different parameters, external forces, or boundary conditions. We propose a model-based meta-learning method called DyAd which can generalize across heterogeneous domains by partitioning them into different tasks. DyAd has two parts: an encoder which infers the time-invariant hidden features of the task with weak supervision, and a forecaster which learns the shared dynamics of the entire domain. The encoder adapts and controls the forecaster during inference using adaptive instance normalization and adaptive padding. Theoretically, we prove that the generalization error of such procedure is related to the task relatedness in the source domain, as well as the domain differences between source and target. Experimentally, we demonstrate that our model outperforms state-of-the-art approaches on both turbulent flow and real-world ocean data forecasting tasks.

Although much research has been done on proposing new models or loss functions to improve the generalisation of artificial neural networks (ANNs), less attention has been directed to the impact of the training data on generalisation. In this work, we start from approximating the interaction between samples, i.e. how learning one sample would modify the model's prediction on other samples. Through analysing the terms involved in weight updates in supervised learning, we find that labels influence the interaction between samples. Therefore, we propose the labelled pseudo Neural Tangent Kernel (lpNTK) which takes label information into consideration when measuring the interactions between samples. We first prove that lpNTK asymptotically converges to the empirical neural tangent kernel in terms of the Frobenius norm under certain assumptions. Secondly, we illustrate how lpNTK helps to understand learning phenomena identified in previous work, specifically the learning difficulty of samples and forgetting events during learning. Moreover, we also show that using lpNTK to identify and remove poisoning training samples does not hurt the generalisation performance of ANNs.

Many learning algorithms used as normative models in neuroscience or as candidate approaches for learning on neuromorphic chips learn by contrasting one set of network states with another. These Contrastive Learning (CL) algorithms are traditionally implemented with rigid, temporally non-local, and periodic learning dynamics that could limit the range of physical systems capable of harnessing CL. In this study, we build on recent work exploring how CL might be implemented by biological or neurmorphic systems and show that this form of learning can be made temporally local, and can still function even if many of the dynamical requirements of standard training procedures are relaxed. Thanks to a set of general theorems corroborated by numerical experiments across several CL models, our results provide theoretical foundations for the study and development of CL methods for biological and neuromorphic neural networks.

Model-based reinforcement learning (RL) often achieves higher sample efficiency in practice than model-free RL by learning a dynamics model to generate samples for policy learning. Previous works learn a dynamics model that fits under the empirical state-action visitation distribution for all historical policies, i.e., the sample replay buffer. However, in this paper, we observe that fitting the dynamics model under the distribution for all historical policies does not necessarily benefit model prediction for the current policy since the policy in use is constantly evolving over time. The evolving policy during training will cause state-action visitation distribution shifts. We theoretically analyze how this distribution shift over historical policies affects the model learning and model rollouts. We then propose a novel dynamics model learning method, named Policy-adapted Dynamics Model Learning (PDML). PDML dynamically adjusts the historical policy mixture distribution to ensure the learned model can continually adapt to the state-action visitation distribution of the evolving policy. Experiments on a range of continuous control environments in MuJoCo show that PDML achieves significant improvement in sample efficiency and higher asymptotic performance combined with the state-of-the-art model-based RL methods.

Modern generative models demonstrate impressive capabilities, likely stemming from an ability to identify and manipulate abstract concepts underlying their training data. However, fundamental questions remain: what determines the concepts a model learns, the order in which it learns them, and its ability to manipulate those concepts? To address these questions, we propose analyzing a model's learning dynamics via a framework we call the concept space, where each axis represents an independent concept underlying the data generating process. By characterizing learning dynamics in this space, we identify how the speed at which a concept is learned, and hence the order of concept learning, is controlled by properties of the data we term concept signal. Further, we observe moments of sudden turns in the direction of a model's learning dynamics in concept space. Surprisingly, these points precisely correspond to the emergence of hidden capabilities, i.e., where latent interventions show the model possesses the capability to manipulate a concept, but these capabilities cannot yet be elicited via naive input prompting. While our results focus on synthetically defined toy datasets, we hypothesize a general claim on emergence of hidden capabilities may hold: generative models possess latent capabilities that emerge suddenly and consistently during training, though a model might not exhibit these capabilities under naive input prompting.

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.

Aligning large language models (LLMs) with human intentions has become a critical task for safely deploying models in real-world systems. While existing alignment approaches have seen empirical success, theoretically understanding how these methods affect model behavior remains an open question. Our work provides an initial attempt to theoretically analyze the learning dynamics of human preference alignment. We formally show how the distribution of preference datasets influences the rate of model updates and provide rigorous guarantees on the training accuracy. Our theory also reveals an intricate phenomenon where the optimization is prone to prioritizing certain behaviors with higher preference distinguishability. We empirically validate our findings on contemporary LLMs and alignment tasks, reinforcing our theoretical insights and shedding light on considerations for future alignment approaches. Disclaimer: This paper contains potentially offensive text; reader discretion is advised.

Large language models (LLMs) trained on huge corpora of text datasets demonstrate intriguing capabilities, achieving state-of-the-art performance on tasks they were not explicitly trained for. The precise nature of LLM capabilities is often mysterious, and different prompts can elicit different capabilities through in-context learning. We propose a framework that enables us to analyze in-context learning dynamics to understand latent concepts underlying LLMs' behavioral patterns. This provides a more nuanced understanding than success-or-failure evaluation benchmarks, but does not require observing internal activations as a mechanistic interpretation of circuits would. Inspired by the cognitive science of human randomness perception, we use random binary sequences as context and study dynamics of in-context learning by manipulating properties of context data, such as sequence length. In the latest GPT-3.5+ models, we find emergent abilities to generate seemingly random numbers and learn basic formal languages, with striking in-context learning dynamics where model outputs transition sharply from seemingly random behaviors to deterministic repetition.

Effective control and prediction of dynamical systems often require appropriate handling of continuous-time and discrete, event-triggered processes. Stochastic hybrid systems (SHSs), common across engineering domains, provide a formalism for dynamical systems subject to discrete, possibly stochastic, state jumps and multi-modal continuous-time flows. Despite the versatility and importance of SHSs across applications, a general procedure for the explicit learning of both discrete events and multi-mode continuous dynamics remains an open problem. This work introduces Neural Hybrid Automata (NHAs), a recipe for learning SHS dynamics without a priori knowledge on the number of modes and inter-modal transition dynamics. NHAs provide a systematic inference method based on normalizing flows, neural differential equations and self-supervision. We showcase NHAs on several tasks, including mode recovery and flow learning in systems with stochastic transitions, and end-to-end learning of hierarchical robot controllers.

While contrastive approaches of self-supervised learning (SSL) learn representations by minimizing the distance between two augmented views of the same data point (positive pairs) and maximizing views from different data points (negative pairs), recent non-contrastive SSL (e.g., BYOL and SimSiam) show remarkable performance {\it without} negative pairs, with an extra learnable predictor and a stop-gradient operation. A fundamental question arises: why do these methods not collapse into trivial representations? We answer this question via a simple theoretical study and propose a novel approach, DirectPred, that directly sets the linear predictor based on the statistics of its inputs, without gradient training. On ImageNet, it performs comparably with more complex two-layer non-linear predictors that employ BatchNorm and outperforms a linear predictor by 2.5% in 300-epoch training (and 5% in 60-epoch). DirectPred is motivated by our theoretical study of the nonlinear learning dynamics of non-contrastive SSL in simple linear networks. Our study yields conceptual insights into how non-contrastive SSL methods learn, how they avoid representational collapse, and how multiple factors, like predictor networks, stop-gradients, exponential moving averages, and weight decay all come into play. Our simple theory recapitulates the results of real-world ablation studies in both STL-10 and ImageNet. Code is released https://github.com/facebookresearch/luckmatters/tree/master/ssl.

Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep learning by systematically analyzing learning dynamics for the restricted case of deep linear neural networks. Despite the linearity of their input-output map, such networks have nonlinear gradient descent dynamics on weights that change with the addition of each new hidden layer. We show that deep linear networks exhibit nonlinear learning phenomena similar to those seen in simulations of nonlinear networks, including long plateaus followed by rapid transitions to lower error solutions, and faster convergence from greedy unsupervised pretraining initial conditions than from random initial conditions. We provide an analytical description of these phenomena by finding new exact solutions to the nonlinear dynamics of deep learning. Our theoretical analysis also reveals the surprising finding that as the depth of a network approaches infinity, learning speed can nevertheless remain finite: for a special class of initial conditions on the weights, very deep networks incur only a finite, depth independent, delay in learning speed relative to shallow networks. We show that, under certain conditions on the training data, unsupervised pretraining can find this special class of initial conditions, while scaled random Gaussian initializations cannot. We further exhibit a new class of random orthogonal initial conditions on weights that, like unsupervised pre-training, enjoys depth independent learning times. We further show that these initial conditions also lead to faithful propagation of gradients even in deep nonlinear networks, as long as they operate in a special regime known as the edge of chaos.

Activation functions are fundamental elements of deep learning architectures as they significantly influence training dynamics. ReLU, while widely used, is prone to the dying neuron problem, which has been mitigated by variants such as LeakyReLU, PReLU, and ELU that better handle negative neuron outputs. Recently, self-gated activations like GELU and Swish have emerged as state-of-the-art alternatives, leveraging their smoothness to ensure stable gradient flow and prevent neuron inactivity. In this work, we introduce the Gompertz Linear Unit (GoLU), a novel self-gated activation function defined as GoLU(x) = x , Gompertz(x), where Gompertz(x) = e^{-e^{-x}}. The GoLU activation leverages the asymmetry in the Gompertz function to reduce variance in the latent space more effectively compared to GELU and Swish, while preserving robust gradient flow. Extensive experiments across diverse tasks, including Image Classification, Language Modeling, Semantic Segmentation, Object Detection, Instance Segmentation, and Diffusion, highlight GoLU's superior performance relative to state-of-the-art activation functions, establishing GoLU as a robust alternative to existing activation functions.

Data imbalance is a common problem in machine learning that can have a critical effect on the performance of a model. Various solutions exist but their impact on the convergence of the learning dynamics is not understood. Here, we elucidate the significant negative impact of data imbalance on learning, showing that the learning curves for minority and majority classes follow sub-optimal trajectories when training with a gradient-based optimizer. This slowdown is related to the imbalance ratio and can be traced back to a competition between the optimization of different classes. Our main contribution is the analysis of the convergence of full-batch (GD) and stochastic gradient descent (SGD), and of variants that renormalize the contribution of each per-class gradient. We find that GD is not guaranteed to decrease the loss for each class but that this problem can be addressed by performing a per-class normalization of the gradient. With SGD, class imbalance has an additional effect on the direction of the gradients: the minority class suffers from a higher directional noise, which reduces the effectiveness of the per-class gradient normalization. Our findings not only allow us to understand the potential and limitations of strategies involving the per-class gradients, but also the reason for the effectiveness of previously used solutions for class imbalance such as oversampling.

We propose a new technique, Singular Vector Canonical Correlation Analysis (SVCCA), a tool for quickly comparing two representations in a way that is both invariant to affine transform (allowing comparison between different layers and networks) and fast to compute (allowing more comparisons to be calculated than with previous methods). We deploy this tool to measure the intrinsic dimensionality of layers, showing in some cases needless over-parameterization; to probe learning dynamics throughout training, finding that networks converge to final representations from the bottom up; to show where class-specific information in networks is formed; and to suggest new training regimes that simultaneously save computation and overfit less. Code: https://github.com/google/svcca/

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.

Large language models accumulate vast knowledge during pre-training, yet the dynamics governing this acquisition remain poorly understood. This work investigates the learning dynamics of language models on a synthetic factual recall task, uncovering three key findings: First, language models learn in three phases, exhibiting a performance plateau before acquiring precise factual knowledge. Mechanistically, this plateau coincides with the formation of attention-based circuits that support recall. Second, the training data distribution significantly impacts learning dynamics, as imbalanced distributions lead to shorter plateaus. Finally, hallucinations emerge simultaneously with knowledge, and integrating new knowledge into the model through fine-tuning is challenging, as it quickly corrupts its existing parametric memories. Our results emphasize the importance of data distribution in knowledge acquisition and suggest novel data scheduling strategies to accelerate neural network training.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

We study the learning dynamics of self-predictive learning for reinforcement learning, a family of algorithms that learn representations by minimizing the prediction error of their own future latent representations. Despite its recent empirical success, such algorithms have an apparent defect: trivial representations (such as constants) minimize the prediction error, yet it is obviously undesirable to converge to such solutions. Our central insight is that careful designs of the optimization dynamics are critical to learning meaningful representations. We identify that a faster paced optimization of the predictor and semi-gradient updates on the representation, are crucial to preventing the representation collapse. Then in an idealized setup, we show self-predictive learning dynamics carries out spectral decomposition on the state transition matrix, effectively capturing information of the transition dynamics. Building on the theoretical insights, we propose bidirectional self-predictive learning, a novel self-predictive algorithm that learns two representations simultaneously. We examine the robustness of our theoretical insights with a number of small-scale experiments and showcase the promise of the novel representation learning algorithm with large-scale experiments.

Modern machine learning research relies on relatively few carefully curated datasets. Even in these datasets, and typically in `untidy' or raw data, practitioners are faced with significant issues of data quality and diversity which can be prohibitively labor intensive to address. Existing methods for dealing with these challenges tend to make strong assumptions about the particular issues at play, and often require a priori knowledge or metadata such as domain labels. Our work is orthogonal to these methods: we instead focus on providing a unified and efficient framework for Metadata Archaeology -- uncovering and inferring metadata of examples in a dataset. We curate different subsets of data that might exist in a dataset (e.g. mislabeled, atypical, or out-of-distribution examples) using simple transformations, and leverage differences in learning dynamics between these probe suites to infer metadata of interest. Our method is on par with far more sophisticated mitigation methods across different tasks: identifying and correcting mislabeled examples, classifying minority-group samples, prioritizing points relevant for training and enabling scalable human auditing of relevant examples.

The superior performance of modern deep networks usually comes with a costly training procedure. This paper presents a new curriculum learning approach for the efficient training of visual backbones (e.g., vision Transformers). Our work is inspired by the inherent learning dynamics of deep networks: we experimentally show that at an earlier training stage, the model mainly learns to recognize some 'easier-to-learn' discriminative patterns within each example, e.g., the lower-frequency components of images and the original information before data augmentation. Driven by this phenomenon, we propose a curriculum where the model always leverages all the training data at each epoch, while the curriculum starts with only exposing the 'easier-to-learn' patterns of each example, and introduces gradually more difficult patterns. To implement this idea, we 1) introduce a cropping operation in the Fourier spectrum of the inputs, which enables the model to learn from only the lower-frequency components efficiently, 2) demonstrate that exposing the features of original images amounts to adopting weaker data augmentation, and 3) integrate 1) and 2) and design a curriculum learning schedule with a greedy-search algorithm. The resulting approach, EfficientTrain, is simple, general, yet surprisingly effective. As an off-the-shelf method, it reduces the wall-time training cost of a wide variety of popular models (e.g., ResNet, ConvNeXt, DeiT, PVT, Swin, and CSWin) by >1.5x on ImageNet-1K/22K without sacrificing accuracy. It is also effective for self-supervised learning (e.g., MAE). Code is available at https://github.com/LeapLabTHU/EfficientTrain.

In federated learning (FL), weighted aggregation of local models is conducted to generate a global model, and the aggregation weights are normalized (the sum of weights is 1) and proportional to the local data sizes. In this paper, we revisit the weighted aggregation process and gain new insights into the training dynamics of FL. First, we find that the sum of weights can be smaller than 1, causing global weight shrinking effect (analogous to weight decay) and improving generalization. We explore how the optimal shrinking factor is affected by clients' data heterogeneity and local epochs. Second, we dive into the relative aggregation weights among clients to depict the clients' importance. We develop client coherence to study the learning dynamics and find a critical point that exists. Before entering the critical point, more coherent clients play more essential roles in generalization. Based on the above insights, we propose an effective method for Federated Learning with Learnable Aggregation Weights, named as FedLAW. Extensive experiments verify that our method can improve the generalization of the global model by a large margin on different datasets and models.

In this paper, we focus on a typical two-phase phenomenon in the learning of multi-layer perceptrons (MLPs), and we aim to explain the reason for the decrease of feature diversity in the first phase. Specifically, people find that, in the training of MLPs, the training loss does not decrease significantly until the second phase. To this end, we further explore the reason why the diversity of features over different samples keeps decreasing in the first phase, which hurts the optimization of MLPs. We explain such a phenomenon in terms of the learning dynamics of MLPs. Furthermore, we theoretically explain why four typical operations can alleviate the decrease of the feature diversity.

Deep learning in the presence of noisy annotations has been studied extensively in classification, but much less in segmentation tasks. In this work, we study the learning dynamics of deep segmentation networks trained on inaccurately-annotated data. We discover a phenomenon that has been previously reported in the context of classification: the networks tend to first fit the clean pixel-level labels during an "early-learning" phase, before eventually memorizing the false annotations. However, in contrast to classification, memorization in segmentation does not arise simultaneously for all semantic categories. Inspired by these findings, we propose a new method for segmentation from noisy annotations with two key elements. First, we detect the beginning of the memorization phase separately for each category during training. This allows us to adaptively correct the noisy annotations in order to exploit early learning. Second, we incorporate a regularization term that enforces consistency across scales to boost robustness against annotation noise. Our method outperforms standard approaches on a medical-imaging segmentation task where noises are synthesized to mimic human annotation errors. It also provides robustness to realistic noisy annotations present in weakly-supervised semantic segmentation, achieving state-of-the-art results on PASCAL VOC 2012. Code is available at https://github.com/Kangningthu/ADELE

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.

Solving the problem of cooperation is fundamentally important for the creation and maintenance of functional societies. Problems of cooperation are omnipresent within human society, with examples ranging from navigating busy road junctions to negotiating treaties. As the use of AI becomes more pervasive throughout society, the need for socially intelligent agents capable of navigating these complex cooperative dilemmas is becoming increasingly evident. Direct punishment is a ubiquitous social mechanism that has been shown to foster the emergence of cooperation in both humans and non-humans. In the natural world, direct punishment is often strongly coupled with partner selection and reputation and used in conjunction with third-party punishment. The interactions between these mechanisms could potentially enhance the emergence of cooperation within populations. However, no previous work has evaluated the learning dynamics and outcomes emerging from Multi-Agent Reinforcement Learning (MARL) populations that combine these mechanisms. This paper addresses this gap. It presents a comprehensive analysis and evaluation of the behaviors and learning dynamics associated with direct punishment, third-party punishment, partner selection, and reputation. Finally, we discuss the implications of using these mechanisms on the design of cooperative AI systems.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

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.

We propose a new algorithm for fine-tuning large language models using reinforcement learning. Tapered Off-Policy REINFORCE (TOPR) uses an asymmetric, tapered variant of importance sampling to speed up learning while maintaining stable learning dynamics, even without the use of KL regularization. TOPR can be applied in a fully offline fashion, allows the handling of positive and negative examples in a unified framework, and benefits from the implementational simplicity that is typical of Monte Carlo algorithms. We demonstrate the effectiveness of our approach with a series of experiments on the GSM8K and MATH reasoning benchmarks, finding performance gains for training both a model for solution generation and as a generative verifier. We show that properly leveraging positive and negative examples alike in the off-policy regime simultaneously increases test-time accuracy and training data efficiency, all the while avoiding the ``wasted inference'' that comes with discarding negative examples. We find that this advantage persists over multiple iterations of training and can be amplified by dataset curation techniques, enabling us to match 70B-parameter model performance with 8B language models. As a corollary to this work, we find that REINFORCE's baseline parameter plays an important and unexpected role in defining dataset composition in the presence of negative examples, and is consequently critical in driving off-policy performance.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

Reward functions are central in reinforcement learning (RL), guiding agents towards optimal decision-making. The complexity of RL tasks requires meticulously designed reward functions that effectively drive learning while avoiding unintended consequences. Effective reward design aims to provide signals that accelerate the agent's convergence to optimal behavior. Crafting rewards that align with task objectives, foster desired behaviors, and prevent undesirable actions is inherently challenging. This thesis delves into the critical role of reward signals in RL, highlighting their impact on the agent's behavior and learning dynamics and addressing challenges such as delayed, ambiguous, or intricate rewards. In this thesis work, we tackle different aspects of reward shaping. First, we address the problem of designing informative and interpretable reward signals from a teacher's/expert's perspective (teacher-driven). Here, the expert, equipped with the optimal policy and the corresponding value function, designs reward signals that expedite the agent's convergence to optimal behavior. Second, we build on this teacher-driven approach by introducing a novel method for adaptive interpretable reward design. In this scenario, the expert tailors the rewards based on the learner's current policy, ensuring alignment and optimal progression. Third, we propose a meta-learning approach, enabling the agent to self-design its reward signals online without expert input (agent-driven). This self-driven method considers the agent's learning and exploration to establish a self-improving feedback loop.

This paper introduces the sparse modular addition task and examines how transformers learn it. We focus on transformers with embeddings in R^2 and introduce a visual sandbox that provides comprehensive visualizations of each layer throughout the training process. We reveal a type of circuit, called "clustering heads," which learns the problem's invariants. We analyze the training dynamics of these circuits, highlighting two-stage learning, loss spikes due to high curvature or normalization layers, and the effects of initialization and curriculum learning.

Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a `forgetting event' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance.

Pre-training has been a popular learning paradigm in deep learning era, especially in annotation-insufficient scenario. Better ImageNet pre-trained models have been demonstrated, from the perspective of architecture, by previous research to have better transferability to downstream tasks. However, in this paper, we found that during the same pre-training process, models at middle epochs, which is inadequately pre-trained, can outperform fully trained models when used as feature extractors (FE), while the fine-tuning (FT) performance still grows with the source performance. This reveals that there is not a solid positive correlation between top-1 accuracy on ImageNet and the transferring result on target data. Based on the contradictory phenomenon between FE and FT that better feature extractor fails to be fine-tuned better accordingly, we conduct comprehensive analyses on features before softmax layer to provide insightful explanations. Our discoveries suggest that, during pre-training, models tend to first learn spectral components corresponding to large singular values and the residual components contribute more when fine-tuning.

We identify incremental learning dynamics in transformers, where the difference between trained and initial weights progressively increases in rank. We rigorously prove this occurs under the simplifying assumptions of diagonal weight matrices and small initialization. Our experiments support the theory and also show that phenomenon can occur in practice without the simplifying assumptions.

The utility of a learned neural representation depends on how well its geometry supports performance in downstream tasks. This geometry depends on the structure of the inputs, the structure of the target outputs, and the architecture of the network. By studying the learning dynamics of networks with one hidden layer, we discovered that the network's activation function has an unexpectedly strong impact on the representational geometry: Tanh networks tend to learn representations that reflect the structure of the target outputs, while ReLU networks retain more information about the structure of the raw inputs. This difference is consistently observed across a broad class of parameterized tasks in which we modulated the degree of alignment between the geometry of the task inputs and that of the task labels. We analyzed the learning dynamics in weight space and show how the differences between the networks with Tanh and ReLU nonlinearities arise from the asymmetric asymptotic behavior of ReLU, which leads feature neurons to specialize for different regions of input space. By contrast, feature neurons in Tanh networks tend to inherit the task label structure. Consequently, when the target outputs are low dimensional, Tanh networks generate neural representations that are more disentangled than those obtained with a ReLU nonlinearity. Our findings shed light on the interplay between input-output geometry, nonlinearity, and learned representations in neural networks.

Our theoretical understanding of the inner workings of general convolutional neural networks (CNN) is limited. We here present a new stepping stone towards such understanding in the form of a theory of learning in linear CNNs. By analyzing the gradient descent equations, we discover that using convolutions leads to a mismatch between the dataset structure and the network structure. We show that linear CNNs discover the statistical structure of the dataset with non-linear, stage-like transitions, and that the speed of discovery changes depending on this structural mismatch. Moreover, we find that the mismatch lies at the heart of what we call the 'dominant frequency bias', where linear CNNs arrive at these discoveries using only the dominant frequencies of the different structural parts present in the dataset. Our findings can help explain several characteristics of general CNNs, such as their shortcut learning and their tendency to rely on texture instead of shape.

Is the lottery ticket phenomenon an idiosyncrasy of gradient-based training or does it generalize to evolutionary optimization? In this paper we establish the existence of highly sparse trainable initializations for evolution strategies (ES) and characterize qualitative differences compared to gradient descent (GD)-based sparse training. We introduce a novel signal-to-noise iterative pruning procedure, which incorporates loss curvature information into the network pruning step. This can enable the discovery of even sparser trainable network initializations when using black-box evolution as compared to GD-based optimization. Furthermore, we find that these initializations encode an inductive bias, which transfers across different ES, related tasks and even to GD-based training. Finally, we compare the local optima resulting from the different optimization paradigms and sparsity levels. In contrast to GD, ES explore diverse and flat local optima and do not preserve linear mode connectivity across sparsity levels and independent runs. The results highlight qualitative differences between evolution and gradient-based learning dynamics, which can be uncovered by the study of iterative pruning procedures.

Frequency analysis is useful for understanding the mechanisms of representation learning in neural networks (NNs). Most research in this area focuses on the learning dynamics of NNs for regression tasks, while little for classification. This study empirically investigates the latter and expands the understanding of frequency shortcuts. First, we perform experiments on synthetic datasets, designed to have a bias in different frequency bands. Our results demonstrate that NNs tend to find simple solutions for classification, and what they learn first during training depends on the most distinctive frequency characteristics, which can be either low- or high-frequencies. Second, we confirm this phenomenon on natural images. We propose a metric to measure class-wise frequency characteristics and a method to identify frequency shortcuts. The results show that frequency shortcuts can be texture-based or shape-based, depending on what best simplifies the objective. Third, we validate the transferability of frequency shortcuts on out-of-distribution (OOD) test sets. Our results suggest that frequency shortcuts can be transferred across datasets and cannot be fully avoided by larger model capacity and data augmentation. We recommend that future research should focus on effective training schemes mitigating frequency shortcut learning.

Recent progress in large-scale language models has enabled breakthroughs in previously intractable computer programming tasks. Prior work in meta-learning and neural architecture search has led to substantial successes across various task domains, spawning myriad approaches for algorithmically optimizing the design and learning dynamics of deep learning models. At the intersection of these research areas, we implement a code-generating language model with the ability to modify its own source code. Self-programming AI algorithms have been of interest since the dawn of AI itself. Although various theoretical formulations of generalized self-programming AI have been posed, no such system has been successfully implemented to date under real-world computational constraints. Applying AI-based code generation to AI itself, we develop and experimentally validate the first practical implementation of a self-programming AI system. We empirically show that a self-programming AI implemented using a code generation model can successfully modify its own source code to improve performance and program sub-models to perform auxiliary tasks. Our model can self-modify various properties including model architecture, computational capacity, and learning dynamics.

Memory-based meta-learning is a powerful technique to build agents that adapt fast to any task within a target distribution. A previous theoretical study has argued that this remarkable performance is because the meta-training protocol incentivises agents to behave Bayes-optimally. We empirically investigate this claim on a number of prediction and bandit tasks. Inspired by ideas from theoretical computer science, we show that meta-learned and Bayes-optimal agents not only behave alike, but they even share a similar computational structure, in the sense that one agent system can approximately simulate the other. Furthermore, we show that Bayes-optimal agents are fixed points of the meta-learning dynamics. Our results suggest that memory-based meta-learning might serve as a general technique for numerically approximating Bayes-optimal agents - that is, even for task distributions for which we currently don't possess tractable models.

Most existing works focus on direct perturbations to the victim's state/action or the underlying transition dynamics to demonstrate the vulnerability of reinforcement learning agents to adversarial attacks. However, such direct manipulations may not be always realizable. In this paper, we consider a multi-agent setting where a well-trained victim agent nu is exploited by an attacker controlling another agent alpha with an adversarial policy. Previous models do not account for the possibility that the attacker may only have partial control over alpha or that the attack may produce easily detectable "abnormal" behaviors. Furthermore, there is a lack of provably efficient defenses against these adversarial policies. To address these limitations, we introduce a generalized attack framework that has the flexibility to model to what extent the adversary is able to control the agent, and allows the attacker to regulate the state distribution shift and produce stealthier adversarial policies. Moreover, we offer a provably efficient defense with polynomial convergence to the most robust victim policy through adversarial training with timescale separation. This stands in sharp contrast to supervised learning, where adversarial training typically provides only empirical defenses. Using the Robosumo competition experiments, we show that our generalized attack formulation results in much stealthier adversarial policies when maintaining the same winning rate as baselines. Additionally, our adversarial training approach yields stable learning dynamics and less exploitable victim policies.

While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and reasoning tasks -- but mathematical understanding is lagging substantially behind. Recent lines of work have begun studying representational aspects of this question: that is, the size/depth/complexity of attention-based networks to perform certain tasks. However, there is no guarantee the learning dynamics will converge to the constructions proposed. In our paper, we provide fine-grained mechanistic understanding of how transformers learn "semantic structure", understood as capturing co-occurrence structure of words. Precisely, we show, through a combination of experiments on synthetic data modeled by Latent Dirichlet Allocation (LDA), Wikipedia data, and mathematical analysis that the embedding layer and the self-attention layer encode the topical structure. In the former case, this manifests as higher average inner product of embeddings between same-topic words. In the latter, it manifests as higher average pairwise attention between same-topic words. The mathematical results involve several assumptions to make the analysis tractable, which we verify on data, and might be of independent interest as well.

Graph neural networks (GNNs) achieve remarkable performance in graph machine learning tasks but can be hard to train on large-graph data, where their learning dynamics are not well understood. We investigate the training dynamics of large-graph GNNs using graph neural tangent kernels (GNTKs) and graphons. In the limit of large width, optimization of an overparametrized NN is equivalent to kernel regression on the NTK. Here, we investigate how the GNTK evolves as another independent dimension is varied: the graph size. We use graphons to define limit objects -- graphon NNs for GNNs, and graphon NTKs for GNTKs -- , and prove that, on a sequence of graphs, the GNTKs converge to the graphon NTK. We further prove that the spectrum of the GNTK, which is related to the directions of fastest learning which becomes relevant during early stopping, converges to the spectrum of the graphon NTK. This implies that in the large-graph limit, the GNTK fitted on a graph of moderate size can be used to solve the same task on the large graph, and to infer the learning dynamics of the large-graph GNN. These results are verified empirically on node regression and classification tasks.

Although large language models (LLMs) have achieved remarkable performance across various tasks, they remain prone to errors. A key challenge is enabling them to self-correct. While prior research has relied on external tools or large proprietary models, this work explores self-correction in small language models (SLMs) through iterative fine-tuning using solely self-generated data. We introduce the Self-Taught Self-Correction (STaSC) algorithm, which incorporates multiple algorithmic design choices. Experimental results on a question-answering task demonstrate that STaSC effectively learns self-correction, leading to significant performance improvements. Our analysis further provides insights into the mechanisms of self-correction and the impact of different design choices on learning dynamics and overall performance. To support future research, we release our user-friendly codebase and lightweight models.

Diffusion Models have achieved remarkable results in video synthesis but require iterative denoising steps, leading to substantial computational overhead. Consistency Models have made significant progress in accelerating diffusion models. However, directly applying them to video diffusion models often results in severe degradation of temporal consistency and appearance details. In this paper, by analyzing the training dynamics of Consistency Models, we identify a key conflicting learning dynamics during the distillation process: there is a significant discrepancy in the optimization gradients and loss contributions across different timesteps. This discrepancy prevents the distilled student model from achieving an optimal state, leading to compromised temporal consistency and degraded appearance details. To address this issue, we propose a parameter-efficient Dual-Expert Consistency Model~(DCM), where a semantic expert focuses on learning semantic layout and motion, while a detail expert specializes in fine detail refinement. Furthermore, we introduce Temporal Coherence Loss to improve motion consistency for the semantic expert and apply GAN and Feature Matching Loss to enhance the synthesis quality of the detail expert.Our approach achieves state-of-the-art visual quality with significantly reduced sampling steps, demonstrating the effectiveness of expert specialization in video diffusion model distillation. Our code and models are available at https://github.com/Vchitect/DCM{https://github.com/Vchitect/DCM}.

Learning representations that generalize under distribution shifts is critical for building robust machine learning models. However, despite significant efforts in recent years, algorithmic advances in this direction have been limited. In this work, we seek to understand the fundamental difficulty of out-of-distribution generalization with deep neural networks. We first empirically show that perhaps surprisingly, even allowing a neural network to explicitly fit the representations obtained from a teacher network that can generalize out-of-distribution is insufficient for the generalization of the student network. Then, by a theoretical study of two-layer ReLU networks optimized by stochastic gradient descent (SGD) under a structured feature model, we identify a fundamental yet unexplored feature learning proclivity of neural networks, feature contamination: neural networks can learn uncorrelated features together with predictive features, resulting in generalization failure under distribution shifts. Notably, this mechanism essentially differs from the prevailing narrative in the literature that attributes the generalization failure to spurious correlations. Overall, our results offer new insights into the non-linear feature learning dynamics of neural networks and highlight the necessity of considering inductive biases in out-of-distribution generalization.

Intelligent tutoring systems optimize the selection and timing of learning materials to enhance understanding and long-term retention. This requires estimates of both the learner's progress (''knowledge tracing''; KT), and the prerequisite structure of the learning domain (''knowledge mapping''). While recent deep learning models achieve high KT accuracy, they do so at the expense of the interpretability of psychologically-inspired models. In this work, we present a solution to this trade-off. PSI-KT is a hierarchical generative approach that explicitly models how both individual cognitive traits and the prerequisite structure of knowledge influence learning dynamics, thus achieving interpretability by design. Moreover, by using scalable Bayesian inference, PSI-KT targets the real-world need for efficient personalization even with a growing body of learners and learning histories. Evaluated on three datasets from online learning platforms, PSI-KT achieves superior multi-step predictive accuracy and scalable inference in continual-learning settings, all while providing interpretable representations of learner-specific traits and the prerequisite structure of knowledge that causally supports learning. In sum, predictive, scalable and interpretable knowledge tracing with solid knowledge mapping lays a key foundation for effective personalized learning to make education accessible to a broad, global audience.

The success of automated medical image analysis depends on large-scale and expert-annotated training sets. Unsupervised domain adaptation (UDA) has been raised as a promising approach to alleviate the burden of labeled data collection. However, they generally operate under the closed-set adaptation setting assuming an identical label set between the source and target domains, which is over-restrictive in clinical practice where new classes commonly exist across datasets due to taxonomic inconsistency. While several methods have been presented to tackle both domain shifts and incoherent label sets, none of them take into account the common characteristics of the two issues and consider the learning dynamics along network training. In this work, we propose optimization trajectory distillation, a unified approach to address the two technical challenges from a new perspective. It exploits the low-rank nature of gradient space and devises a dual-stream distillation algorithm to regularize the learning dynamics of insufficiently annotated domain and classes with the external guidance obtained from reliable sources. Our approach resolves the issue of inadequate navigation along network optimization, which is the major obstacle in the taxonomy adaptive cross-domain adaptation scenario. We evaluate the proposed method extensively on several tasks towards various endpoints with clinical and open-world significance. The results demonstrate its effectiveness and improvements over previous methods.

In this work, we investigate the implicit regularization induced by teacher-student learning dynamics in self-distillation. To isolate its effect, we describe a simple experiment where we consider teachers at random initialization instead of trained teachers. Surprisingly, when distilling a student into such a random teacher, we observe that the resulting model and its representations already possess very interesting characteristics; (1) we observe a strong improvement of the distilled student over its teacher in terms of probing accuracy. (2) The learned representations are data-dependent and transferable between different tasks but deteriorate strongly if trained on random inputs. (3) The student checkpoint contains sparse subnetworks, so-called lottery tickets, and lies on the border of linear basins in the supervised loss landscape. These observations have interesting consequences for several important areas in machine learning: (1) Self-distillation can work solely based on the implicit regularization present in the gradient dynamics without relying on any dark knowledge, (2) self-supervised learning can learn features even in the absence of data augmentation and (3) training dynamics during the early phase of supervised training do not necessarily require label information. Finally, we shed light on an intriguing local property of the loss landscape: the process of feature learning is strongly amplified if the student is initialized closely to the teacher. These results raise interesting questions about the nature of the landscape that have remained unexplored so far. Code is available at https://github.com/safelix/dinopl.

One of the grand challenges of artificial general intelligence is developing agents capable of conducting scientific research and discovering new knowledge. While frontier models have already been used as aids to human scientists, e.g. for brainstorming ideas, writing code, or prediction tasks, they still conduct only a small part of the scientific process. This paper presents the first comprehensive framework for fully automatic scientific discovery, enabling frontier large language models to perform research independently and communicate their findings. We introduce The AI Scientist, which generates novel research ideas, writes code, executes experiments, visualizes results, describes its findings by writing a full scientific paper, and then runs a simulated review process for evaluation. In principle, this process can be repeated to iteratively develop ideas in an open-ended fashion, acting like the human scientific community. We demonstrate its versatility by applying it to three distinct subfields of machine learning: diffusion modeling, transformer-based language modeling, and learning dynamics. Each idea is implemented and developed into a full paper at a cost of less than $15 per paper. To evaluate the generated papers, we design and validate an automated reviewer, which we show achieves near-human performance in evaluating paper scores. The AI Scientist can produce papers that exceed the acceptance threshold at a top machine learning conference as judged by our automated reviewer. This approach signifies the beginning of a new era in scientific discovery in machine learning: bringing the transformative benefits of AI agents to the entire research process of AI itself, and taking us closer to a world where endless affordable creativity and innovation can be unleashed on the world's most challenging problems. Our code is open-sourced at https://github.com/SakanaAI/AI-Scientist

LayerNorm is a critical component in modern large language models (LLMs) for stabilizing training and ensuring smooth optimization. However, it introduces significant challenges in mechanistic interpretability, outlier feature suppression, faithful signal propagation, and computational and communication complexity of private inference. This work explores desirable activation functions in normalization-free decoder-only LLMs. Contrary to the conventional preference for the GELU in transformer-based models, our empirical findings demonstrate an {\em opposite trend} -- ReLU significantly outperforms GELU in LayerNorm-free models, leading to an {\bf 8.2\%} perplexity improvement. We discover a key issue with GELU, where early layers experience entropic overload, leading to the under-utilization of the representational capacity of attention heads. This highlights that smoother activations like GELU are {\em ill-suited} for LayerNorm-free architectures, whereas ReLU's geometrical properties -- specialization in input space and intra-class selectivity -- lead to improved learning dynamics and better information retention in the absence of LayerNorm. This study offers key insights for optimizing transformer architectures where LayerNorm introduces significant challenges.

The goal of this work is to characterize the representational impact that foveation operations have for machine vision systems, inspired by the foveated human visual system, which has higher acuity at the center of gaze and texture-like encoding in the periphery. To do so, we introduce models consisting of a first-stage fixed image transform followed by a second-stage learnable convolutional neural network, and we varied the first stage component. The primary model has a foveated-textural input stage, which we compare to a model with foveated-blurred input and a model with spatially-uniform blurred input (both matched for perceptual compression), and a final reference model with minimal input-based compression. We find that: 1) the foveated-texture model shows similar scene classification accuracy as the reference model despite its compressed input, with greater i.i.d. generalization than the other models; 2) the foveated-texture model has greater sensitivity to high-spatial frequency information and greater robustness to occlusion, w.r.t the comparison models; 3) both the foveated systems, show a stronger center image-bias relative to the spatially-uniform systems even with a weight sharing constraint. Critically, these results are preserved over different classical CNN architectures throughout their learning dynamics. Altogether, this suggests that foveation with peripheral texture-based computations yields an efficient, distinct, and robust representational format of scene information, and provides symbiotic computational insight into the representational consequences that texture-based peripheral encoding may have for processing in the human visual system, while also potentially inspiring the next generation of computer vision models via spatially-adaptive computation. Code + Data available here: https://github.com/ArturoDeza/EmergentProperties

Mixture of Experts (MoE) models have emerged as a promising paradigm for scaling language models efficiently by activating only a subset of parameters for each input token. In this report, we present dots.llm1, a large-scale MoE model that activates 14B parameters out of a total of 142B parameters, delivering performance on par with state-of-the-art models while reducing training and inference costs. Leveraging our meticulously crafted and efficient data processing pipeline, dots.llm1 achieves performance comparable to Qwen2.5-72B after pretraining on 11.2T high-quality tokens and post-training to fully unlock its capabilities. Notably, no synthetic data is used during pretraining. To foster further research, we open-source intermediate training checkpoints at every one trillion tokens, providing valuable insights into the learning dynamics of large language models.

Increasing the number of parameters in language models is a common strategy to enhance their performance. However, smaller language models remain valuable due to their lower operational costs. Despite their advantages, smaller models frequently underperform compared to their larger counterparts, even when provided with equivalent data and computational resources. Specifically, their performance tends to degrade in the late pretraining phase. This is anecdotally attributed to their reduced representational capacity. Yet, the exact causes of this performance degradation remain unclear. We use the Pythia model suite to analyse the training dynamics that underlie this phenomenon. Across different model sizes, we investigate the convergence of the Attention and MLP activations to their final state and examine how the effective rank of their parameters influences this process. We find that nearly all layers in larger models stabilise early in training - within the first 20% - whereas layers in smaller models exhibit slower and less stable convergence, especially when their parameters have lower effective rank. By linking the convergence of layers' activations to their parameters' effective rank, our analyses can guide future work to address inefficiencies in the learning dynamics of small models.

We create two German-only decoder models, LL\"aMmlein 120M and 1B, transparently from scratch and publish them, along with the training data, for the German NLP research community to use. The model training involved several key steps, including extensive data preprocessing, the creation of a custom German tokenizer, the training itself, as well as the evaluation of the final models on various benchmarks. Throughout the training process, multiple checkpoints were saved and analyzed using the SuperGLEBer benchmark to monitor the models' learning dynamics. Compared to state-of-the-art models on the SuperGLEBer benchmark, both LL\"aMmlein models performed competitively, consistently matching or surpassing models with similar parameter sizes. The results show that the models' quality scales with size as expected, but performance improvements on some tasks plateaued early, offering valuable insights into resource allocation for future model development.

Recent advances in Multimodal Large Language Models (MLLMs) have shown promising results in integrating diverse modalities such as texts and images. MLLMs are heavily influenced by modality bias, often relying on language while under-utilizing other modalities like visual inputs. This position paper argues that MLLMs are deeply affected by modality bias. Firstly, we diagnose the current state of modality bias, highlighting its manifestations across various tasks. Secondly, we propose a systematic research road-map related to modality bias in MLLMs. Thirdly, we identify key factors of modality bias in MLLMs and offer actionable suggestions for future research to mitigate it. To substantiate these findings, we conduct experiments that demonstrate the influence of each factor: 1. Data Characteristics: Language data is compact and abstract, while visual data is redundant and complex, creating an inherent imbalance in learning dynamics. 2. Imbalanced Backbone Capabilities: The dominance of pretrained language models in MLLMs leads to overreliance on language and neglect of visual information. 3. Training Objectives: Current objectives often fail to promote balanced cross-modal alignment, resulting in shortcut learning biased toward language. These findings highlight the need for balanced training strategies and model architectures to better integrate multiple modalities in MLLMs. We call for interdisciplinary efforts to tackle these challenges and drive innovation in MLLM research. Our work provides a fresh perspective on modality bias in MLLMs and offers insights for developing more robust and generalizable multimodal systems-advancing progress toward Artificial General Intelligence.

Large Language Models (LLMs) rely on safety alignment to produce socially acceptable responses. This is typically achieved through instruction tuning and reinforcement learning from human feedback. However, this alignment is known to be brittle: further fine-tuning, even on benign or lightly contaminated data, can degrade safety and reintroduce harmful behaviors. A growing body of work suggests that alignment may correspond to identifiable geometric directions in weight space, forming subspaces that could, in principle, be isolated or preserved to defend against misalignment. In this work, we conduct a comprehensive empirical study of this geometric perspective. We examine whether safety-relevant behavior is concentrated in specific subspaces, whether it can be separated from general-purpose learning, and whether harmfulness arises from distinguishable patterns in internal representations. Across both parameter and activation space, our findings are consistent: subspaces that amplify safe behaviors also amplify unsafe ones, and prompts with different safety implications activate overlapping representations. We find no evidence of a subspace that selectively governs safety. These results challenge the assumption that alignment is geometrically localized. Rather than residing in distinct directions, safety appears to emerge from entangled, high-impact components of the model's broader learning dynamics. This suggests that subspace-based defenses may face fundamental limitations and underscores the need for alternative strategies to preserve alignment under continued training. We corroborate these findings through multiple experiments on five open-source LLMs. Our code is publicly available at: https://github.com/CERT-Lab/safety-subspaces.

Experiments with pre-trained models such as BERT are often based on a single checkpoint. While the conclusions drawn apply to the artifact tested in the experiment (i.e., the particular instance of the model), it is not always clear whether they hold for the more general procedure which includes the architecture, training data, initialization scheme, and loss function. Recent work has shown that repeating the pre-training process can lead to substantially different performance, suggesting that an alternate strategy is needed to make principled statements about procedures. To enable researchers to draw more robust conclusions, we introduce the MultiBERTs, a set of 25 BERT-Base checkpoints, trained with similar hyper-parameters as the original BERT model but differing in random weight initialization and shuffling of training data. We also define the Multi-Bootstrap, a non-parametric bootstrap method for statistical inference designed for settings where there are multiple pre-trained models and limited test data. To illustrate our approach, we present a case study of gender bias in coreference resolution, in which the Multi-Bootstrap lets us measure effects that may not be detected with a single checkpoint. We release our models and statistical library along with an additional set of 140 intermediate checkpoints captured during pre-training to facilitate research on learning dynamics.

This paper proposes a novel problem: vision-based perception to learn and predict the collective dynamics of multi-agent systems, specifically focusing on interaction strength and convergence time. Multi-agent systems are defined as collections of more than ten interacting agents that exhibit complex group behaviors. Unlike prior studies that assume knowledge of agent positions, we focus on deep learning models to directly predict collective dynamics from visual data, captured as frames or events. Due to the lack of relevant datasets, we create a simulated dataset using a state-of-the-art flocking simulator, coupled with a vision-to-event conversion framework. We empirically demonstrate the effectiveness of event-based representation over traditional frame-based methods in predicting these collective behaviors. Based on our analysis, we present event-based vision for Multi-Agent dynamic Prediction (evMAP), a deep learning architecture designed for real-time, accurate understanding of interaction strength and collective behavior emergence in multi-agent systems.

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.

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.

With the rapid advancement of large language models (LLMs) and vision-language models (VLMs), significant progress has been made in developing open-vocabulary robotic manipulation systems. However, many existing approaches overlook the importance of object dynamics, limiting their applicability to more complex, dynamic tasks. In this work, we introduce KUDA, an open-vocabulary manipulation system that integrates dynamics learning and visual prompting through keypoints, leveraging both VLMs and learning-based neural dynamics models. Our key insight is that a keypoint-based target specification is simultaneously interpretable by VLMs and can be efficiently translated into cost functions for model-based planning. Given language instructions and visual observations, KUDA first assigns keypoints to the RGB image and queries the VLM to generate target specifications. These abstract keypoint-based representations are then converted into cost functions, which are optimized using a learned dynamics model to produce robotic trajectories. We evaluate KUDA on a range of manipulation tasks, including free-form language instructions across diverse object categories, multi-object interactions, and deformable or granular objects, demonstrating the effectiveness of our framework. The project page is available at http://kuda-dynamics.github.io.

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections is commonly used by prior studies to enable multi-scale processing, our analysis shows that the need for features to evolve across layers results in temporally misaligned features in skip connections, which limits the model's performance. To address this limitation, we propose SineNet, consisting of multiple sequentially connected U-shaped network blocks, referred to as waves. In SineNet, high-resolution features are evolved progressively through multiple stages, thereby reducing the amount of misalignment within each stage. We furthermore analyze the role of skip connections in enabling both parallel and sequential processing of multi-scale information. Our method is rigorously tested on multiple PDE datasets, including the Navier-Stokes equations and shallow water equations, showcasing the advantages of our proposed approach over conventional U-Nets with a comparable parameter budget. We further demonstrate that increasing the number of waves in SineNet while maintaining the same number of parameters leads to a monotonically improved performance. The results highlight the effectiveness of SineNet and the potential of our approach in advancing the state-of-the-art in neural PDE solver design. Our code is available as part of AIRS (https://github.com/divelab/AIRS).

Active learning (AL) aims to select the most useful data samples from an unlabeled data pool and annotate them to expand the labeled dataset under a limited budget. Especially, uncertainty-based methods choose the most uncertain samples, which are known to be effective in improving model performance. However, AL literature often overlooks training dynamics (TD), defined as the ever-changing model behavior during optimization via stochastic gradient descent, even though other areas of literature have empirically shown that TD provides important clues for measuring the sample uncertainty. In this paper, we propose a novel AL method, Training Dynamics for Active Learning (TiDAL), which leverages the TD to quantify uncertainties of unlabeled data. Since tracking the TD of all the large-scale unlabeled data is impractical, TiDAL utilizes an additional prediction module that learns the TD of labeled data. To further justify the design of TiDAL, we provide theoretical and empirical evidence to argue the usefulness of leveraging TD for AL. Experimental results show that our TiDAL achieves better or comparable performance on both balanced and imbalanced benchmark datasets compared to state-of-the-art AL methods, which estimate data uncertainty using only static information after model training.

We present a neural operator architecture to simulate Lagrangian dynamics, such as fluid flow, granular flows, and elastoplasticity. Traditional numerical methods, such as the finite element method (FEM), suffer from long run times and large memory consumption. On the other hand, approaches based on graph neural networks are faster but still suffer from long computation times on dense graphs, which are often required for high-fidelity simulations. Our model, GIOROM or Graph Interaction Operator for Reduced-Order Modeling, learns temporal dynamics within a reduced-order setting, capturing spatial features from a highly sparse graph representation of the input and generalizing to arbitrary spatial locations during inference. The model is geometry-aware and discretization-agnostic and can generalize to different initial conditions, velocities, and geometries after training. We show that point clouds of the order of 100,000 points can be inferred from sparse graphs with sim1000 points, with negligible change in computation time. We empirically evaluate our model on elastic solids, Newtonian fluids, Non-Newtonian fluids, Drucker-Prager granular flows, and von Mises elastoplasticity. On these benchmarks, our approach results in a 25times speedup compared to other neural network-based physics simulators while delivering high-fidelity predictions of complex physical systems and showing better performance on most benchmarks. The code and the demos are provided at https://github.com/HrishikeshVish/GIOROM.

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.

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they incorrectly assume a flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmospheric dynamics, and demonstrate stable auto\-regressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

This paper introduces a novel human pose estimation approach using sparse inertial sensors, addressing the shortcomings of previous methods reliant on synthetic data. It leverages a diverse array of real inertial motion capture data from different skeleton formats to improve motion diversity and model generalization. This method features two innovative components: a pseudo-velocity regression model for dynamic motion capture with inertial sensors, and a part-based model dividing the body and sensor data into three regions, each focusing on their unique characteristics. The approach demonstrates superior performance over state-of-the-art models across five public datasets, notably reducing pose error by 19\% on the DIP-IMU dataset, thus representing a significant improvement in inertial sensor-based human pose estimation. Our codes are available at {https://github.com/dx118/dynaip}.

Learning complex dynamics driven by partial differential equations directly from data holds great promise for fast and accurate simulations of complex physical systems. In most cases, this problem can be formulated as an operator learning task, where one aims to learn the operator representing the physics of interest, which entails discretization of the continuous system. However, preserving key continuous properties at the discrete level, such as boundary conditions, and addressing physical systems with complex geometries is challenging for most existing approaches. We introduce a family of operator learning architectures, structure-preserving operator networks (SPONs), that allows to preserve key mathematical and physical properties of the continuous system by leveraging finite element (FE) discretizations of the input-output spaces. SPONs are encode-process-decode architectures that are end-to-end differentiable, where the encoder and decoder follows from the discretizations of the input-output spaces. SPONs can operate on complex geometries, enforce certain boundary conditions exactly, and offer theoretical guarantees. Our framework provides a flexible way of devising structure-preserving architectures tailored to specific applications, and offers an explicit trade-off between performance and efficiency, all thanks to the FE discretization of the input-output spaces. Additionally, we introduce a multigrid-inspired SPON architecture that yields improved performance at higher efficiency. Finally, we release a software to automate the design and training of SPON architectures.

Dynamics models learned from visual observations have shown to be effective in various robotic manipulation tasks. One of the key questions for learning such dynamics models is what scene representation to use. Prior works typically assume representation at a fixed dimension or resolution, which may be inefficient for simple tasks and ineffective for more complicated tasks. In this work, we investigate how to learn dynamic and adaptive representations at different levels of abstraction to achieve the optimal trade-off between efficiency and effectiveness. Specifically, we construct dynamic-resolution particle representations of the environment and learn a unified dynamics model using graph neural networks (GNNs) that allows continuous selection of the abstraction level. During test time, the agent can adaptively determine the optimal resolution at each model-predictive control (MPC) step. We evaluate our method in object pile manipulation, a task we commonly encounter in cooking, agriculture, manufacturing, and pharmaceutical applications. Through comprehensive evaluations both in the simulation and the real world, we show that our method achieves significantly better performance than state-of-the-art fixed-resolution baselines at the gathering, sorting, and redistribution of granular object piles made with various instances like coffee beans, almonds, corn, etc.

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.

Ensuring safety is of paramount importance in physical human-robot interaction applications. This requires both adherence to safety constraints defined on the system state, as well as guaranteeing compliant behavior of the robot. If the underlying dynamical system is known exactly, the former can be addressed with the help of control barrier functions. The incorporation of elastic actuators in the robot's mechanical design can address the latter requirement. However, this elasticity can increase the complexity of the resulting system, leading to unmodeled dynamics, such that control barrier functions cannot directly ensure safety. In this paper, we mitigate this issue by learning the unknown dynamics using Gaussian process regression. By employing the model in a feedback linearizing control law, the safety conditions resulting from control barrier functions can be robustified to take into account model errors, while remaining feasible. In order to enforce them on-line, we formulate the derived safety conditions in the form of a second-order cone program. We demonstrate our proposed approach with simulations on a two-degree-of-freedom planar robot with elastic joints.

This paper presents an effective approach for learning novel 4D embodied world models, which predict the dynamic evolution of 3D scenes over time in response to an embodied agent's actions, providing both spatial and temporal consistency. We propose to learn a 4D world model by training on RGB-DN (RGB, Depth, and Normal) videos. This not only surpasses traditional 2D models by incorporating detailed shape, configuration, and temporal changes into their predictions, but also allows us to effectively learn accurate inverse dynamic models for an embodied agent. Specifically, we first extend existing robotic manipulation video datasets with depth and normal information leveraging off-the-shelf models. Next, we fine-tune a video generation model on this annotated dataset, which jointly predicts RGB-DN (RGB, Depth, and Normal) for each frame. We then present an algorithm to directly convert generated RGB, Depth, and Normal videos into a high-quality 4D scene of the world. Our method ensures temporal and spatial coherence in 4D scene predictions from embodied scenarios, enables novel view synthesis for embodied environments, and facilitates policy learning that significantly outperforms those derived from prior video-based world models.

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

Future link prediction is a fundamental challenge in various real-world dynamic systems. To address this, numerous temporal graph neural networks (temporal GNNs) and benchmark datasets have been developed. However, these datasets often feature excessive repeated edges and lack complex sequential dynamics, a key characteristic inherent in many real-world applications such as recommender systems and ``Who-To-Follow'' on social networks. This oversight has led existing methods to inadvertently downplay the importance of learning sequential dynamics, focusing primarily on predicting repeated edges. In this study, we demonstrate that existing methods, such as GraphMixer and DyGFormer, are inherently incapable of learning simple sequential dynamics, such as ``a user who has followed OpenAI and Anthropic is more likely to follow AI at Meta next.'' Motivated by this issue, we introduce the Temporal Graph Benchmark with Sequential Dynamics (TGB-Seq), a new benchmark carefully curated to minimize repeated edges, challenging models to learn sequential dynamics and generalize to unseen edges. TGB-Seq comprises large real-world datasets spanning diverse domains, including e-commerce interactions, movie ratings, business reviews, social networks, citation networks and web link networks. Benchmarking experiments reveal that current methods usually suffer significant performance degradation and incur substantial training costs on TGB-Seq, posing new challenges and opportunities for future research. TGB-Seq datasets, leaderboards, and example codes are available at https://tgb-seq.github.io/.

Extracting informative representations from videos is fundamental for effectively learning various downstream tasks. We present a novel approach for unsupervised learning of meaningful representations from videos, leveraging the concept of image spatial entropy (ISE) that quantifies the per-pixel information in an image. We argue that local entropy of pixel neighborhoods and their temporal evolution create valuable intrinsic supervisory signals for learning prominent features. Building on this idea, we abstract visual features into a concise representation of keypoints that act as dynamic information transmitters, and design a deep learning model that learns, purely unsupervised, spatially and temporally consistent representations directly from video frames. Two original information-theoretic losses, computed from local entropy, guide our model to discover consistent keypoint representations; a loss that maximizes the spatial information covered by the keypoints and a loss that optimizes the keypoints' information transportation over time. We compare our keypoint representation to strong baselines for various downstream tasks, \eg, learning object dynamics. Our empirical results show superior performance for our information-driven keypoints that resolve challenges like attendance to static and dynamic objects or objects abruptly entering and leaving the scene.

Humanoid robots hold the potential for unparalleled versatility in performing human-like, whole-body skills. However, achieving agile and coordinated whole-body motions remains a significant challenge due to the dynamics mismatch between simulation and the real world. Existing approaches, such as system identification (SysID) and domain randomization (DR) methods, often rely on labor-intensive parameter tuning or result in overly conservative policies that sacrifice agility. In this paper, we present ASAP (Aligning Simulation and Real-World Physics), a two-stage framework designed to tackle the dynamics mismatch and enable agile humanoid whole-body skills. In the first stage, we pre-train motion tracking policies in simulation using retargeted human motion data. In the second stage, we deploy the policies in the real world and collect real-world data to train a delta (residual) action model that compensates for the dynamics mismatch. Then, ASAP fine-tunes pre-trained policies with the delta action model integrated into the simulator to align effectively with real-world dynamics. We evaluate ASAP across three transfer scenarios: IsaacGym to IsaacSim, IsaacGym to Genesis, and IsaacGym to the real-world Unitree G1 humanoid robot. Our approach significantly improves agility and whole-body coordination across various dynamic motions, reducing tracking error compared to SysID, DR, and delta dynamics learning baselines. ASAP enables highly agile motions that were previously difficult to achieve, demonstrating the potential of delta action learning in bridging simulation and real-world dynamics. These results suggest a promising sim-to-real direction for developing more expressive and agile humanoids.

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.

Video-language pre-trained models have shown remarkable success in guiding video question-answering (VideoQA) tasks. However, due to the length of video sequences, training large-scale video-based models incurs considerably higher costs than training image-based ones. This motivates us to leverage the knowledge from image-based pretraining, despite the obvious gaps between image and video domains. To bridge these gaps, in this paper, we propose Tem-Adapter, which enables the learning of temporal dynamics and complex semantics by a visual Temporal Aligner and a textual Semantic Aligner. Unlike conventional pretrained knowledge adaptation methods that only concentrate on the downstream task objective, the Temporal Aligner introduces an extra language-guided autoregressive task aimed at facilitating the learning of temporal dependencies, with the objective of predicting future states based on historical clues and language guidance that describes event progression. Besides, to reduce the semantic gap and adapt the textual representation for better event description, we introduce a Semantic Aligner that first designs a template to fuse question and answer pairs as event descriptions and then learns a Transformer decoder with the whole video sequence as guidance for refinement. We evaluate Tem-Adapter and different pre-train transferring methods on two VideoQA benchmarks, and the significant performance improvement demonstrates the effectiveness of our method.

The published MLP-based DRL in finance has difficulties in learning the dynamics of the environment when the action scale increases. If the buying and selling increase to one thousand shares, the MLP agent will not be able to effectively adapt to the environment. To address this, we designed a CNN agent that concatenates the data from the last ninety days of the daily feature vector to create the CNN input matrix. Our extensive experiments demonstrate that the MLP-based agent experiences a loss corresponding to the initial environment setup, while our designed CNN remains stable, effectively learns the environment, and leads to an increase in rewards.

Large language models (LLMs) are shown to possess a wealth of actionable knowledge that can be extracted for robot manipulation in the form of reasoning and planning. Despite the progress, most still rely on pre-defined motion primitives to carry out the physical interactions with the environment, which remains a major bottleneck. In this work, we aim to synthesize robot trajectories, i.e., a dense sequence of 6-DoF end-effector waypoints, for a large variety of manipulation tasks given an open-set of instructions and an open-set of objects. We achieve this by first observing that LLMs excel at inferring affordances and constraints given a free-form language instruction. More importantly, by leveraging their code-writing capabilities, they can interact with a visual-language model (VLM) to compose 3D value maps to ground the knowledge into the observation space of the agent. The composed value maps are then used in a model-based planning framework to zero-shot synthesize closed-loop robot trajectories with robustness to dynamic perturbations. We further demonstrate how the proposed framework can benefit from online experiences by efficiently learning a dynamics model for scenes that involve contact-rich interactions. We present a large-scale study of the proposed method in both simulated and real-robot environments, showcasing the ability to perform a large variety of everyday manipulation tasks specified in free-form natural language. Project website: https://voxposer.github.io

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.

Pretraining RL models on offline video datasets is a promising way to improve their training efficiency in online tasks, but challenging due to the inherent mismatch in tasks, dynamics, and behaviors across domains. A recent model, APV, sidesteps the accompanied action records in offline datasets and instead focuses on pretraining a task-irrelevant, action-free world model within the source domains. We present Vid2Act, a model-based RL method that learns to transfer valuable action-conditioned dynamics and potentially useful action demonstrations from offline to online settings. The main idea is to use the world models not only as simulators for behavior learning but also as tools to measure the domain relevance for both dynamics representation transfer and policy transfer. Specifically, we train the world models to generate a set of time-varying task similarities using a domain-selective knowledge distillation loss. These similarities serve two purposes: (i) adaptively transferring the most useful source knowledge to facilitate dynamics learning, and (ii) learning to replay the most relevant source actions to guide the target policy. We demonstrate the advantages of Vid2Act over the action-free visual RL pretraining method in both Meta-World and DeepMind Control Suite.

Although various image-based domain adaptation (DA) techniques have been proposed in recent years, domain shift in videos is still not well-explored. Most previous works only evaluate performance on small-scale datasets which are saturated. Therefore, we first propose two large-scale video DA datasets with much larger domain discrepancy: UCF-HMDB_full and Kinetics-Gameplay. Second, we investigate different DA integration methods for videos, and show that simultaneously aligning and learning temporal dynamics achieves effective alignment even without sophisticated DA methods. Finally, we propose Temporal Attentive Adversarial Adaptation Network (TA3N), which explicitly attends to the temporal dynamics using domain discrepancy for more effective domain alignment, achieving state-of-the-art performance on four video DA datasets (e.g. 7.9% accuracy gain over "Source only" from 73.9% to 81.8% on "HMDB --> UCF", and 10.3% gain on "Kinetics --> Gameplay"). The code and data are released at http://github.com/cmhungsteve/TA3N.

Although various image-based domain adaptation (DA) techniques have been proposed in recent years, domain shift in videos is still not well-explored. Most previous works only evaluate performance on small-scale datasets which are saturated. Therefore, we first propose a larger-scale dataset with larger domain discrepancy: UCF-HMDB_full. Second, we investigate different DA integration methods for videos, and show that simultaneously aligning and learning temporal dynamics achieves effective alignment even without sophisticated DA methods. Finally, we propose Temporal Attentive Adversarial Adaptation Network (TA3N), which explicitly attends to the temporal dynamics using domain discrepancy for more effective domain alignment, achieving state-of-the-art performance on three video DA datasets. The code and data are released at http://github.com/cmhungsteve/TA3N.

Learning a precise dynamics model can be crucial for offline reinforcement learning, which, unfortunately, has been found to be quite challenging. Dynamics models that are learned by fitting historical transitions often struggle to generalize to unseen transitions. In this study, we identify a hidden but pivotal factor termed dynamics reward that remains consistent across transitions, offering a pathway to better generalization. Therefore, we propose the idea of reward-consistent dynamics models: any trajectory generated by the dynamics model should maximize the dynamics reward derived from the data. We implement this idea as the MOREC (Model-based Offline reinforcement learning with Reward Consistency) method, which can be seamlessly integrated into previous offline model-based reinforcement learning (MBRL) methods. MOREC learns a generalizable dynamics reward function from offline data, which is subsequently employed as a transition filter in any offline MBRL method: when generating transitions, the dynamics model generates a batch of transitions and selects the one with the highest dynamics reward value. On a synthetic task, we visualize that MOREC has a strong generalization ability and can surprisingly recover some distant unseen transitions. On 21 offline tasks in D4RL and NeoRL benchmarks, MOREC improves the previous state-of-the-art performance by a significant margin, i.e., 4.6% on D4RL tasks and 25.9% on NeoRL tasks. Notably, MOREC is the first method that can achieve above 95% online RL performance in 6 out of 12 D4RL tasks and 3 out of 9 NeoRL tasks.

Tactile feedback is critical for understanding the dynamics of both rigid and deformable objects in many manipulation tasks, such as non-prehensile manipulation and dense packing. We introduce an approach that combines visual and tactile sensing for robotic manipulation by learning a neural, tactile-informed dynamics model. Our proposed framework, RoboPack, employs a recurrent graph neural network to estimate object states, including particles and object-level latent physics information, from historical visuo-tactile observations and to perform future state predictions. Our tactile-informed dynamics model, learned from real-world data, can solve downstream robotics tasks with model-predictive control. We demonstrate our approach on a real robot equipped with a compliant Soft-Bubble tactile sensor on non-prehensile manipulation and dense packing tasks, where the robot must infer the physics properties of objects from direct and indirect interactions. Trained on only an average of 30 minutes of real-world interaction data per task, our model can perform online adaptation and make touch-informed predictions. Through extensive evaluations in both long-horizon dynamics prediction and real-world manipulation, our method demonstrates superior effectiveness compared to previous learning-based and physics-based simulation systems.

Molecular dynamics (MD) simulation is a widely used technique to simulate molecular systems, most commonly at the all-atom resolution where equations of motion are integrated with timesteps on the order of femtoseconds (1fs=10^{-15}s). MD is often used to compute equilibrium properties, which requires sampling from an equilibrium distribution such as the Boltzmann distribution. However, many important processes, such as binding and folding, occur over timescales of milliseconds or beyond, and cannot be efficiently sampled with conventional MD. Furthermore, new MD simulations need to be performed for each molecular system studied. We present Timewarp, an enhanced sampling method which uses a normalising flow as a proposal distribution in a Markov chain Monte Carlo method targeting the Boltzmann distribution. The flow is trained offline on MD trajectories and learns to make large steps in time, simulating the molecular dynamics of 10^{5} - 10^{6}:fs. Crucially, Timewarp is transferable between molecular systems: once trained, we show that it generalises to unseen small peptides (2-4 amino acids) at all-atom resolution, exploring their metastable states and providing wall-clock acceleration of sampling compared to standard MD. Our method constitutes an important step towards general, transferable algorithms for accelerating MD.

Existing imitation learning works mainly assume that the demonstrator who collects demonstrations shares the same dynamics as the imitator. However, the assumption limits the usage of imitation learning, especially when collecting demonstrations for the imitator is difficult. In this paper, we study out-of-dynamics imitation learning (OOD-IL), which relaxes the assumption to that the demonstrator and the imitator have the same state spaces but could have different action spaces and dynamics. OOD-IL enables imitation learning to utilize demonstrations from a wide range of demonstrators but introduces a new challenge: some demonstrations cannot be achieved by the imitator due to the different dynamics. Prior works try to filter out such demonstrations by feasibility measurements, but ignore the fact that the demonstrations exhibit a multimodal distribution since the different demonstrators may take different policies in different dynamics. We develop a better transferability measurement to tackle this newly-emerged challenge. We firstly design a novel sequence-based contrastive clustering algorithm to cluster demonstrations from the same mode to avoid the mutual interference of demonstrations from different modes, and then learn the transferability of each demonstration with an adversarial-learning based algorithm in each cluster. Experiment results on several MuJoCo environments, a driving environment, and a simulated robot environment show that the proposed transferability measurement more accurately finds and down-weights non-transferable demonstrations and outperforms prior works on the final imitation learning performance. We show the videos of our experiment results on our website.

We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material models). Without explicit PDE knowledge, these approaches cannot guarantee physical correctness and have limited generalizability. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. Instead, constitutive models are particularly suitable for learning due to their data-fitting nature. To this end, we introduce a new framework termed "Neural Constitutive Laws" (NCLaw), which utilizes a network architecture that strictly guarantees standard constitutive priors, including rotation equivariance and undeformed state equilibrium. We embed this network inside a differentiable simulation and train the model by minimizing a loss function based on the difference between the simulation and the motion observation. We validate NCLaw on various large-deformation dynamical systems, ranging from solids to fluids. After training on a single motion trajectory, our method generalizes to new geometries, initial/boundary conditions, temporal ranges, and even multi-physics systems. On these extremely out-of-distribution generalization tasks, NCLaw is orders-of-magnitude more accurate than previous NN approaches. Real-world experiments demonstrate our method's ability to learn constitutive laws from videos.

We introduce UniReal, a unified framework designed to address various image generation and editing tasks. Existing solutions often vary by tasks, yet share fundamental principles: preserving consistency between inputs and outputs while capturing visual variations. Inspired by recent video generation models that effectively balance consistency and variation across frames, we propose a unifying approach that treats image-level tasks as discontinuous video generation. Specifically, we treat varying numbers of input and output images as frames, enabling seamless support for tasks such as image generation, editing, customization, composition, etc. Although designed for image-level tasks, we leverage videos as a scalable source for universal supervision. UniReal learns world dynamics from large-scale videos, demonstrating advanced capability in handling shadows, reflections, pose variation, and object interaction, while also exhibiting emergent capability for novel applications.

Videos of robots interacting with objects encode rich information about the objects' dynamics. However, existing video prediction approaches typically do not explicitly account for the 3D information from videos, such as robot actions and objects' 3D states, limiting their use in real-world robotic applications. In this work, we introduce a framework to learn object dynamics directly from multi-view RGB videos by explicitly considering the robot's action trajectories and their effects on scene dynamics. We utilize the 3D Gaussian representation of 3D Gaussian Splatting (3DGS) to train a particle-based dynamics model using Graph Neural Networks. This model operates on sparse control particles downsampled from the densely tracked 3D Gaussian reconstructions. By learning the neural dynamics model on offline robot interaction data, our method can predict object motions under varying initial configurations and unseen robot actions. The 3D transformations of Gaussians can be interpolated from the motions of control particles, enabling the rendering of predicted future object states and achieving action-conditioned video prediction. The dynamics model can also be applied to model-based planning frameworks for object manipulation tasks. We conduct experiments on various kinds of deformable materials, including ropes, clothes, and stuffed animals, demonstrating our framework's ability to model complex shapes and dynamics. Our project page is available at https://gs-dynamics.github.io.

Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.

Sequential decision making, commonly formalized as Markov Decision Process (MDP) optimization, is a important challenge in artificial intelligence. Two key approaches to this problem are reinforcement learning (RL) and planning. This paper presents a survey of the integration of both fields, better known as model-based reinforcement learning. Model-based RL has two main steps. First, we systematically cover approaches to dynamics model learning, including challenges like dealing with stochasticity, uncertainty, partial observability, and temporal abstraction. Second, we present a systematic categorization of planning-learning integration, including aspects like: where to start planning, what budgets to allocate to planning and real data collection, how to plan, and how to integrate planning in the learning and acting loop. After these two sections, we also discuss implicit model-based RL as an end-to-end alternative for model learning and planning, and we cover the potential benefits of model-based RL. Along the way, the survey also draws connections to several related RL fields, like hierarchical RL and transfer learning. Altogether, the survey presents a broad conceptual overview of the combination of planning and learning for MDP optimization.

Human beings are endowed with a complementary learning system, which bridges the slow learning of general world dynamics with fast storage of episodic memory from a new experience. Previous video generation models, however, primarily focus on slow learning by pre-training on vast amounts of data, overlooking the fast learning phase crucial for episodic memory storage. This oversight leads to inconsistencies across temporally distant frames when generating longer videos, as these frames fall beyond the model's context window. To this end, we introduce SlowFast-VGen, a novel dual-speed learning system for action-driven long video generation. Our approach incorporates a masked conditional video diffusion model for the slow learning of world dynamics, alongside an inference-time fast learning strategy based on a temporal LoRA module. Specifically, the fast learning process updates its temporal LoRA parameters based on local inputs and outputs, thereby efficiently storing episodic memory in its parameters. We further propose a slow-fast learning loop algorithm that seamlessly integrates the inner fast learning loop into the outer slow learning loop, enabling the recall of prior multi-episode experiences for context-aware skill learning. To facilitate the slow learning of an approximate world model, we collect a large-scale dataset of 200k videos with language action annotations, covering a wide range of scenarios. Extensive experiments show that SlowFast-VGen outperforms baselines across various metrics for action-driven video generation, achieving an FVD score of 514 compared to 782, and maintaining consistency in longer videos, with an average of 0.37 scene cuts versus 0.89. The slow-fast learning loop algorithm significantly enhances performances on long-horizon planning tasks as well. Project Website: https://slowfast-vgen.github.io

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the generalization error and training error dynamics of learning and analyze how they depend on the dimensionality of data and signal to noise ratio of the learning problem. We find that the dynamics of gradient descent learning naturally protect against overtraining and overfitting in large networks. Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger. Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights. We then turn to non-linear neural networks, and show that making networks very large does not harm their generalization performance. On the contrary, it can in fact reduce overtraining, even without early stopping or regularization of any sort. We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations which protect against overtraining. We demonstrate that naive application of worst-case theories such as Rademacher complexity are inaccurate in predicting the generalization performance of deep neural networks, and derive an alternative bound which incorporates the frozen subspace and conditioning effects and qualitatively matches the behavior observed in simulation.

Learning efficient representations for decision-making policies is a challenge in imitation learning (IL). Current IL methods require expert demonstrations, which are expensive to collect. Consequently, they often have underdeveloped world models. Self-supervised learning (SSL) offers an alternative by allowing models to learn from diverse, unlabeled data, including failures. However, SSL methods often operate in raw input space, making them inefficient. In this work, we propose ACT-JEPA, a novel architecture that integrates IL and SSL to enhance policy representations. We train a policy to predict (1) action sequences and (2) abstract observation sequences. The first objective uses action chunking to improve action prediction and reduce compounding errors. The second objective extends this idea of chunking by predicting abstract observation sequences. We utilize Joint-Embedding Predictive Architecture to predict in abstract representation space, allowing the model to filter out irrelevant details, improve efficiency, and develop a robust world model. Our experiments show that ACT-JEPA improves the quality of representations by learning temporal environment dynamics. Additionally, the model's ability to predict abstract observation sequences results in representations that effectively generalize to action sequence prediction. ACT-JEPA performs on par with established baselines across a range of decision-making tasks.

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

We consider the problem of novel view synthesis (NVS) for dynamic scenes. Recent neural approaches have accomplished exceptional NVS results for static 3D scenes, but extensions to 4D time-varying scenes remain non-trivial. Prior efforts often encode dynamics by learning a canonical space plus implicit or explicit deformation fields, which struggle in challenging scenarios like sudden movements or capturing high-fidelity renderings. In this paper, we introduce 4D Gaussian Splatting (4DGS), a novel method that represents dynamic scenes with anisotropic 4D XYZT Gaussians, inspired by the success of 3D Gaussian Splatting in static scenes. We model dynamics at each timestamp by temporally slicing the 4D Gaussians, which naturally compose dynamic 3D Gaussians and can be seamlessly projected into images. As an explicit spatial-temporal representation, 4DGS demonstrates powerful capabilities for modeling complicated dynamics and fine details, especially for scenes with abrupt motions. We further implement our temporal slicing and splatting techniques in a highly optimized CUDA acceleration framework, achieving real-time inference rendering speeds of up to 277 FPS on an RTX 3090 GPU and 583 FPS on an RTX 4090 GPU. Rigorous evaluations on scenes with diverse motions showcase the superior efficiency and effectiveness of 4DGS, which consistently outperforms existing methods both quantitatively and qualitatively.

Data augmentation is essential to achieve state-of-the-art performance in many deep learning applications. However, the most effective augmentation techniques become computationally prohibitive for even medium-sized datasets. To address this, we propose a rigorous technique to select subsets of data points that when augmented, closely capture the training dynamics of full data augmentation. We first show that data augmentation, modeled as additive perturbations, improves learning and generalization by relatively enlarging and perturbing the smaller singular values of the network Jacobian, while preserving its prominent directions. This prevents overfitting and enhances learning the harder to learn information. Then, we propose a framework to iteratively extract small subsets of training data that when augmented, closely capture the alignment of the fully augmented Jacobian with labels/residuals. We prove that stochastic gradient descent applied to the augmented subsets found by our approach has similar training dynamics to that of fully augmented data. Our experiments demonstrate that our method achieves 6.3x speedup on CIFAR10 and 2.2x speedup on SVHN, and outperforms the baselines by up to 10% across various subset sizes. Similarly, on TinyImageNet and ImageNet, our method beats the baselines by up to 8%, while achieving up to 3.3x speedup across various subset sizes. Finally, training on and augmenting 50% subsets using our method on a version of CIFAR10 corrupted with label noise even outperforms using the full dataset. Our code is available at: https://github.com/tianyu139/data-efficient-augmentation

We propose to train a subject-driven customized video generation model through decoupling the subject-specific learning from temporal dynamics in zero-shot without additional tuning. A traditional method for video customization that is tuning-free often relies on large, annotated video datasets, which are computationally expensive and require extensive annotation. In contrast to the previous approach, we introduce the use of an image customization dataset directly on training video customization models, factorizing the video customization into two folds: (1) identity injection through image customization dataset and (2) temporal modeling preservation with a small set of unannotated videos through the image-to-video training method. Additionally, we employ random image token dropping with randomized image initialization during image-to-video fine-tuning to mitigate the copy-and-paste issue. To further enhance learning, we introduce stochastic switching during joint optimization of subject-specific and temporal features, mitigating catastrophic forgetting. Our method achieves strong subject consistency and scalability, outperforming existing video customization models in zero-shot settings, demonstrating the effectiveness of our framework.

To achieve seamless collaboration between robots and humans in a shared environment, accurately predicting future human movements is essential. Human motion prediction has traditionally been approached as a sequence prediction problem, leveraging historical human motion data to estimate future poses. Beginning with vanilla recurrent networks, the research community has investigated a variety of methods for learning human motion dynamics, encompassing graph-based and generative approaches. Despite these efforts, achieving accurate long-term predictions continues to be a significant challenge. In this regard, we present the Adversarial Motion Transformer (AdvMT), a novel model that integrates a transformer-based motion encoder and a temporal continuity discriminator. This combination effectively captures spatial and temporal dependencies simultaneously within frames. With adversarial training, our method effectively reduces the unwanted artifacts in predictions, thereby ensuring the learning of more realistic and fluid human motions. The evaluation results indicate that AdvMT greatly enhances the accuracy of long-term predictions while also delivering robust short-term predictions

In this paper, we present VideoGen, a text-to-video generation approach, which can generate a high-definition video with high frame fidelity and strong temporal consistency using reference-guided latent diffusion. We leverage an off-the-shelf text-to-image generation model, e.g., Stable Diffusion, to generate an image with high content quality from the text prompt, as a reference image to guide video generation. Then, we introduce an efficient cascaded latent diffusion module conditioned on both the reference image and the text prompt, for generating latent video representations, followed by a flow-based temporal upsampling step to improve the temporal resolution. Finally, we map latent video representations into a high-definition video through an enhanced video decoder. During training, we use the first frame of a ground-truth video as the reference image for training the cascaded latent diffusion module. The main characterises of our approach include: the reference image generated by the text-to-image model improves the visual fidelity; using it as the condition makes the diffusion model focus more on learning the video dynamics; and the video decoder is trained over unlabeled video data, thus benefiting from high-quality easily-available videos. VideoGen sets a new state-of-the-art in text-to-video generation in terms of both qualitative and quantitative evaluation.

Relational video customization refers to the creation of personalized videos that depict user-specified relations between two subjects, a crucial task for comprehending real-world visual content. While existing methods can personalize subject appearances and motions, they still struggle with complex relational video customization, where precise relational modeling and high generalization across subject categories are essential. The primary challenge arises from the intricate spatial arrangements, layout variations, and nuanced temporal dynamics inherent in relations; consequently, current models tend to overemphasize irrelevant visual details rather than capturing meaningful interactions. To address these challenges, we propose DreamRelation, a novel approach that personalizes relations through a small set of exemplar videos, leveraging two key components: Relational Decoupling Learning and Relational Dynamics Enhancement. First, in Relational Decoupling Learning, we disentangle relations from subject appearances using relation LoRA triplet and hybrid mask training strategy, ensuring better generalization across diverse relationships. Furthermore, we determine the optimal design of relation LoRA triplet by analyzing the distinct roles of the query, key, and value features within MM-DiT's attention mechanism, making DreamRelation the first relational video generation framework with explainable components. Second, in Relational Dynamics Enhancement, we introduce space-time relational contrastive loss, which prioritizes relational dynamics while minimizing the reliance on detailed subject appearances. Extensive experiments demonstrate that DreamRelation outperforms state-of-the-art methods in relational video customization. Code and models will be made publicly available.

We present MicroCinema, a straightforward yet effective framework for high-quality and coherent text-to-video generation. Unlike existing approaches that align text prompts with video directly, MicroCinema introduces a Divide-and-Conquer strategy which divides the text-to-video into a two-stage process: text-to-image generation and image\&text-to-video generation. This strategy offers two significant advantages. a) It allows us to take full advantage of the recent advances in text-to-image models, such as Stable Diffusion, Midjourney, and DALLE, to generate photorealistic and highly detailed images. b) Leveraging the generated image, the model can allocate less focus to fine-grained appearance details, prioritizing the efficient learning of motion dynamics. To implement this strategy effectively, we introduce two core designs. First, we propose the Appearance Injection Network, enhancing the preservation of the appearance of the given image. Second, we introduce the Appearance Noise Prior, a novel mechanism aimed at maintaining the capabilities of pre-trained 2D diffusion models. These design elements empower MicroCinema to generate high-quality videos with precise motion, guided by the provided text prompts. Extensive experiments demonstrate the superiority of the proposed framework. Concretely, MicroCinema achieves SOTA zero-shot FVD of 342.86 on UCF-101 and 377.40 on MSR-VTT. See https://wangyanhui666.github.io/MicroCinema.github.io/ for video samples.

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.

We propose Heterogeneous Masked Autoregression (HMA) for modeling action-video dynamics to generate high-quality data and evaluation in scaling robot learning. Building interactive video world models and policies for robotics is difficult due to the challenge of handling diverse settings while maintaining computational efficiency to run in real time. HMA uses heterogeneous pre-training from observations and action sequences across different robotic embodiments, domains, and tasks. HMA uses masked autoregression to generate quantized or soft tokens for video predictions. \ourshort achieves better visual fidelity and controllability than the previous robotic video generation models with 15 times faster speed in the real world. After post-training, this model can be used as a video simulator from low-level action inputs for evaluating policies and generating synthetic data. See this link https://liruiw.github.io/hma for more information.

Learning effective reinforcement learning (RL) policies to solve real-world complex tasks can be quite challenging without a high-fidelity simulation environment. In most cases, we are only given imperfect simulators with simplified dynamics, which inevitably lead to severe sim-to-real gaps in RL policy learning. The recently emerged field of offline RL provides another possibility to learn policies directly from pre-collected historical data. However, to achieve reasonable performance, existing offline RL algorithms need impractically large offline data with sufficient state-action space coverage for training. This brings up a new question: is it possible to combine learning from limited real data in offline RL and unrestricted exploration through imperfect simulators in online RL to address the drawbacks of both approaches? In this study, we propose the Dynamics-Aware Hybrid Offline-and-Online Reinforcement Learning (H2O) framework to provide an affirmative answer to this question. H2O introduces a dynamics-aware policy evaluation scheme, which adaptively penalizes the Q function learning on simulated state-action pairs with large dynamics gaps, while also simultaneously allowing learning from a fixed real-world dataset. Through extensive simulation and real-world tasks, as well as theoretical analysis, we demonstrate the superior performance of H2O against other cross-domain online and offline RL algorithms. H2O provides a brand new hybrid offline-and-online RL paradigm, which can potentially shed light on future RL algorithm design for solving practical real-world tasks.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

Dynamic 3D interaction has been attracting a lot of attention recently. However, creating such 4D content remains challenging. One solution is to animate 3D scenes with physics-based simulation, which requires manually assigning precise physical properties to the object or the simulated results would become unnatural. Another solution is to learn the deformation of 3D objects with the distillation of video generative models, which, however, tends to produce 3D videos with small and discontinuous motions due to the inappropriate extraction and application of physics priors. In this work, to combine the strengths and complementing shortcomings of the above two solutions, we propose to learn the physical properties of a material field with video diffusion priors, and then utilize a physics-based Material-Point-Method (MPM) simulator to generate 4D content with realistic motions. In particular, we propose motion distillation sampling to emphasize video motion information during distillation. In addition, to facilitate the optimization, we further propose a KAN-based material field with frame boosting. Experimental results demonstrate that our method enjoys more realistic motions than state-of-the-arts do.

Recently, data augmentation (DA) has emerged as a method for leveraging domain knowledge to inexpensively generate additional data in reinforcement learning (RL) tasks, often yielding substantial improvements in data efficiency. While prior work has demonstrated the utility of incorporating augmented data directly into model-free RL updates, it is not well-understood when a particular DA strategy will improve data efficiency. In this paper, we seek to identify general aspects of DA responsible for observed learning improvements. Our study focuses on sparse-reward tasks with dynamics-invariant data augmentation functions, serving as an initial step towards a more general understanding of DA and its integration into RL training. Experimentally, we isolate three relevant aspects of DA: state-action coverage, reward density, and the number of augmented transitions generated per update (the augmented replay ratio). From our experiments, we draw two conclusions: (1) increasing state-action coverage often has a much greater impact on data efficiency than increasing reward density, and (2) decreasing the augmented replay ratio substantially improves data efficiency. In fact, certain tasks in our empirical study are solvable only when the replay ratio is sufficiently low.

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.

Sim-to-real transfer remains a significant challenge in robotics due to the discrepancies between simulated and real-world dynamics. Traditional methods like Domain Randomization often fail to capture fine-grained dynamics, limiting their effectiveness for precise control tasks. In this work, we propose a novel approach that dynamically adjusts simulation environment parameters online using in-context learning. By leveraging past interaction histories as context, our method adapts the simulation environment dynamics to real-world dynamics without requiring gradient updates, resulting in faster and more accurate alignment between simulated and real-world performance. We validate our approach across two tasks: object scooping and table air hockey. In the sim-to-sim evaluations, our method significantly outperforms the baselines on environment parameter estimation by 80% and 42% in the object scooping and table air hockey setups, respectively. Furthermore, our method achieves at least 70% success rate in sim-to-real transfer on object scooping across three different objects. By incorporating historical interaction data, our approach delivers efficient and smooth system identification, advancing the deployment of robots in dynamic real-world scenarios. Demos are available on our project page: https://sim2real-capture.github.io/

The emergence of in-context learning (ICL) is potentially attributed to two major abilities: task recognition (TR) for recognizing the task from demonstrations and utilizing pre-trained priors, and task learning (TL) for learning from demonstrations. However, relationships between the two abilities and how such relationships affect the emergence of ICL is unclear. In this paper, we take the first step by examining the pre-training dynamics of the emergence of ICL. With carefully designed metrics, we find that these two abilities are, in fact, competitive during pre-training. Moreover, we observe a strong negative correlation between the competition and ICL performance. Further analysis of common pre-training factors (i.e., model size, dataset size, and data curriculum) demonstrates possible ways to manage the competition. Based on these insights, we propose a simple yet effective method to better integrate these two abilities for ICL at inference time. Through adaptive ensemble learning, the performance of ICL can be significantly boosted, enabling two small models to outperform a larger one with more than twice the parameters. The code is available at https://github.com/RUCAIBox/Competitive-ICL.

Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

Generating images with a Text-to-Image model often requires multiple trials, where human users iteratively update their prompt based on feedback, namely the output image. Taking inspiration from cognitive work on reference games and dialogue alignment, this paper analyzes the dynamics of the user prompts along such iterations. We compile a dataset of iterative interactions of human users with Midjourney. Our analysis then reveals that prompts predictably converge toward specific traits along these iterations. We further study whether this convergence is due to human users, realizing they missed important details, or due to adaptation to the model's ``preferences'', producing better images for a specific language style. We show initial evidence that both possibilities are at play. The possibility that users adapt to the model's preference raises concerns about reusing user data for further training. The prompts may be biased towards the preferences of a specific model, rather than align with human intentions and natural manner of expression.

TD-learning is a foundation reinforcement learning (RL) algorithm for value prediction. Critical to the accuracy of value predictions is the quality of state representations. In this work, we consider the question: how does end-to-end TD-learning impact the representation over time? Complementary to prior work, we provide a set of analysis that sheds further light on the representation dynamics under TD-learning. We first show that when the environments are reversible, end-to-end TD-learning strictly decreases the value approximation error over time. Under further assumptions on the environments, we can connect the representation dynamics with spectral decomposition over the transition matrix. This latter finding establishes fitting multiple value functions from randomly generated rewards as a useful auxiliary task for representation learning, as we empirically validate on both tabular and Atari game suites.

We present an unsupervised representation learning approach that compactly encodes the motion dependencies in videos. Given a pair of images from a video clip, our framework learns to predict the long-term 3D motions. To reduce the complexity of the learning framework, we propose to describe the motion as a sequence of atomic 3D flows computed with RGB-D modality. We use a Recurrent Neural Network based Encoder-Decoder framework to predict these sequences of flows. We argue that in order for the decoder to reconstruct these sequences, the encoder must learn a robust video representation that captures long-term motion dependencies and spatial-temporal relations. We demonstrate the effectiveness of our learned temporal representations on activity classification across multiple modalities and datasets such as NTU RGB+D and MSR Daily Activity 3D. Our framework is generic to any input modality, i.e., RGB, Depth, and RGB-D videos.

In recent years, domains such as natural language processing and image recognition have popularized the paradigm of using large datasets to pretrain representations that can be effectively transferred to downstream tasks. In this work we evaluate how such a paradigm should be done in imitation learning, where both pretraining and finetuning data are trajectories collected by experts interacting with an unknown environment. Namely, we consider a setting where the pretraining corpus consists of multitask demonstrations and the task for each demonstration is set by an unobserved latent context variable. The goal is to use the pretraining corpus to learn a low dimensional representation of the high dimensional (e.g., visual) observation space which can be transferred to a novel context for finetuning on a limited dataset of demonstrations. Among a variety of possible pretraining objectives, we argue that inverse dynamics modeling -- i.e., predicting an action given the observations appearing before and after it in the demonstration -- is well-suited to this setting. We provide empirical evidence of this claim through evaluations on a variety of simulated visuomotor manipulation problems. While previous work has attempted various theoretical explanations regarding the benefit of inverse dynamics modeling, we find that these arguments are insufficient to explain the empirical advantages often observed in our settings, and so we derive a novel analysis using a simple but general environment model.

With the global refugee crisis at a historic high, there is a growing need to assess the impact of refugee settlements on their hosting countries and surrounding environments. Because fires are an important land management practice in smallholder agriculture in sub-Saharan Africa, burned area (BA) mappings can help provide information about the impacts of land management practices on local environments. However, a lack of BA ground-truth data in much of sub-Saharan Africa limits the use of highly scalable deep learning (DL) techniques for such BA mappings. In this work, we propose a scalable transfer learning approach to study BA dynamics in areas with little to no ground-truth data such as the West Nile region in Northern Uganda. We train a deep learning model on BA ground-truth data in Portugal and propose the application of that model on refugee-hosting districts in West Nile between 2015 and 2020. By comparing the district-level BA dynamic with the wider West Nile region, we aim to add understanding of the land management impacts of refugee settlements on their surrounding environments.

Visual environments are structured, consisting of distinct objects or entities. These entities have properties -- both visible and latent -- that determine the manner in which they interact with one another. To partition images into entities, deep-learning researchers have proposed structural inductive biases such as slot-based architectures. To model interactions among entities, equivariant graph neural nets (GNNs) are used, but these are not particularly well suited to the task for two reasons. First, GNNs do not predispose interactions to be sparse, as relationships among independent entities are likely to be. Second, GNNs do not factorize knowledge about interactions in an entity-conditional manner. As an alternative, we take inspiration from cognitive science and resurrect a classic approach, production systems, which consist of a set of rule templates that are applied by binding placeholder variables in the rules to specific entities. Rules are scored on their match to entities, and the best fitting rules are applied to update entity properties. In a series of experiments, we demonstrate that this architecture achieves a flexible, dynamic flow of control and serves to factorize entity-specific and rule-based information. This disentangling of knowledge achieves robust future-state prediction in rich visual environments, outperforming state-of-the-art methods using GNNs, and allows for the extrapolation from simple (few object) environments to more complex environments.

In recent years, applying deep learning to solve physics problems has attracted much attention. Data-driven deep learning methods produce fast numerical operators that can learn approximate solutions to the whole system of partial differential equations (i.e., surrogate modeling). Although these neural networks may have lower accuracy than traditional numerical methods, they, once trained, are orders of magnitude faster at inference. Hence, one crucial feature is that these operators can generalize to unseen PDE parameters without expensive re-training.In this paper, we construct CFDBench, a benchmark tailored for evaluating the generalization ability of neural operators after training in computational fluid dynamics (CFD) problems. It features four classic CFD problems: lid-driven cavity flow, laminar boundary layer flow in circular tubes, dam flows through the steps, and periodic Karman vortex street. The data contains a total of 302K frames of velocity and pressure fields, involving 739 cases with different operating condition parameters, generated with numerical methods. We evaluate the effectiveness of popular neural operators including feed-forward networks, DeepONet, FNO, U-Net, etc. on CFDBnech by predicting flows with non-periodic boundary conditions, fluid properties, and flow domain shapes that are not seen during training. Appropriate modifications were made to apply popular deep neural networks to CFDBench and enable the accommodation of more changing inputs. Empirical results on CFDBench show many baseline models have errors as high as 300% in some problems, and severe error accumulation when performing autoregressive inference. CFDBench facilitates a more comprehensive comparison between different neural operators for CFD compared to existing benchmarks.

Large language models (LLMs) have recently gained much attention in building autonomous agents. However, the performance of current LLM-based web agents in long-horizon tasks is far from optimal, often yielding errors such as repeatedly buying a non-refundable flight ticket. By contrast, humans can avoid such an irreversible mistake, as we have an awareness of the potential outcomes (e.g., losing money) of our actions, also known as the "world model". Motivated by this, our study first starts with preliminary analyses, confirming the absence of world models in current LLMs (e.g., GPT-4o, Claude-3.5-Sonnet, etc.). Then, we present a World-model-augmented (WMA) web agent, which simulates the outcomes of its actions for better decision-making. To overcome the challenges in training LLMs as world models predicting next observations, such as repeated elements across observations and long HTML inputs, we propose a transition-focused observation abstraction, where the prediction objectives are free-form natural language descriptions exclusively highlighting important state differences between time steps. Experiments on WebArena and Mind2Web show that our world models improve agents' policy selection without training and demonstrate our agents' cost- and time-efficiency compared to recent tree-search-based agents.

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and the Navier-Stokes equations with incompressible and compressible flow, regular and complex geometries, and different buoyancy settings. This work presents a new transformer-based multi-operator learning approach that fuses symbolic information to perform operator-based data prediction, i.e. non-autoregressive. By incorporating multiple modalities in the inputs, the PDE foundation model builds in a pathway for including mathematical descriptions of the physical behavior. We pre-train our foundation model on 6 parametric families of equations collected from 13 datasets, including over 60K trajectories. Our model outperforms popular operator learning, computer vision, and multi-physics models, in benchmark forward prediction tasks. We test our architecture choices with ablation studies.

We present DrivAerNet++, the largest and most comprehensive multimodal dataset for aerodynamic car design. DrivAerNet++ comprises 8,000 diverse car designs modeled with high-fidelity computational fluid dynamics (CFD) simulations. The dataset includes diverse car configurations such as fastback, notchback, and estateback, with different underbody and wheel designs to represent both internal combustion engines and electric vehicles. Each entry in the dataset features detailed 3D meshes, parametric models, aerodynamic coefficients, and extensive flow and surface field data, along with segmented parts for car classification and point cloud data. This dataset supports a wide array of machine learning applications including data-driven design optimization, generative modeling, surrogate model training, CFD simulation acceleration, and geometric classification. With more than 39 TB of publicly available engineering data, DrivAerNet++ fills a significant gap in available resources, providing high-quality, diverse data to enhance model training, promote generalization, and accelerate automotive design processes. Along with rigorous dataset validation, we also provide ML benchmarking results on the task of aerodynamic drag prediction, showcasing the breadth of applications supported by our dataset. This dataset is set to significantly impact automotive design and broader engineering disciplines by fostering innovation and improving the fidelity of aerodynamic evaluations.

We investigate the use of transformer sequence models as dynamics models (TDMs) for control. In a number of experiments in the DeepMind control suite, we find that first, TDMs perform well in a single-environment learning setting when compared to baseline models. Second, TDMs exhibit strong generalization capabilities to unseen environments, both in a few-shot setting, where a generalist model is fine-tuned with small amounts of data from the target environment, and in a zero-shot setting, where a generalist model is applied to an unseen environment without any further training. We further demonstrate that generalizing system dynamics can work much better than generalizing optimal behavior directly as a policy. This makes TDMs a promising ingredient for a foundation model of control.

Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many existing approaches do not explicitly model the dynamics. To bridge this gap, we introduce DeepEDM, a framework that integrates nonlinear dynamical systems modeling with deep neural networks. Inspired by empirical dynamic modeling (EDM) and rooted in Takens' theorem, DeepEDM presents a novel deep model that learns a latent space from time-delayed embeddings, and employs kernel regression to approximate the underlying dynamics, while leveraging efficient implementation of softmax attention and allowing for accurate prediction of future time steps. To evaluate our method, we conduct comprehensive experiments on synthetic data of nonlinear dynamical systems as well as real-world time series across domains. Our results show that DeepEDM is robust to input noise, and outperforms state-of-the-art methods in forecasting accuracy. Our code is available at: https://abrarmajeedi.github.io/deep_edm.

Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a simple teacher-student setup with Gaussian inputs. In this setting, the full training dynamics is derived in terms of the training and generalization data covariance matrix. We present exact predictions on how the grokking time depends on input and output dimensionality, train sample size, regularization, and network initialization. We demonstrate that the sharp increase in generalization accuracy may not imply a transition from "memorization" to "understanding", but can simply be an artifact of the accuracy measure. We provide empirical verification for our calculations, along with preliminary results indicating that some predictions also hold for deeper networks, with non-linear activations.

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.

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.

Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in learning methods. Koopman operators have emerged as a dominant approach because they allow the study of nonlinear dynamics using linear techniques by solving an infinite-dimensional spectral problem. However, current algorithms face challenges such as lack of convergence, hindering practical progress. This paper addresses a fundamental open question: When can we robustly learn the spectral properties of Koopman operators from trajectory data of dynamical systems, and when can we not? Understanding these boundaries is crucial for analysis, applications, and designing algorithms. We establish a foundational approach that combines computational analysis and ergodic theory, revealing the first fundamental barriers -- universal for any algorithm -- associated with system geometry and complexity, regardless of data quality and quantity. For instance, we demonstrate well-behaved smooth dynamical systems on tori where non-trivial eigenfunctions of the Koopman operator cannot be determined by any sequence of (even randomized) algorithms, even with unlimited training data. Additionally, we identify when learning is possible and introduce optimal algorithms with verification that overcome issues in standard methods. These results pave the way for a sharp classification theory of data-driven dynamical systems based on how many limits are needed to solve a problem. These limits characterize all previous methods, presenting a unified view. Our framework systematically determines when and how Koopman spectral properties can be learned.

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.

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.

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging. Inaccuracies in model estimates can compound, resulting in increased errors over long horizons. We approach this problem from the lens of Koopman theory, where the nonlinear dynamics of the environment can be linearized in a high-dimensional latent space. This allows us to efficiently parallelize the sequential problem of long-range prediction using convolution while accounting for the agent's action at every time step. Our approach also enables stability analysis and better control over gradients through time. Taken together, these advantages result in significant improvement over the existing approaches, both in the efficiency and the accuracy of modeling dynamics over extended horizons. We also show that this model can be easily incorporated into dynamics modeling for model-based planning and model-free RL and report promising experimental results.

Pretraining on noisy, internet-scale datasets has been heavily studied as a technique for training models with broad, general capabilities for text, images, and other modalities. However, for many sequential decision domains such as robotics, video games, and computer use, publicly available data does not contain the labels required to train behavioral priors in the same way. We extend the internet-scale pretraining paradigm to sequential decision domains through semi-supervised imitation learning wherein agents learn to act by watching online unlabeled videos. Specifically, we show that with a small amount of labeled data we can train an inverse dynamics model accurate enough to label a huge unlabeled source of online data -- here, online videos of people playing Minecraft -- from which we can then train a general behavioral prior. Despite using the native human interface (mouse and keyboard at 20Hz), we show that this behavioral prior has nontrivial zero-shot capabilities and that it can be fine-tuned, with both imitation learning and reinforcement learning, to hard-exploration tasks that are impossible to learn from scratch via reinforcement learning. For many tasks our models exhibit human-level performance, and we are the first to report computer agents that can craft diamond tools, which can take proficient humans upwards of 20 minutes (24,000 environment actions) of gameplay to accomplish.

Data-driven learning is rapidly evolving and places a new perspective on realizing state-space dynamical systems. However, dynamical systems derived from nonlinear ordinary differential equations (ODEs) suffer from limitations in computational efficiency. Thus, this paper stems from data-driven learning to advance states of dynamical systems utilizing a structured neural network (StNN). The proposed learning technique also seeks to identify an optimal, low-complexity operator to solve dynamical systems, the so-called Hankel operator, derived from time-delay measurements. Thus, we utilize the StNN based on the Hankel operator to solve dynamical systems as an alternative to existing data-driven techniques. We show that the proposed StNN reduces the number of parameters and computational complexity compared with the conventional neural networks and also with the classical data-driven techniques, such as Sparse Identification of Nonlinear Dynamics (SINDy) and Hankel Alternative view of Koopman (HAVOK), which is commonly known as delay-Dynamic Mode Decomposition(DMD) or Hankel-DMD. More specifically, we present numerical simulations to solve dynamical systems utilizing the StNN based on the Hankel operator beginning from the fundamental Lotka-Volterra model, where we compare the StNN with the LEarning Across Dynamical Systems (LEADS), and extend our analysis to highly nonlinear and chaotic Lorenz systems, comparing the StNN with conventional neural networks, SINDy, and HAVOK. Hence, we show that the proposed StNN paves the way for realizing state-space dynamical systems with a low-complexity learning algorithm, enabling prediction and understanding of future states.

We present a Learning from Demonstration method for teaching robots to perform search strategies imitated from humans in scenarios where alignment tasks fail due to position uncertainty. The method utilizes human demonstrations to learn both a state invariant dynamics model and an exploration distribution that captures the search area covered by the demonstrator. We present two alternative algorithms for computing a search trajectory from the exploration distribution, one based on sampling and another based on deterministic ergodic control. We augment the search trajectory with forces learnt through the dynamics model to enable searching both in force and position domains. An impedance controller with superposed forces is used for reproducing the learnt strategy. We experimentally evaluate the method on a KUKA LWR4+ performing a 2D peg-in-hole and a 3D electricity socket task. Results show that the proposed method can, with only few human demonstrations, learn to complete the search task.