Daily Papers

Building general-purpose embodied agents across diverse hardware remains a central challenge in robotics, often framed as the ''one-brain, many-forms'' paradigm. Progress is hindered by fragmented data, inconsistent representations, and misaligned training objectives. We present ABot-M0, a framework that builds a systematic data curation pipeline while jointly optimizing model architecture and training strategies, enabling end-to-end transformation of heterogeneous raw data into unified, efficient representations. From six public datasets, we clean, standardize, and balance samples to construct UniACT-dataset, a large-scale dataset with over 6 million trajectories and 9,500 hours of data, covering diverse robot morphologies and task scenarios. Unified pre-training improves knowledge transfer and generalization across platforms and tasks, supporting general-purpose embodied intelligence. To improve action prediction efficiency and stability, we propose the Action Manifold Hypothesis: effective robot actions lie not in the full high-dimensional space but on a low-dimensional, smooth manifold governed by physical laws and task constraints. Based on this, we introduce Action Manifold Learning (AML), which uses a DiT backbone to predict clean, continuous action sequences directly. This shifts learning from denoising to projection onto feasible manifolds, improving decoding speed and policy stability. ABot-M0 supports modular perception via a dual-stream mechanism that integrates VLM semantics with geometric priors and multi-view inputs from plug-and-play 3D modules such as VGGT and Qwen-Image-Edit, enhancing spatial understanding without modifying the backbone and mitigating standard VLM limitations in 3D reasoning. Experiments show components operate independently with additive benefits. We will release all code and pipelines for reproducibility and future research.

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are neural networks by introducing a distance between the hidden layer representations of the neural networks. These distances are then fed to the non-linear dimensionality reduction algorithm PHATE to create a manifold of neural networks. We characterize this manifold using features of the representation, including class separation, hierarchical cluster structure, spectral entropy, and topological structure. Our analysis reveals that high-performing networks cluster together in the manifold, displaying consistent embedding patterns across all these features. Finally, we demonstrate the utility of this approach for guiding hyperparameter optimization and neural architecture search by sampling from the manifold.

Intelligent agents progress by continually refining their capabilities through actively exploring environments. Yet robot policies often lack sufficient exploration capability due to action mode collapse. Existing methods that encourage exploration typically rely on random perturbations, which are unsafe and induce unstable, erratic behaviors, thereby limiting their effectiveness. We propose Self-Improvement via On-Manifold Exploration (SOE), a framework that enhances policy exploration and improvement in robotic manipulation. SOE learns a compact latent representation of task-relevant factors and constrains exploration to the manifold of valid actions, ensuring safety, diversity, and effectiveness. It can be seamlessly integrated with arbitrary policy models as a plug-in module, augmenting exploration without degrading the base policy performance. Moreover, the structured latent space enables human-guided exploration, further improving efficiency and controllability. Extensive experiments in both simulation and real-world tasks demonstrate that SOE consistently outperforms prior methods, achieving higher task success rates, smoother and safer exploration, and superior sample efficiency. These results establish on-manifold exploration as a principled approach to sample-efficient policy self-improvement. Project website: https://ericjin2002.github.io/SOE

The manifold hypothesis posits that high-dimensional data often lies on a lower-dimensional manifold and that utilizing this manifold as the target space yields more efficient representations. While numerous traditional manifold-based techniques exist for dimensionality reduction, their application in self-supervised learning has witnessed slow progress. The recent MSimCLR method combines manifold encoding with SimCLR but requires extremely low target encoding dimensions to outperform SimCLR, limiting its applicability. This paper introduces a novel learning paradigm using an unbalanced atlas (UA), capable of surpassing state-of-the-art self-supervised learning approaches. We investigated and engineered the DeepInfomax with an unbalanced atlas (DIM-UA) method by adapting the Spatiotemporal DeepInfomax (ST-DIM) framework to align with our proposed UA paradigm. The efficacy of DIM-UA is demonstrated through training and evaluation on the Atari Annotated RAM Interface (AtariARI) benchmark, a modified version of the Atari 2600 framework that produces annotated image samples for representation learning. The UA paradigm improves existing algorithms significantly as the number of target encoding dimensions grows. For instance, the mean F1 score averaged over categories of DIM-UA is ~75% compared to ~70% of ST-DIM when using 16384 hidden units.

This paper tackles spatial perception and manipulation challenges in Vision-Language-Action (VLA) models. To address depth ambiguity from monocular input, we leverage a pre-trained multi-view diffusion model to synthesize latent novel views and propose a Geometry-Guided Gated Transformer (G3T) that aligns multi-view features under 3D geometric guidance while adaptively filtering occlusion noise. To improve action learning efficiency, we introduce Action Manifold Learning (AML), which directly predicts actions on the valid action manifold, bypassing inefficient regression of unstructured targets like noise or velocity. Experiments on LIBERO, RoboTwin 2.0, and real-robot tasks show our method achieves superior success rate and robustness over SOTA baselines. Project page: https://junjxiao.github.io/Multi-view-VLA.github.io/.

Neural representations carry rich geometric structure; but does that structure causally shape behavior? To address this question, we intervene along paths through activation space defined by different geometries, and measure the behavioral trajectories they induce. In particular, we test whether interventions that respect the geometry of activation space will yield behaviors close to those the model exhibits naturally. Concretely, we first fit an activation manifold M_h to representations and a behavior manifold M_y to output probability distributions. We then test the link M_h leftrightarrow M_y via interventions: we find that steering along M_h, which we term manifold steering, yields behavioral trajectories that follow M_y, while linear steering -- which assumes a Euclidean geometry -- cuts through off-manifold regions and hence produces unnatural outputs. Moreover, optimizing interventions in activation space to produce paths along M_y recovers activation trajectories that trace the curvature of M_h. We demonstrate this bidirectional relationship between the geometry of representation and behavior across tasks and modalities. In language models, we use reasoning tasks with cyclic and sequential geometries as well as in-context learning tasks with more complex graph geometries. In a video world model, we use a task with geometry corresponding to physical dynamics. Overall, our work shows that geometry in neural representation is not merely incidental, but is in fact the proper object for enabling principled control via intervention on internals. This recasts the core problem of steering from finding the right direction to finding the right geometry.

Recent works in robotic manipulation through reinforcement learning (RL) or imitation learning (IL) have shown potential for tackling a range of tasks e.g., opening a drawer or a cupboard. However, these techniques generalize poorly to unseen objects. We conjecture that this is due to the high-dimensional action space for joint control. In this paper, we take an alternative approach and separate the task of learning 'what to do' from 'how to do it' i.e., whole-body control. We pose the RL problem as one of determining the skill dynamics for a disembodied virtual manipulator interacting with articulated objects. The whole-body robotic kinematic control is optimized to execute the high-dimensional joint motion to reach the goals in the workspace. It does so by solving a quadratic programming (QP) model with robotic singularity and kinematic constraints. Our experiments on manipulating complex articulated objects show that the proposed approach is more generalizable to unseen objects with large intra-class variations, outperforming previous approaches. The evaluation results indicate that our approach generates more compliant robotic motion and outperforms the pure RL and IL baselines in task success rates. Additional information and videos are available at https://kl-research.github.io/decoupskill

Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD) matrices and Grassmann manifolds, appear in many applications. Recently, by applying the theory of gyrogroups and gyrovector spaces that is a powerful framework for studying hyperbolic geometry, some works have attempted to build principled generalizations of Euclidean neural networks on matrix manifolds. However, due to the lack of many concepts in gyrovector spaces for the considered manifolds, e.g., the inner product and gyroangles, techniques and mathematical tools provided by these works are still limited compared to those developed for studying hyperbolic geometry. In this paper, we generalize some notions in gyrovector spaces for SPD and Grassmann manifolds, and propose new models and layers for building neural networks on these manifolds. We show the effectiveness of our approach in two applications, i.e., human action recognition and knowledge graph completion.

Training tool-use agents typically relies on outcome-based filtering: Supervised Fine-Tuning (SFT) on successful trajectories and Reinforcement Learning (RL) on pass-rate-selected tasks. However, this paradigm ignores interaction dynamics: successful trajectories may lack error recovery or exhibit redundancy, while pass rates fail to distinguish structurally informative tasks from trivial ones. We propose TopoCurate, an interaction-aware framework that projects multi-trial rollouts from the same task into a unified semantic quotient topology. By merging equivalent action-observation states, this projection transforms scattered linear trajectories into a structured manifold that explicitly captures how tool invocations and environmental responses drive the divergence between effective strategies and failure modes. Leveraging this representation, we introduce a dual-selection mechanism: for SFT, we prioritize trajectories demonstrating reflective recovery, semantic efficiency, and strategic diversity to mitigate covariate shift and mode collapse; for RL, we select tasks with high error branch ratios and strategic heterogeneity, maximizing gradient Signal-to-Noise Ratio to address vanishing signals in sparse-reward settings. Evaluations on BFCLv3 and Tau2 Bench show that TopoCurate achieves consistent gains of 4.2\% (SFT) and 6.9\% (RL) over state-of-the-art baselines. We will release the code and data soon for further investigations.

We argue that progress toward AGI is theory limited rather than data or scale limited. Building on the critical rationalism of Popper and Deutsch, we challenge the Platonic Representation Hypothesis. Observationally equivalent worlds can diverge under interventions, so observational adequacy alone cannot guarantee interventional competence. We begin by laying foundations, definitions of knowledge, learning, intelligence, counterfactual competence and AGI, and then analyze the limits of observational learning that motivate an error centric shift. We recast the problem as three questions about how explicit and implicit errors evolve under an agent's actions, which errors are unreachable within a fixed hypothesis space, and how conjecture and criticism expand that space. From these questions we propose Causal Mechanics, a mechanisms first program in which hypothesis space change is a first class operation and probabilistic structure is used when useful rather than presumed. We advance structural principles that make error discovery and correction tractable, including a differential Locality and Autonomy Principle for modular interventions, a gauge invariant form of Independent Causal Mechanisms for separability, and the Compositional Autonomy Principle for analogy preservation, together with actionable diagnostics. The aim is a scaffold for systems that can convert unreachable errors into reachable ones and correct them.

The varying significance of distinct primitive behaviors during the policy learning process has been overlooked by prior model-free RL algorithms. Leveraging this insight, we explore the causal relationship between different action dimensions and rewards to evaluate the significance of various primitive behaviors during training. We introduce a causality-aware entropy term that effectively identifies and prioritizes actions with high potential impacts for efficient exploration. Furthermore, to prevent excessive focus on specific primitive behaviors, we analyze the gradient dormancy phenomenon and introduce a dormancy-guided reset mechanism to further enhance the efficacy of our method. Our proposed algorithm, ACE: Off-policy Actor-critic with Causality-aware Entropy regularization, demonstrates a substantial performance advantage across 29 diverse continuous control tasks spanning 7 domains compared to model-free RL baselines, which underscores the effectiveness, versatility, and efficient sample efficiency of our approach. Benchmark results and videos are available at https://ace-rl.github.io/.

Real-world phenomena do not generate arbitrary variability: their signals concentrate on compact, low-variability subsets of functional space, enabling rapid generalization from few examples. A small child can recognize a dog after extremely limited exposure because the perceptual manifold of "dog" is compact, structured, and low-dimensional. We formalize this principle through a deterministic functional-topological framework in which the set of valid realizations produced by a physical process forms a compact subset of a Banach space, endowed with stable invariants, a finite Hausdorff radius, and an induced continuous perceptual functional. This geometry provides explicit limits on knowledge, conditions for identifiability, and guarantees for generalization from sparse evidence -- properties fundamental to both natural and artificial intelligence. Across electromechanical, electrochemical, and physiological domains, we show that real-world processes consistently generate compact perceptual manifolds with the same geometric characteristics. Their boundaries can be discovered in a fully self-supervised manner as the empirical radius saturates with increasing sampling, even when the governing equations are unknown. These results demonstrate that deterministic functional topology offers a unified mathematical foundation for perception, representation, and world-model construction. It provides a geometric explanation for why biological learners and self-supervised AI systems can generalize from few observations, and establishes compact perceptual manifolds as a fundamental building block for future AI architectures. Finally, this work unifies biological perception and modern self-supervised models under a single geometric principle: both derive their generalization ability from the compactness and invariants of real-world perceptual manifolds.

In an effort to better understand the different ways in which the discount factor affects the optimization process in reinforcement learning, we designed a set of experiments to study each effect in isolation. Our analysis reveals that the common perception that poor performance of low discount factors is caused by (too) small action-gaps requires revision. We propose an alternative hypothesis that identifies the size-difference of the action-gap across the state-space as the primary cause. We then introduce a new method that enables more homogeneous action-gaps by mapping value estimates to a logarithmic space. We prove convergence for this method under standard assumptions and demonstrate empirically that it indeed enables lower discount factors for approximate reinforcement-learning methods. This in turn allows tackling a class of reinforcement-learning problems that are challenging to solve with traditional methods.

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by learning the inherent structure of action-wise similar MDP to appropriately balance the performance degradation versus sample/computational complexity. In particular, we partition the action spaces into multiple groups based on the similarity in transition distribution and reward function, and build a linear decomposition model to capture the difference between the intra-group transition kernel and the intra-group rewards. Both our theoretical analysis and experiments reveal a surprising and counter-intuitive result: while a more refined grouping strategy can reduce the approximation error caused by treating actions in the same group as identical, it also leads to increased estimation error when the size of samples or the computation resources is limited. This finding highlights the grouping strategy as a new degree of freedom that can be optimized to minimize the overall performance loss. To address this issue, we formulate a general optimization problem for determining the optimal grouping strategy, which strikes a balance between performance loss and sample/computational complexity. We further propose a computationally efficient method for selecting a nearly-optimal grouping strategy, which maintains its computational complexity independent of the size of the action space.

Is there a canonical way to think of agency beyond reward maximisation? In this paper, we show that any type of behaviour complying with physically sound assumptions about how macroscopic biological agents interact with the world canonically integrates exploration and exploitation in the sense of minimising risk and ambiguity about states of the world. This description, known as active inference, refines the free energy principle, a popular descriptive framework for action and perception originating in neuroscience. Active inference provides a normative Bayesian framework to simulate and model agency that is widely used in behavioural neuroscience, reinforcement learning (RL) and robotics. The usefulness of active inference for RL is three-fold. a) Active inference provides a principled solution to the exploration-exploitation dilemma that usefully simulates biological agency. b) It provides an explainable recipe to simulate behaviour, whence behaviour follows as an explainable mixture of exploration and exploitation under a generative world model, and all differences in behaviour are explicit in differences in world model. c) This framework is universal in the sense that it is theoretically possible to rewrite any RL algorithm conforming to the descriptive assumptions of active inference as an active inference algorithm. Thus, active inference can be used as a tool to uncover and compare the commitments and assumptions of more specific models of agency.

Sparse autoencoders (SAEs) are widely used to extract interpretable features from neural network representations, often under the implicit assumption that concepts correspond to independent linear directions. However, a growing body of evidence suggests that many concepts are instead organized along low-dimensional manifolds encoding continuous geometric relationships. This raises three basic questions: what does it mean for an SAE to capture a manifold, when do existing SAE architectures do so, and how? We develop a theoretical framework that answers these questions and show that SAEs can capture manifolds in two fundamentally different ways: globally, by allocating a compact group of atoms whose linear span contains the entire manifold, or locally, by distributing it across features that each selectively tile a restricted region of the underlying geometry. Empirically, we find that SAEs suboptimally recover continuous structures, mixing the global subspace and local tiling solutions in a fragmented regime we call dilution. This explains why manifold structure is rarely visible at the level of individual concepts and motivates post-hoc unsupervised discovery methods that search for coherent groups of atoms rather than isolated directions. More broadly, our results suggest that future representation learning methods should treat geometric objects, not just individual directions, as the basic units of interpretability.

Temporal abstraction and efficient planning pose significant challenges in offline reinforcement learning, mainly when dealing with domains that involve temporally extended tasks and delayed sparse rewards. Existing methods typically plan in the raw action space and can be inefficient and inflexible. Latent action spaces offer a more flexible paradigm, capturing only possible actions within the behavior policy support and decoupling the temporal structure between planning and modeling. However, current latent-action-based methods are limited to discrete spaces and require expensive planning. This paper presents a unified framework for continuous latent action space representation learning and planning by leveraging latent, score-based diffusion models. We establish the theoretical equivalence between planning in the latent action space and energy-guided sampling with a pretrained diffusion model and incorporate a novel sequence-level exact sampling method. Our proposed method, LatentDiffuser, demonstrates competitive performance on low-dimensional locomotion control tasks and surpasses existing methods in higher-dimensional tasks.

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.

We present Chain-of-Action (CoA), a novel visuo-motor policy paradigm built upon Trajectory Autoregressive Modeling. Unlike conventional approaches that predict next step action(s) forward, CoA generates an entire trajectory by explicit backward reasoning with task-specific goals through an action-level Chain-of-Thought (CoT) process. This process is unified within a single autoregressive structure: (1) the first token corresponds to a stable keyframe action that encodes the task-specific goals; and (2) subsequent action tokens are generated autoregressively, conditioned on the initial keyframe and previously predicted actions. This backward action reasoning enforces a global-to-local structure, allowing each local action to be tightly constrained by the final goal. To further realize the action reasoning structure, CoA incorporates four complementary designs: continuous action token representation; dynamic stopping for variable-length trajectory generation; reverse temporal ensemble; and multi-token prediction to balance action chunk modeling with global structure. As a result, CoA gives strong spatial generalization capabilities while preserving the flexibility and simplicity of a visuo-motor policy. Empirically, we observe CoA achieves the state-of-the-art performance across 60 RLBench tasks and 8 real-world manipulation tasks.

Humans rarely plan whole-body interactions with objects at the level of explicit whole-body movements. High-level intentions, such as affordance, define the goal, while coordinated balance, contact, and manipulation can emerge naturally from underlying physical and motor priors. Scaling such priors is key to enabling humanoids to compose and generalize loco-manipulation skills across diverse contexts while maintaining physically coherent whole-body coordination. To this end, we introduce InterPrior, a scalable framework that learns a unified generative controller through large-scale imitation pretraining and post-training by reinforcement learning. InterPrior first distills a full-reference imitation expert into a versatile, goal-conditioned variational policy that reconstructs motion from multimodal observations and high-level intent. While the distilled policy reconstructs training behaviors, it does not generalize reliably due to the vast configuration space of large-scale human-object interactions. To address this, we apply data augmentation with physical perturbations, and then perform reinforcement learning finetuning to improve competence on unseen goals and initializations. Together, these steps consolidate the reconstructed latent skills into a valid manifold, yielding a motion prior that generalizes beyond the training data, e.g., it can incorporate new behaviors such as interactions with unseen objects. We further demonstrate its effectiveness for user-interactive control and its potential for real robot deployment.

Action Quality Assessment (AQA) evaluates diverse skills but models struggle with non-stationary data. We propose Continual AQA (CAQA) to refine models using sparse new data. Feature replay preserves memory without storing raw inputs. However, the misalignment between static old features and the dynamically changing feature manifold causes severe catastrophic forgetting. To address this novel problem, we propose Manifold-Aligned Graph Regularization (MAGR), which first aligns deviated old features to the current feature manifold, ensuring representation consistency. It then constructs a graph jointly arranging old and new features aligned with quality scores. Experiments show MAGR outperforms recent strong baselines with up to 6.56%, 5.66%, 15.64%, and 9.05% correlation gains on the MTL-AQA, FineDiving, UNLV-Dive, and JDM-MSA split datasets, respectively. This validates MAGR for continual assessment challenges arising from non-stationary skill variations.

Dynamical systems theory and reinforcement learning view world evolution as latent-state dynamics driven by actions, with visual observations providing partial information about the state. Recent video world models attempt to learn this action-conditioned dynamics from data. However, existing datasets rarely match the requirement: they typically lack diverse and semantically meaningful action spaces, and actions are directly tied to visual observations rather than mediated by underlying states. As a result, actions are often entangled with pixel-level changes, making it difficult for models to learn structured world dynamics and maintain consistent evolution over long horizons. In this paper, we propose WildWorld, a large-scale action-conditioned world modeling dataset with explicit state annotations, automatically collected from a photorealistic AAA action role-playing game (Monster Hunter: Wilds). WildWorld contains over 108 million frames and features more than 450 actions, including movement, attacks, and skill casting, together with synchronized per-frame annotations of character skeletons, world states, camera poses, and depth maps. We further derive WildBench to evaluate models through Action Following and State Alignment. Extensive experiments reveal persistent challenges in modeling semantically rich actions and maintaining long-horizon state consistency, highlighting the need for state-aware video generation. The project page is https://shandaai.github.io/wildworld-project/.

Understanding the physical structure is essential for real-world applications such as embodied agents, interactive design, and long-horizon manipulation. Yet, prevailing Vision-Language Model (VLM) evaluations still center on structure-agnostic, single-turn setups (e.g., VQA), which fail to assess agents' ability to reason about how geometry, contact, and support relations jointly constrain what actions are possible in a dynamic environment. To address this gap, we introduce the Causal Hierarchy of Actions and Interactions (CHAIN) benchmark, an interactive 3D, physics-driven testbed designed to evaluate whether models can understand, plan, and execute structured action sequences grounded in physical constraints. CHAIN shifts evaluation from passive perception to active problem solving, spanning tasks such as interlocking mechanical puzzles and 3D stacking and packing. We conduct a comprehensive study of state-of-the-art VLMs and diffusion-based models under unified interactive settings. Our results show that top-performing models still struggle to internalize physical structure and causal constraints, often failing to produce reliable long-horizon plans and cannot robustly translate perceived structure into effective actions. The project is available at https://social-ai-studio.github.io/CHAIN/.

Agents capable of reasoning and planning in the real world require the ability of predicting the consequences of their actions. While world models possess this capability, they most often require action labels, that can be complex to obtain at scale. This motivates the learning of latent action models, that can learn an action space from videos alone. Our work addresses the problem of learning latent actions world models on in-the-wild videos, expanding the scope of existing works that focus on simple robotics simulations, video games, or manipulation data. While this allows us to capture richer actions, it also introduces challenges stemming from the video diversity, such as environmental noise, or the lack of a common embodiment across videos. To address some of the challenges, we discuss properties that actions should follow as well as relevant architectural choices and evaluations. We find that continuous, but constrained, latent actions are able to capture the complexity of actions from in-the-wild videos, something that the common vector quantization does not. We for example find that changes in the environment coming from agents, such as humans entering the room, can be transferred across videos. This highlights the capability of learning actions that are specific to in-the-wild videos. In the absence of a common embodiment across videos, we are mainly able to learn latent actions that become localized in space, relative to the camera. Nonetheless, we are able to train a controller that maps known actions to latent ones, allowing us to use latent actions as a universal interface and solve planning tasks with our world model with similar performance as action-conditioned baselines. Our analyses and experiments provide a step towards scaling latent action models to the real world.

In this article, we develop an asymptotic method for constructing confidence regions for the set of all linear subspaces arising from PCA, from which we derive hypothesis tests on this set. Our method is based on the geometry of Riemannian manifolds with which some sets of linear subspaces are endowed.

Recent advances in diffusion and flow matching models have highlighted a shift in the preferred prediction target -- moving from noise (varepsilon) and velocity (v) to direct data (x) prediction -- particularly in high-dimensional settings. However, a formal explanation of why the optimal target depends on the specific properties of the data remains elusive. In this work, we provide a theoretical framework based on a generalized prediction formulation that accommodates arbitrary output targets, of which varepsilon-, v-, and x-prediction are special cases. We derive the analytical relationship between data's geometry and the optimal prediction target, offering a rigorous justification for why x-prediction becomes superior when the ambient dimension significantly exceeds the data's intrinsic dimension. Furthermore, while our theory identifies dimensionality as the governing factor for the optimal prediction target, the intrinsic dimension of manifold-bound data is typically intractable to estimate in practice. To bridge this gap, we propose k-Diff, a framework that employs a data-driven approach to learn the optimal prediction parameter k directly from data, bypassing the need for explicit dimension estimation. Extensive experiments in both latent-space and pixel-space image generation demonstrate that k-Diff consistently outperforms fixed-target baselines across varying architectures and data scales, providing a principled and automated approach to enhancing generative performance.

Practitioners prune neural networks for efficiency gains and generalization improvements, but few scrutinize the factors determining the prunability of a neural network the maximum fraction of weights that pruning can remove without compromising the model's test accuracy. In this work, we study the properties of input data that may contribute to the prunability of a neural network. For high dimensional input data such as images, text, and audio, the manifold hypothesis suggests that these high dimensional inputs approximately lie on or near a significantly lower dimensional manifold. Prior work demonstrates that the underlying low dimensional structure of the input data may affect the sample efficiency of learning. In this paper, we investigate whether the low dimensional structure of the input data affects the prunability of a neural network.

Inspired by the emergent behaviors in large language models that generalized human intelligence, the research community is pursuing similar emergent capabilities within world models, with a emphasis on modeling the physical world. Within the scope of physical world model, objects are the fundamental primitives that constitute physical reality. From humans to computers, nearly everything we interact with is an object. These objects are rarely static; they are actionable entities with varying states determined by their intrinsic properties. While current methods approach object action states either via video generation or dynamic scene reconstruction, none explicitly model this basic element in a unified, principled way to build an actionable object representation. We propose WorldString, a neural architecture capable of modeling the state manifold of real-world objects by learning directly from point clouds or RGB-D video streams. Serving as a versatile digital twin, it acts as a foundational building block for physical world models; thus, we name it WorldString. Sweetly, its fully differentiable structure seamlessly enables future integration with policy learning and neural dynamics.

Recently, unsupervised representation learning (URL) has improved the sample efficiency of Reinforcement Learning (RL) by pretraining a model from a large unlabeled dataset. The underlying principle of these methods is to learn temporally predictive representations by predicting future states in the latent space. However, an important challenge of this approach is the representational collapse, where the subspace of the latent representations collapses into a low-dimensional manifold. To address this issue, we propose a novel URL framework that causally predicts future states while increasing the dimension of the latent manifold by decorrelating the features in the latent space. Through extensive empirical studies, we demonstrate that our framework effectively learns predictive representations without collapse, which significantly improves the sample efficiency of state-of-the-art URL methods on the Atari 100k benchmark. The code is available at https://github.com/dojeon-ai/SimTPR.

Pre-training large models on vast amounts of web data has proven to be an effective approach for obtaining powerful, general models in domains such as language and vision. However, this paradigm has not yet taken hold in reinforcement learning. This is because videos, the most abundant form of embodied behavioral data on the web, lack the action labels required by existing methods for imitating behavior from demonstrations. We introduce Latent Action Policies (LAPO), a method for recovering latent action information, and thereby latent-action policies, world models, and inverse dynamics models, purely from videos. LAPO is the first method able to recover the structure of the true action space just from observed dynamics, even in challenging procedurally-generated environments. LAPO enables training latent-action policies that can be rapidly fine-tuned into expert-level policies, either offline using a small action-labeled dataset, or online with rewards. LAPO takes a first step towards pre-training powerful, generalist policies and world models on the vast amounts of videos readily available on the web.

The efficient coding hypothesis proposes that the response properties of sensory systems are adapted to the statistics of their inputs such that they capture maximal information about the environment, subject to biological constraints. While elegant, information theoretic properties are notoriously difficult to measure in practical settings or to employ as objective functions in optimization. This difficulty has necessitated that computational models designed to test the hypothesis employ several different information metrics ranging from approximations and lower bounds to proxy measures like reconstruction error. Recent theoretical advances have characterized a novel and ecologically relevant efficiency metric, the manifold capacity, which is the number of object categories that may be represented in a linearly separable fashion. However, calculating manifold capacity is a computationally intensive iterative procedure that until now has precluded its use as an objective. Here we outline the simplifying assumptions that allow manifold capacity to be optimized directly, yielding Maximum Manifold Capacity Representations (MMCR). The resulting method is closely related to and inspired by advances in the field of self supervised learning (SSL), and we demonstrate that MMCRs are competitive with state of the art results on standard SSL benchmarks. Empirical analyses reveal differences between MMCRs and representations learned by other SSL frameworks, and suggest a mechanism by which manifold compression gives rise to class separability. Finally we evaluate a set of SSL methods on a suite of neural predictivity benchmarks, and find MMCRs are higly competitive as models of the ventral stream.

Vision-Language-Action (VLA) models have achieved strong semantic generalization for embodied policy learning, yet they learn reactive observation-to-action mappings without explicitly modeling how the physical world evolves under intervention. A growing body of work addresses this limitation by integrating world models, predictive models of environment dynamics, into the action generation pipeline. We term this emerging paradigm World Action Models (WAMs): embodied foundation models that unify predictive state modeling with action generation, targeting a joint distribution over future states and actions rather than actions alone. However, the literature remains fragmented across architectures, learning objectives, and application scenarios, lacking a unified conceptual framework. We formally define WAMs and disambiguate them from related concepts, and trace the foundations and early integration of VLA and world model research that gave rise to this paradigm. We organize existing methods into a structured taxonomy of Cascaded and Joint WAMs, with further subdivision by generation modality, conditioning mechanism, and action decoding strategy. We systematically analyze the data ecosystem fueling WAMs development, spanning robot teleoperation, portable human demonstrations, simulation, and internet-scale egocentric video, and synthesize emerging evaluation protocols organized around visual fidelity, physical commonsense, and action plausibility. Overall, this survey provides the first systematic account of the WAMs landscape, clarifies key architectural paradigms and their trade-offs, and identifies open challenges and future opportunities for this rapidly evolving field.

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Large language model (LLM)-driven agents are emerging as a powerful new paradigm for solving complex problems. Despite the empirical success of these practices, a theoretical framework to understand and unify their macroscopic dynamics remains lacking. This Letter proposes a method based on the least action principle to estimate the underlying generative directionality of LLMs embedded within agents. By experimentally measuring the transition probabilities between LLM-generated states, we statistically discover a detailed balance in LLM-generated transitions, indicating that LLM generation may not be achieved by generally learning rule sets and strategies, but rather by implicitly learning a class of underlying potential functions that may transcend different LLM architectures and prompt templates. To our knowledge, this is the first discovery of a macroscopic physical law in LLM generative dynamics that does not depend on specific model details. This work is an attempt to establish a macroscopic dynamics theory of complex AI systems, aiming to elevate the study of AI agents from a collection of engineering practices to a science built on effective measurements that are predictable and quantifiable.

As trajectories sampled by policies used by reinforcement learning (RL) and generative flow networks (GFlowNets) grow longer, credit assignment and exploration become more challenging, and the long planning horizon hinders mode discovery and generalization. The challenge is particularly pronounced in entropy-seeking RL methods, such as generative flow networks, where the agent must learn to sample from a structured distribution and discover multiple high-reward states, each of which take many steps to reach. To tackle this challenge, we propose an approach to incorporate the discovery of action abstractions, or high-level actions, into the policy optimization process. Our approach involves iteratively extracting action subsequences commonly used across many high-reward trajectories and `chunking' them into a single action that is added to the action space. In empirical evaluation on synthetic and real-world environments, our approach demonstrates improved sample efficiency performance in discovering diverse high-reward objects, especially on harder exploration problems. We also observe that the abstracted high-order actions are interpretable, capturing the latent structure of the reward landscape of the action space. This work provides a cognitively motivated approach to action abstraction in RL and is the first demonstration of hierarchical planning in amortized sequential sampling.

Understanding how Large Language Models (LLMs) perform complex reasoning and their failure mechanisms is a challenge in interpretability research. To provide a measurable geometric analysis perspective, we define the concept of the Reasoning Manifold, a latent low-dimensional geometric structure formed by the internal representations corresponding to all correctly reasoned generations. This structure can be conceptualized as the embodiment of the effective thinking paths that the model has learned to successfully solve a given task. Based on this concept, we build REMA, a framework that explains the origins of failures by quantitatively comparing the spatial relationships of internal model representations corresponding to both erroneous and correct reasoning samples. Specifically, REMA first quantifies the geometric deviation of each erroneous representation by calculating its k-nearest neighbors distance to the approximated manifold formed by correct representations, thereby providing a unified failure signal. It then localizes the divergence points where these deviations first become significant by tracking this deviation metric across the model's layers and comparing it against a baseline of internal fluctuations from correct representations, thus identifying where the reasoning chain begins to go off-track. Our extensive experiments on diverse language and multimodal models and tasks demonstrate the low-dimensional nature of the reasoning manifold and the high separability between erroneous and correct reasoning representations. The results also validate the effectiveness of the REMA framework in analyzing the origins of reasoning failures. This research connects abstract reasoning failures to measurable geometric deviations in representations, providing new avenues for in-depth understanding and diagnosis of the internal computational processes of black-box models.

Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been adapted to several manifolds, referred to as Riemannian normalization. Nonetheless, most of the existing Riemannian normalization methods have been derived in an ad hoc manner and only apply to specific manifolds. This paper establishes a unified framework for Riemannian Batch Normalization (RBN) techniques on Lie groups. Our framework offers the theoretical guarantee of controlling both the Riemannian mean and variance. Empirically, we focus on Symmetric Positive Definite (SPD) manifolds, which possess three distinct types of Lie group structures. Using the deformation concept, we generalize the existing Lie groups on SPD manifolds into three families of parameterized Lie groups. Specific normalization layers induced by these Lie groups are then proposed for SPD neural networks. We demonstrate the effectiveness of our approach through three sets of experiments: radar recognition, human action recognition, and electroencephalography (EEG) classification. The code is available at https://github.com/GitZH-Chen/LieBN.git.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

Vision-based robotic policies often struggle with even minor viewpoint changes, underscoring the need for view-invariant visual representations. This challenge becomes more pronounced in real-world settings, where viewpoint variability is unavoidable and can significantly disrupt policy performance. Existing methods typically learn invariance from multi-view observations at the scene level, but such approaches rely on visual appearance and fail to incorporate the physical dynamics essential for robust generalization. We propose View-Invariant Latent Action (VILA), which models a latent action capturing transition patterns across trajectories to learn view-invariant representations grounded in physical dynamics. VILA aligns these latent actions across viewpoints using an action-guided objective based on ground-truth action sequences. Experiments in both simulation and the real world show that VILA-based policies generalize effectively to unseen viewpoints and transfer well to new tasks, establishing VILA as a strong pretraining framework that improves robustness and downstream learning performance.

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.

Despite rapid advances in video generative models, robust metrics for evaluating visual and temporal correctness of complex human actions remain elusive. Critically, existing pure-vision encoders and Multimodal Large Language Models (MLLMs) are strongly appearance-biased, lack temporal understanding, and thus struggle to discern intricate motion dynamics and anatomical implausibilities in generated videos. We tackle this gap by introducing a novel evaluation metric derived from a learned latent space of real-world human actions. Our method first captures the nuances, constraints, and temporal smoothness of real-world motion by fusing appearance-agnostic human skeletal geometry features with appearance-based features. We posit that this combined feature space provides a robust representation of action plausibility. Given a generated video, our metric quantifies its action quality by measuring the distance between its underlying representations and this learned real-world action distribution. For rigorous validation, we develop a new multi-faceted benchmark specifically designed to probe temporally challenging aspects of human action fidelity. Through extensive experiments, we show that our metric achieves substantial improvement of more than 68% compared to existing state-of-the-art methods on our benchmark, performs competitively on established external benchmarks, and has a stronger correlation with human perception. Our in-depth analysis reveals critical limitations in current video generative models and establishes a new standard for advanced research in video generation.

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much more amenable to computation. By leveraging and combining various ans\"{a}tze, we can quickly compute relevant quantities to high precision. On low dimensional datasets, our correction produces a noticeable improvement, allowing diffusion to compete with other methods. Additionally, we show that our method enables us to scale to high dimensional tasks on nontrivial manifolds. In particular, we model QCD densities on SU(n) lattices and contrastively learned embeddings on high dimensional hyperspheres.

While the shortage of explicit action data limits Vision-Language-Action (VLA) models, human action videos offer a scalable yet unlabeled data source. A critical challenge in utilizing large-scale human video datasets lies in transforming visual signals into ontology-independent representations, known as latent actions. However, the capacity of latent action representation to derive robust control from visual observations has yet to be rigorously evaluated. We introduce the Latent Action Representation Yielding (LARY) Benchmark, a unified framework for evaluating latent action representations on both high-level semantic actions (what to do) and low-level robotic control (how to do). The comprehensively curated dataset encompasses over one million videos (1,000 hours) spanning 151 action categories, alongside 620K image pairs and 595K motion trajectories across diverse embodiments and environments. Our experiments reveal two crucial insights: (i) General visual foundation models, trained without any action supervision, consistently outperform specialized embodied latent action models. (ii) Latent-based visual space is fundamentally better aligned to physical action space than pixel-based space. These results suggest that general visual representations inherently encode action-relevant knowledge for physical control, and that semantic-level abstraction serves as a fundamentally more effective pathway from vision to action than pixel-level reconstruction.

Diffusion models operate in a reflexive System 1 mode, constrained by a fixed, content-agnostic sampling schedule. This rigidity arises from the curse of state dimensionality, where the combinatorial explosion of possible states in the high-dimensional noise manifold renders explicit trajectory planning intractable and leads to systematic computational misallocation. To address this, we introduce Chain-of-Trajectories (CoTj), a train-free framework enabling System 2 deliberative planning. Central to CoTj is Diffusion DNA, a low-dimensional signature that quantifies per-stage denoising difficulty and serves as a proxy for the high-dimensional state space, allowing us to reformulate sampling as graph planning on a directed acyclic graph. Through a Predict-Plan-Execute paradigm, CoTj dynamically allocates computational effort to the most challenging generative phases. Experiments across multiple generative models demonstrate that CoTj discovers context-aware trajectories, improving output quality and stability while reducing redundant computation. This work establishes a new foundation for resource-aware, planning-based diffusion modeling. The code is available at https://github.com/UnicomAI/CoTj.

Action-conditioned world models (ACWMs) have shown strong promise for video prediction and decision-making. However, existing benchmarks are largely restricted to egocentric navigation or narrow, task-specific robotics datasets, offering only limited coverage of the rich physical interactions required for generalized world understanding. We introduce ACWM-Phys, a new benchmark for evaluating action-conditioned prediction under diverse physical dynamics in a clean, controllable simulation environment with a carefully designed action space. ACWM-Phys contains training and evaluation data spanning rigid-body dynamics, kinematics, deformable-object interactions, and particle dynamics. To evaluate both interpolation and generalization, we design in-distribution and out-of-distribution protocols with controlled shifts in interaction patterns or scene configurations. By building the benchmark in a fully controllable simulator, ACWM-Phys enables precise data collection, reproducible evaluation, and systematic analysis of model capabilities for physically grounded world modeling. Through systematic experiments on ACWM-DiT, we find that OoD generalization depends not only on the physical regime but also on effective task complexity: models generalize well on visually simple, low-dimensional interactions with clear geometric structure, but suffer larger drops on deformable contacts, high-dimensional control, and complex articulated motion. This suggests that the model still relies heavily on visual appearance patterns instead of fully learning the underlying physics. Ablations show that cross-attention improves high-dimensional action conditioning, causal VAEs outperform frame-wise encoders, and larger action spaces are harder to model but can improve generalization by providing richer control signals. These findings guide the design of physically grounded world models.

We formalize action emergence as a target capability for end-to-end autonomous driving: the ability to generate physically feasible, semantically appropriate, and safety-compliant actions in arbitrary, long-tail traffic scenes through scene-conditioned reasoning rather than retrieval or interpolation of learned scene-action mappings. We show that previous paradigms cannot deliver action emergence: autoregressive trajectory decoders collapse the inherently multimodal future into a single averaged output, while diffusion and flow-matching generators express multimodality but are not steerable by reasoned intent. We propose Streaming Intent as a concrete way to approach action emergence: a mechanism that makes driving intent (i) semantically streamed through a continuous chain-of-thought that causally derives the intent from scene understanding, and (ii) temporally streamed across clips so that intent commitments remain coherent along the driving horizon. We realize Streaming Intent in a VLA model we call SI (Streaming Intent). SI autoregressively decodes a four-step chain-of-thought and emits an intent token; the decoded intent then drives classifier-free guidance (CFG) on a flow-matching action head, requiring only two denoising steps to generate the final trajectory. On the Waymo End-to-End benchmark, SI achieves competitive aggregate performance, with an RFS score of 7.96 on the validation set and 7.74 on the test set. Beyond aggregate metrics, the model demonstrates -- to our knowledge for the first time in a fully end-to-end VLA -- intent-faithful controllability: for a fixed scene, varying the intent class at inference yields qualitatively distinct yet consistently high-quality plans, arising purely from data-driven learning without any pre-built trajectory bank or hand-coded post-hoc selector.

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the following phenomena that relate to the structure of the space of tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress even on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) episodic meta-learning algorithms and supervised learning traverse different trajectories during training but they fit similar models eventually; (5) contrastive and semi-supervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena.

Many important real-world problems have action spaces that are high-dimensional, continuous or both, making full enumeration of all possible actions infeasible. Instead, only small subsets of actions can be sampled for the purpose of policy evaluation and improvement. In this paper, we propose a general framework to reason in a principled way about policy evaluation and improvement over such sampled action subsets. This sample-based policy iteration framework can in principle be applied to any reinforcement learning algorithm based upon policy iteration. Concretely, we propose Sampled MuZero, an extension of the MuZero algorithm that is able to learn in domains with arbitrarily complex action spaces by planning over sampled actions. We demonstrate this approach on the classical board game of Go and on two continuous control benchmark domains: DeepMind Control Suite and Real-World RL Suite.

Large discrete action spaces (LDAS) remain a central challenge in reinforcement learning. Existing solution approaches can handle unstructured LDAS with up to a few million actions. However, many real-world applications in logistics, production, and transportation systems have combinatorial action spaces, whose size grows well beyond millions of actions, even on small instances. Fortunately, such action spaces exhibit structure, e.g., equally spaced discrete resource units. With this work, we focus on handling structured LDAS (SLDAS) with sizes that cannot be handled by current benchmarks: we propose Dynamic Neighborhood Construction (DNC), a novel exploitation paradigm for SLDAS. We present a scalable neighborhood exploration heuristic that utilizes this paradigm and efficiently explores the discrete neighborhood around the continuous proxy action in structured action spaces with up to 10^{73} actions. We demonstrate the performance of our method by benchmarking it against three state-of-the-art approaches designed for large discrete action spaces across two distinct environments. Our results show that DNC matches or outperforms state-of-the-art approaches while being computationally more efficient. Furthermore, our method scales to action spaces that so far remained computationally intractable for existing methodologies.

Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to hundreds of neural network evaluations at inference time, which can become a computational bottleneck in large-scale scientific sampling workflows. We introduce Riemannian MeanFlow~(RMF), a framework for learning flow maps directly on manifolds, enabling high-quality generations with as few as one forward pass. We derive three equivalent characterizations of the manifold average velocity (Eulerian, Lagrangian, and semigroup identities), and analyze parameterizations and stabilization techniques to improve training on high-dimensional manifolds. In promoter DNA design and protein backbone generation settings, RMF achieves comparable sample quality to prior methods while requiring up to 10times fewer function evaluations. Finally, we show that few-step flow maps enable efficient reward-guided design through reward look-ahead, where terminal states can be predicted from intermediate steps at minimal additional cost.

The Distributional Principal Autoencoder (DPA) combines distributionally correct reconstruction with principal-component-like interpretability of the encodings. In this work, we provide exact theoretical guarantees on both fronts. First, we derive a closed-form relation linking each optimal level-set geometry to the data-distribution score. This result explains DPA's empirical ability to disentangle factors of variation of the data, as well as allows the score to be recovered directly from samples. When the data follows the Boltzmann distribution, we demonstrate that this relation yields an approximation of the minimum free-energy path for the Mueller-Brown potential in a single fit. Second, we prove that if the data lies on a manifold that can be approximated by the encoder, latent components beyond the manifold dimension are conditionally independent of the data distribution - carrying no additional information - and thus reveal the intrinsic dimension. Together, these results show that a single model can learn the data distribution and its intrinsic dimension with exact guarantees simultaneously, unifying two longstanding goals of unsupervised learning.

We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise covariance spectrum of activations, where C^{(ell)}=E[h^{(ell)}h^{(ell)top}], and track deviations from a random-matrix bulk. Across model scales (1.5B--30B), we observe a sharp reduction in effective dimensionality consistent with a phase transition: an order parameter based on sparsity/localization, Ω(h)=1-|h|_1/(d|h|_2), exhibits a discontinuity near a critical normalized depth γ_capprox 0.42 in sufficiently large models. We formalize the forward pass as a discrete coarse-graining map and relate the appearance of stable "concept basins" to fixed points of this renormalization-like dynamics. The resulting low-entropy regime is characterized by a spectral tail collapse and by the formation of transient, reusable object-like structures in representation space, which we call Transient Class Objects (TCOs). We provide theoretical conditions connecting logical separability to spectral decay and validate the predicted signatures with layerwise probes on multiple open-weight model families.

The choice of action spaces is a critical yet unresolved challenge in developing capable, end-to-end trainable agents. This paper first presents a large-scale, systematic comparison of prominent abstracted action spaces and tokenizers for Vision-Language-Action (VLA) or hierarchical agent models in the open-ended Minecraft. Our analysis reveals that no single action space is universally optimal; instead, the most effective abstraction is highly task-dependent, creating a dilemma for building generalist agents. To resolve this, we introduce Chain of Action (CoA), a novel framework that unifies high-level planning and low-level control within a single, monolithic VLA model. CoA treats an abstracted action not as a command for a separate policy, but as an intermediate reasoning step--akin to a chain of thought--that guides the generation of the final, executable action. Furthermore, we demonstrate that an All-in-One agent trained on a diverse mixture of action spaces using the CoA paradigm learns a more robust and generalizable policy. This unified agent achieves a new state-of-the-art, improving the overall task success rate over strong, specialized baselines. To foster reproducible research, we release the OpenHA (Open Hierarchical Agents) suite, which includes our comprehensive benchmark of over 800 distinct tasks, curated datasets, source code, and all pretrained model checkpoints at https://github.com/CraftJarvis/OpenHA

Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology and physics. While it is thought that these methods preserve underlying manifold structure of data by learning a proxy for geodesic distances, no specific theoretical links have been established. Here, we establish such a link via results in Riemannian geometry explicitly connecting heat diffusion to manifold distances. In this process, we also formulate a more general heat kernel based manifold embedding method that we call heat geodesic embeddings. This novel perspective makes clearer the choices available in manifold learning and denoising. Results show that our method outperforms existing state of the art in preserving ground truth manifold distances, and preserving cluster structure in toy datasets. We also showcase our method on single cell RNA-sequencing datasets with both continuum and cluster structure, where our method enables interpolation of withheld timepoints of data. Finally, we show that parameters of our more general method can be configured to give results similar to PHATE (a state-of-the-art diffusion based manifold learning method) as well as SNE (an attraction/repulsion neighborhood based method that forms the basis of t-SNE).

Power grid operation is becoming more complex due to the increase in generation of renewable energy. The recent series of Learning To Run a Power Network (L2RPN) competitions have encouraged the use of artificial agents to assist human dispatchers in operating power grids. However, the combinatorial nature of the action space poses a challenge to both conventional optimizers and learned controllers. Action space factorization, which breaks down decision-making into smaller sub-tasks, is one approach to tackle the curse of dimensionality. In this study, we propose a centrally coordinated multi-agent (CCMA) architecture for action space factorization. In this approach, regional agents propose actions and subsequently a coordinating agent selects the final action. We investigate several implementations of the CCMA architecture, and benchmark in different experimental settings against various L2RPN baseline approaches. The CCMA architecture exhibits higher sample efficiency and superior final performance than the baseline approaches. The results suggest high potential of the CCMA approach for further application in higher-dimensional L2RPN as well as real-world power grid settings.

Recent advances in video diffusion have enabled the development of "world models" capable of simulating interactive environments. However, these models are largely restricted to single-agent settings, failing to control multiple agents simultaneously in a scene. In this work, we tackle a fundamental issue of action binding in existing video diffusion models, which struggle to associate specific actions with their corresponding subjects. For this purpose, we propose ActionParty, an action controllable multi-subject world model for generative video games. It introduces subject state tokens, i.e. latent variables that persistently capture the state of each subject in the scene. By jointly modeling state tokens and video latents with a spatial biasing mechanism, we disentangle global video frame rendering from individual action-controlled subject updates. We evaluate ActionParty on the Melting Pot benchmark, demonstrating the first video world model capable of controlling up to seven players simultaneously across 46 diverse environments. Our results show significant improvements in action-following accuracy and identity consistency, while enabling robust autoregressive tracking of subjects through complex interactions.

Humans anticipate, from a glance and a contemplated action of their bodies, how the 3D world will respond, a capability that is equally vital for robotic manipulation. We introduce PointWorld, a large pre-trained 3D world model that unifies state and action in a shared 3D space as 3D point flows: given one or few RGB-D images and a sequence of low-level robot action commands, PointWorld forecasts per-pixel displacements in 3D that respond to the given actions. By representing actions as 3D point flows instead of embodiment-specific action spaces (e.g., joint positions), this formulation directly conditions on physical geometries of robots while seamlessly integrating learning across embodiments. To train our 3D world model, we curate a large-scale dataset spanning real and simulated robotic manipulation in open-world environments, enabled by recent advances in 3D vision and simulated environments, totaling about 2M trajectories and 500 hours across a single-arm Franka and a bimanual humanoid. Through rigorous, large-scale empirical studies of backbones, action representations, learning objectives, partial observability, data mixtures, domain transfers, and scaling, we distill design principles for large-scale 3D world modeling. With a real-time (0.1s) inference speed, PointWorld can be efficiently integrated in the model-predictive control (MPC) framework for manipulation. We demonstrate that a single pre-trained checkpoint enables a real-world Franka robot to perform rigid-body pushing, deformable and articulated object manipulation, and tool use, without requiring any demonstrations or post-training and all from a single image captured in-the-wild. Project website at https://point-world.github.io/.

Generalization, the ability to perform well beyond the training context, is a hallmark of biological and artificial intelligence, yet anticipating unseen failures remains a central challenge. Conventional approaches often take a ``bottom-up'' mechanistic route by reverse-engineering interpretable features or circuits to build explanatory models. While insightful, these methods often struggle to provide the high-level, predictive signals for anticipating failure in real-world deployment. Here, we propose using a ``top-down'' approach to studying generalization failures inspired by medical biomarkers: identifying system-level measurements that serve as robust indicators of a model's future performance. Rather than mapping out detailed internal mechanisms, we systematically design and test network markers to probe structure, function links, identify prognostic indicators, and validate predictions in real-world settings. In image classification, we find that task-relevant geometric properties of in-distribution (ID) object manifolds consistently forecast poor out-of-distribution (OOD) generalization. In particular, reductions in two geometric measures, effective manifold dimensionality and utility, predict weaker OOD performance across diverse architectures, optimizers, and datasets. We apply this finding to transfer learning with ImageNet-pretrained models. We consistently find that the same geometric patterns predict OOD transfer performance more reliably than ID accuracy. This work demonstrates that representational geometry can expose hidden vulnerabilities, offering more robust guidance for model selection and AI interpretability.

Recent years, multimodal models have made remarkable strides and pave the way for intelligent browser use agents. However, when solving tasks on real world webpages in multi-turn, long-horizon trajectories, current agents still suffer from disordered action sequencing and excessive trial and error during execution. This paper introduces Recon-Act, a self-evolving multi-agent framework grounded in Reconnaissance-Action behavioral paradigm. The system comprises a Reconnaissance Team and an Action Team: the former conducts comparative analysis and tool generation, while the latter handles intent decomposition, tool orchestration, and execution. By contrasting the erroneous trajectories with successful ones, the Reconnaissance Team infers remedies, and abstracts them into a unified notion of generalized tools, either expressed as hints or as rule-based codes, and register to the tool archive in real time. The Action Team reinference the process empowered with these targeting tools, thus establishing a closed-loop training pipeline of data-tools-action-feedback. Following the 6 level implementation roadmap proposed in this work, we have currently reached Level 3 (with limited human-in-the-loop intervention). Leveraging generalized tools obtained through reconnaissance, Recon-Act substantially improves adaptability to unseen websites and solvability on long-horizon tasks, and achieves state-of-the-art performance on the challenging VisualWebArena dataset.

Latent Action Models (LAMs) enable Vision-Language-Action (VLA) systems to learn semantic action representations from large-scale unannotated data. Yet, we identify two bottlenecks of LAMs: 1) the commonly adopted end-to-end trained image encoder suffers from poor spatial understanding; 2) LAMs can be fragile when input frames are distant, leading to limited temporal perception. Such factors inevitably hinder stable and clear action modeling. To this end, we propose Farsighted-LAM, a latent action framework with geometry-aware spatial encoding and multi-scale temporal modeling, capturing structural priors and dynamic motion patterns from consecutive frames. We further propose SSM-VLA, an end-to-end VLA framework built upon Farsighted-LAM, which integrates structured perception with a visual Chain-of-Thought module to explicitly reason about environmental dynamics, enhancing decision consistency and interpretability. We validate SSM-VLA on multiple VLA tasks in both simulation and real-world settings, and achieve state-of-the-art performance. Our results demonstrate that our strategy of combining geometry-aware modeling, temporal coherence, and explicit reasoning is effective in enhancing the robustness and generalizability of embodied intelligence.

The specification of the action space plays a pivotal role in imitation-based robotic manipulation policy learning, fundamentally shaping the optimization landscape of policy learning. While recent advances have focused heavily on scaling training data and model capacity, the choice of action space remains guided by ad-hoc heuristics or legacy designs, leading to an ambiguous understanding of robotic policy design philosophies. To address this ambiguity, we conducted a large-scale and systematic empirical study, confirming that the action space does have significant and complex impacts on robotic policy learning. We dissect the action design space along temporal and spatial axes, facilitating a structured analysis of how these choices govern both policy learnability and control stability. Based on 13,000+ real-world rollouts on a bimanual robot and evaluation on 500+ trained models over four scenarios, we examine the trade-offs between absolute vs. delta representations, and joint-space vs. task-space parameterizations. Our large-scale results suggest that properly designing the policy to predict delta actions consistently improves performance, while joint-space and task-space representations offer complementary strengths, favoring control stability and generalization, respectively.

Recent advances in large language models (LLMs) have enabled the development of AI agents that exhibit increasingly human-like behaviors, including planning, adaptation, and social dynamics across diverse, interactive, and open-ended scenarios. These behaviors are not solely the product of the internal architectures of the underlying models, but emerge from their integration into agentic systems operating within specific contexts, where environmental factors, social cues, and interaction feedbacks shape behavior over time. This evolution necessitates a new scientific perspective: AI Agent Behavioral Science. Rather than focusing only on internal mechanisms, this perspective emphasizes the systematic observation of behavior, design of interventions to test hypotheses, and theory-guided interpretation of how AI agents act, adapt, and interact over time. We systematize a growing body of research across individual agent, multi-agent, and human-agent interaction settings, and further demonstrate how this perspective informs responsible AI by treating fairness, safety, interpretability, accountability, and privacy as behavioral properties. By unifying recent findings and laying out future directions, we position AI Agent Behavioral Science as a necessary complement to traditional model-centric approaches, providing essential tools for understanding, evaluating, and governing the real-world behavior of increasingly autonomous AI systems.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

We present a new approach for understanding the periodicity structure and semantics of motion datasets, independently of the morphology and skeletal structure of characters. Unlike existing methods using an overly sparse high-dimensional latent, we propose a phase manifold consisting of multiple closed curves, each corresponding to a latent amplitude. With our proposed vector quantized periodic autoencoder, we learn a shared phase manifold for multiple characters, such as a human and a dog, without any supervision. This is achieved by exploiting the discrete structure and a shallow network as bottlenecks, such that semantically similar motions are clustered into the same curve of the manifold, and the motions within the same component are aligned temporally by the phase variable. In combination with an improved motion matching framework, we demonstrate the manifold's capability of timing and semantics alignment in several applications, including motion retrieval, transfer and stylization. Code and pre-trained models for this paper are available at https://peizhuoli.github.io/walkthedog.

The present few-shot temporal action localization model can't handle the situation where videos contain multiple action instances. So the purpose of this paper is to achieve manifold action instances localization in a lengthy untrimmed query video using limited trimmed support videos. To address this challenging problem effectively, we proposed a novel solution involving a spatial-channel relation transformer with probability learning and cluster refinement. This method can accurately identify the start and end boundaries of actions in the query video, utilizing only a limited number of labeled videos. Our proposed method is adept at capturing both temporal and spatial contexts to effectively classify and precisely locate actions in videos, enabling a more comprehensive utilization of these crucial details. The selective cosine penalization algorithm is designed to suppress temporal boundaries that do not include action scene switches. The probability learning combined with the label generation algorithm alleviates the problem of action duration diversity and enhances the model's ability to handle fuzzy action boundaries. The interval cluster can help us get the final results with multiple instances situations in few-shot temporal action localization. Our model achieves competitive performance through meticulous experimentation utilizing the benchmark datasets ActivityNet1.3 and THUMOS14. Our code is readily available at https://github.com/ycwfs/FMI-TAL.

A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction. However, the parameterized way a neural network and other machine learning models use to partition the space has imperfections, e.g., the compromised interpretability for complex models, the inflexibility in decision boundary construction due to the generic character of the model, and the risk of being trapped into shortcut solutions. In contrast, although the non-parameterized models can adorably avoid or downplay these issues, they are usually insufficiently powerful either due to over-simplification or the failure to accommodate the manifold structures of data. In this context, we first propose a new type of machine learning models referred to as Manifoldron that directly derives decision boundaries from data and partitions the space via manifold structure discovery. Then, we systematically analyze the key characteristics of the Manifoldron such as manifold characterization capability and its link to neural networks. The experimental results on 4 synthetic examples, 20 public benchmark datasets, and 1 real-world application demonstrate that the proposed Manifoldron performs competitively compared to the mainstream machine learning models. We have shared our code in https://github.com/wdayang/Manifoldron for free download and evaluation.

Humanoid loco-manipulation, which integrates whole-body locomotion with dexterous manipulation, remains a fundamental challenge in robotics. Beyond whole-body coordination and balance, a central difficulty lies in understanding human instructions and translating them into coherent sequences of embodied actions. Recent advances in foundation models provide transferable multimodal representations and reasoning capabilities, yet existing efforts remain largely restricted to either locomotion or manipulation in isolation, with limited applicability to humanoid settings. In this paper, we propose Humanoid-COA, the first humanoid agent framework that integrates foundation model reasoning with an Embodied Chain-of-Action (CoA) mechanism for zero-shot loco-manipulation. Within the perception--reasoning--action paradigm, our key contribution lies in the reasoning stage, where the proposed CoA mechanism decomposes high-level human instructions into structured sequences of locomotion and manipulation primitives through affordance analysis, spatial inference, and whole-body action reasoning. Extensive experiments on two humanoid robots, Unitree H1-2 and G1, in both an open test area and an apartment environment, demonstrate that our framework substantially outperforms prior baselines across manipulation, locomotion, and loco-manipulation tasks, achieving robust generalization to long-horizon and unstructured scenarios. Project page: https://humanoid-coa.github.io/

Vision-Language Models (VLMs) frequently "hallucinate" - generate plausible yet factually incorrect statements - posing a critical barrier to their trustworthy deployment. In this work, we propose a new paradigm for diagnosing hallucinations, recasting them from static output errors into dynamic pathologies of a model's computational cognition. Our framework is grounded in a normative principle of computational rationality, allowing us to model a VLM's generation as a dynamic cognitive trajectory. We design a suite of information-theoretic probes that project this trajectory onto an interpretable, low-dimensional Cognitive State Space. Our central discovery is a governing principle we term the geometric-information duality: a cognitive trajectory's geometric abnormality within this space is fundamentally equivalent to its high information-theoretic surprisal. Hallucination detection is counts as a geometric anomaly detection problem. Evaluated across diverse settings - from rigorous binary QA (POPE) and comprehensive reasoning (MME) to unconstrained open-ended captioning (MS-COCO) - our framework achieves state-of-the-art performance. Crucially, it operates with high efficiency under weak supervision and remains highly robust even when calibration data is heavily contaminated. This approach enables a causal attribution of failures, mapping observable errors to distinct pathological states: perceptual instability (measured by Perceptual Entropy), logical-causal failure (measured by Inferential Conflict), and decisional ambiguity (measured by Decision Entropy). Ultimately, this opens a path toward building AI systems whose reasoning is transparent, auditable, and diagnosable by design.

Vision-language-action (VLA) models have shown remarkable capabilities in robotic manipulation, but their performance is sensitive to the action chunk length used during training, termed horizon. Our empirical study reveals an inherent trade-off: longer horizons provide stronger global foresight but degrade fine-grained accuracy, while shorter ones sharpen local control yet struggle on long-term tasks, implying fixed choice of single horizons being suboptimal. To mitigate the trade-off, we propose a mixture of horizons (MoH) strategy. MoH rearranges the action chunk into several segments with different horizons, processes them in parallel with a shared action transformer, and fuses outputs with a light linear gate. It has three appealing benefits. 1) MoH exploits long-term foresight and short-term precision jointly within a single model, improving both performance and generalizability to complex tasks. 2) MoH is plug-and-play for full-attention action modules with minimal training or inference overhead. 3) MoH enables dynamic inference with adaptive horizons, which selects stable actions through cross-horizon consensus, achieving 2.5times higher throughput than baselines while preserving superior performance. Extensive experiments over flow-based policies π_0, π_{0.5}, and one-step regression policy π_{reg} demonstrate that MoH yields consistent and significant gains on both simulations and real-world tasks. Notably, under mixed-task setting, π_{0.5} with MoH reaches a new state-of-the-art with 99% average success rate on LIBERO after only 30k training iterations. Project page: https://github.com/Timsty1/MixtureOfHorizons

World Action Models (WAMs) are an emerging family of policies that tie robot action generation to future-observation modeling. In this work, we focus on the joint video--action modeling paradigm, where actions and imagined future observations are co-generated along a shared denoising or flow trajectory, so that perception, prediction, and control are coupled within one generative process. Existing WAMs typically realize this paradigm with a Mixture-of-Transformers (MoT), where video and action tokens interact through shared self-attention. This architecture can in principle assign a separate timestep t_f to each predicted latent frame, yet current systems collapse this degree of freedom onto a single shared scalar t. Under the noise-as-masking view of Diffusion Forcing, this shared schedule imposes the unjustified prior that every predicted latent is equally reliable for action generation. We instead view the per-latent schedule as a learnable information-gating policy: by changing a latent frame's noise level, the policy modulates the reliability of its Key/Value contribution to the action tokens. We propose NoiseGate, which combines independent per-latent timestep sampling during backbone training, a lightweight Gating Policy Network that emits per-latent time increments during denoising, and task-reward optimization that trains the schedule policy without hand-crafted shape priors. Built on a joint video--action MoT backbone, NoiseGate delivers consistent gains on diverse RoboTwin random-scene manipulation tasks.

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce RVGP, a generalisation of GPs for learning vector signals over latent Riemannian manifolds. Our method uses positional encoding with eigenfunctions of the connection Laplacian, associated with the tangent bundle, readily derived from common graph-based approximation of data. We demonstrate that RVGP possesses global regularity over the manifold, which allows it to super-resolve and inpaint vector fields while preserving singularities. Furthermore, we use RVGP to reconstruct high-density neural dynamics derived from low-density EEG recordings in healthy individuals and Alzheimer's patients. We show that vector field singularities are important disease markers and that their reconstruction leads to a comparable classification accuracy of disease states to high-density recordings. Thus, our method overcomes a significant practical limitation in experimental and clinical applications.

Large language models (LLMs) generalize smoothly across continuous semantic spaces, yet strict logical reasoning demands the formation of discrete decision boundaries. Prevailing theories relying on linear isometric projections fail to resolve this fundamental tension. In this work, we argue that task context operates as a non-isometric dynamical operator that enforces a necessary "topological distortion." By applying Gram-Schmidt decomposition to residual-stream activations , we reveal a dual-modulation mechanism driving this process: a class-agnostic topological preservation that anchors global structure to prevent semantic collapse, and a specific algebraic divergence that directionally tears apart cross-class concepts to forge logical boundaries. We validate this geometric evolution across a gradient of tasks, from simple mapping to complex primality testing. Crucially, targeted specific vector ablation establishes a strict causal binding between this topology and model function: algebraically erasing the divergence component collapses parity classification accuracy from 100% to chance levels (38.57%). Furthermore, we uncover a three-phase layer-wise geometric dynamic and demonstrate that under social pressure prompts, models fail to generate sufficient divergence. This results in a "manifold entanglement" that geometrically explains sycophancy and hallucination. Ultimately, our findings revise the linear-isometric presumption, demonstrating that the emergence of discrete logic in LLMs is purchased at an irreducible cost of topological deformation.

Inferring physical actions from visual observations is a fundamental capability for advancing machine intelligence in the physical world. Achieving this requires large-scale, open-vocabulary video action datasets that span broad domains. We introduce Action100M, a large-scale dataset constructed from 1.2M Internet instructional videos (14.6 years of duration), yielding O(100 million) temporally localized segments with open-vocabulary action supervision and rich captions. Action100M is generated by a fully automated pipeline that (i) performs hierarchical temporal segmentation using V-JEPA 2 embeddings, (ii) produces multi-level frame and segment captions organized as a Tree-of-Captions, and (iii) aggregates evidence with a reasoning model (GPT-OSS-120B) under a multi-round Self-Refine procedure to output structured annotations (brief/detailed action, actor, brief/detailed caption). Training VL-JEPA on Action100M demonstrates consistent data-scaling improvements and strong zero-shot performance across diverse action recognition benchmarks, establishing Action100M as a new foundation for scalable research in video understanding and world modeling.

Humans are highly adaptable, swiftly switching between different modes to progressively handle different tasks, situations and contexts. In Human-object interaction (HOI) activities, these modes can be attributed to two mechanisms: (1) the large-scale consistent plan for the whole activity and (2) the small-scale children interactive actions that start and end along the timeline. While neuroscience and cognitive science have confirmed this multi-mechanism nature of human behavior, machine modeling approaches for human motion are trailing behind. While attempted to use gradually morphing structures (e.g., graph attention networks) to model the dynamic HOI patterns, they miss the expeditious and discrete mode-switching nature of the human motion. To bridge that gap, this work proposes to model two concurrent mechanisms that jointly control human motion: the Persistent process that runs continually on the global scale, and the Transient sub-processes that operate intermittently on the local context of the human while interacting with objects. These two mechanisms form an interactive Persistent-Transient Duality that synergistically governs the activity sequences. We model this conceptual duality by a parent-child neural network of Persistent and Transient channels with a dedicated neural module for dynamic mechanism switching. The framework is trialed on HOI motion forecasting. On two rich datasets and a wide variety of settings, the model consistently delivers superior performances, proving its suitability for the challenge.

In robotic manipulation, vision-language-action (VLA) models have emerged as a promising paradigm for learning generalizable and scalable robot policies. Most existing VLA frameworks rely on standard supervised objectives, typically cross-entropy for discrete actions and mean squared error (MSE) for continuous action regression, which impose strong pointwise constraints on individual predictions. In this work, we focus on continuous-action VLA models and move beyond conventional MSE-based regression by reshaping action error distributions during training. Drawing on information-theoretic principles, we introduce Minimum Error Entropy (MEE) into modern VLA architectures and propose a trajectory-level MEE objective, together with two weighted variants, combined with MSE for continuous-action VLA training. We evaluate our approaches across standard, few-shot, and noisy settings on multiple representative VLA architectures, using simulation benchmarks such as LIBERO and SimplerEnv as well as real-world robotic manipulation tasks. Experimental results demonstrate consistent improvements in success rates and robustness across these settings. Under imbalanced data regimes, the gains persist within a well-characterized operating range, while incurring negligible additional training cost and no impact on inference efficiency. We further provide theoretical analyses that explain why MEE-based supervision is effective and characterize its practical range. Project Page: https://cognition2actionlab.github.io/VLA-TMEE.github.io/

Action localization networks are often structured as a feature encoder sub-network and a localization sub-network, where the feature encoder learns to transform an input video to features that are useful for the localization sub-network to generate reliable action proposals. While some of the encoded features may be more useful for generating action proposals, prior action localization approaches do not include any attention mechanism that enables the localization sub-network to attend more to the more important features. In this paper, we propose a novel attention mechanism, the Class Semantics-based Attention (CSA), that learns from the temporal distribution of semantics of action classes present in an input video to find the importance scores of the encoded features, which are used to provide attention to the more useful encoded features. We demonstrate on two popular action detection datasets that incorporating our novel attention mechanism provides considerable performance gains on competitive action detection models (e.g., around 6.2% improvement over BMN action detection baseline to obtain 47.5% mAP on the THUMOS-14 dataset), and a new state-of-the-art of 36.25% mAP on the ActivityNet v1.3 dataset. Further, the CSA localization model family which includes BMN-CSA, was part of the second-placed submission at the 2021 ActivityNet action localization challenge. Our attention mechanism outperforms prior self-attention modules such as the squeeze-and-excitation in action detection task. We also observe that our attention mechanism is complementary to such self-attention modules in that performance improvements are seen when both are used together.

Human motion generation is often learned in Euclidean spaces, although valid motions follow structured non-Euclidean geometry. We present Riemannian Motion Generation (RMG), a unified framework that represents motion on a product manifold and learns dynamics via Riemannian flow matching. RMG factorizes motion into several manifold factors, yielding a scale-free representation with intrinsic normalization, and uses geodesic interpolation, tangent-space supervision, and manifold-preserving ODE integration for training and sampling. On HumanML3D, RMG achieves state-of-the-art FID in the HumanML3D format (0.043) and ranks first on all reported metrics under the MotionStreamer format. On MotionMillion, it also surpasses strong baselines (FID 5.6, R@1 0.86). Ablations show that the compact T+R (translation + rotations) representation is the most stable and effective, highlighting geometry-aware modeling as a practical and scalable route to high-fidelity motion generation.

Latent action representations learned from unlabeled videos have recently emerged as a promising paradigm for pretraining vision-language-action (VLA) models without explicit robot action supervision. However, latent actions derived solely from RGB observations primarily encode appearance-driven dynamics and lack explicit 3D geometric structure, which is essential for precise and contact-rich manipulation. To address this limitation, we introduce UniLACT, a transformer-based VLA model that incorporates geometric structure through depth-aware latent pretraining, enabling downstream policies to inherit stronger spatial priors. To facilitate this process, we propose UniLARN, a unified latent action learning framework based on inverse and forward dynamics objectives that learns a shared embedding space for RGB and depth while explicitly modeling their cross-modal interactions. This formulation produces modality-specific and unified latent action representations that serve as pseudo-labels for the depth-aware pretraining of UniLACT. Extensive experiments in both simulation and real-world settings demonstrate the effectiveness of depth-aware unified latent action representations. UniLACT consistently outperforms RGB-based latent action baselines under in-domain and out-of-domain pretraining regimes, as well as on both seen and unseen manipulation tasks.

In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and performance of neural networks. We pull together major strands of ongoing research in deep learning theory and identify five growing bodies of work that point toward such a theory: (a) solvable idealized settings that provide intuition for learning dynamics in realistic systems; (b) tractable limits that reveal insights into fundamental learning phenomena; (c) simple mathematical laws that capture important macroscopic observables; (d) theories of hyperparameters that disentangle them from the rest of the training process, leaving simpler systems behind; and (e) universal behaviors shared across systems and settings which clarify which phenomena call for explanation. Taken together, these bodies of work share certain broad traits: they are concerned with the dynamics of the training process; they primarily seek to describe coarse aggregate statistics; and they emphasize falsifiable quantitative predictions. We argue that the emerging theory is best thought of as a mechanics of the learning process, and suggest the name learning mechanics. We discuss the relationship between this mechanics perspective and other approaches for building a theory of deep learning, including the statistical and information-theoretic perspectives. In particular, we anticipate a symbiotic relationship between learning mechanics and mechanistic interpretability. We also review and address common arguments that fundamental theory will not be possible or is not important. We conclude with a portrait of important open directions in learning mechanics and advice for beginners. We host further introductory materials, perspectives, and open questions at learningmechanics.pub.

World models have emerged as promising neural simulators for autonomous driving, with the potential to supplement scarce real-world data and enable closed-loop evaluations. However, current research primarily evaluates these models based on visual realism or downstream task performance, with limited focus on fidelity to specific action instructions - a crucial property for generating targeted simulation scenes. Although some studies address action fidelity, their evaluations rely on closed-source mechanisms, limiting reproducibility. To address this gap, we develop an open-access evaluation framework, ACT-Bench, for quantifying action fidelity, along with a baseline world model, Terra. Our benchmarking framework includes a large-scale dataset pairing short context videos from nuScenes with corresponding future trajectory data, which provides conditional input for generating future video frames and enables evaluation of action fidelity for executed motions. Furthermore, Terra is trained on multiple large-scale trajectory-annotated datasets to enhance action fidelity. Leveraging this framework, we demonstrate that the state-of-the-art model does not fully adhere to given instructions, while Terra achieves improved action fidelity. All components of our benchmark framework will be made publicly available to support future research.

We present a method for training multi-task vision-language robotic diffusion policies that reduces training time and memory usage by an order of magnitude. This improvement arises from a previously underexplored distinction between action diffusion and the image diffusion techniques that inspired it: image generation targets are high-dimensional, while robot actions lie in a much lower-dimensional space. Meanwhile, the vision-language conditions for action generation remain high-dimensional. Our approach, Mini-Diffuser, exploits this asymmetry by introducing Level-2 minibatching, which pairs multiple noised action samples with each vision-language condition, instead of the conventional one-to-one sampling strategy. To support this batching scheme, we introduce architectural adaptations to the diffusion transformer that prevent information leakage across samples while maintaining full conditioning access. In RLBench simulations, Mini-Diffuser achieves 95\% of the performance of state-of-the-art multi-task diffusion policies, while using only 5\% of the training time and 7\% of the memory. Real-world experiments further validate that Mini-Diffuser preserves the key strengths of diffusion-based policies, including the ability to model multimodal action distributions and produce behavior conditioned on diverse perceptual inputs. Code available at github.com/utomm/mini-diffuse-actor.

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical systems acting on the latent manifold. Specifically, we show that autoencoder models implicitly define a latent vector field on the manifold, derived by iteratively applying the encoding-decoding map, without any additional training. We observe that standard training procedures introduce inductive biases that lead to the emergence of attractor points within this vector field. Drawing on this insight, we propose to leverage the vector field as a representation for the network, providing a novel tool to analyze the properties of the model and the data. This representation enables to: (i) analyze the generalization and memorization regimes of neural models, even throughout training; (ii) extract prior knowledge encoded in the network's parameters from the attractors, without requiring any input data; (iii) identify out-of-distribution samples from their trajectories in the vector field. We further validate our approach on vision foundation models, showcasing the applicability and effectiveness of our method in real-world scenarios.

A plausible scene evolution depends on the maneuver being considered, while a good maneuver depends on how the scene may evolve. Existing World Action Models (WAMs) largely miss this reciprocity, treating world prediction and action generation as either isolated parallel branches or rigid predict-then-plan pipelines. We formalize this perspective as World-Action Interactive Models (WAIMs), and instantiate it in autonomous driving with DAWN (Denoising Actions and World iNteractive model), a simple yet strong latent generative baseline. DAWN operates in a compact semantic latent space and couples a World Predictor with a World-Conditioned Action Denoiser: the predicted world hypothesis conditions action denoising, while the denoised action hypothesis is fed back to update the world prediction, so that both are recursively refined during inference. Rather than eliminating test-time world evolution altogether or rolling out the full future in pixel space, DAWN performs a short explicit latent rollout that is sufficient to support long-horizon trajectory generation in complex interactive scenes. Experiments show that DAWN achieves strong planning performance and favorable safety-related results across multiple autonomous driving benchmarks. More broadly, our results suggest that interactive world-action generation is a principled path toward truly actionable world models.

We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces (d=128), transformer training trajectories rapidly collapse onto low-dimensional execution manifolds of dimension 3--4. This dimensional collapse is robust across random seeds and moderate task difficulties, though the orientation of the manifold in parameter space varies between runs. We demonstrate that this geometric structure underlies several empirically observed phenomena: (1) sharp attention concentration emerges as saturation along routing coordinates within the execution manifold, (2) SGD commutators are preferentially aligned with the execution subspace (up to 10times random baseline) early in training, with >92% of non-commutativity confined to orthogonal staging directions and this alignment decreasing as training converges, and (3) sparse autoencoders capture auxiliary routing structure but fail to isolate execution itself, which remains distributed across the low-dimensional manifold. Our results suggest a unifying geometric framework for understanding transformer learning, where the vast majority of parameters serve to absorb optimization interference while core computation occurs in a dramatically reduced subspace. These findings have implications for interpretability, training curriculum design, and understanding the role of overparameterization in neural network learning.

Enabling Vision-Language-Action (VLA) models to "think before acting" via Chain-of-Thought (CoT) is a promising path to overcoming the data-hungry nature of end-to-end robot policies. However, progress is stalled by a fundamental conflict: existing models use a single autoregressive decoder for both sequential CoT reasoning and high-dimensional, parallelizable robot actions. This architectural mismatch degrades motor control and fails to forge a strong causal link between thought and action. We introduce DeepThinkVLA, which resolves this conflict through a tightly integrated architecture and training strategy. Architecturally, our hybrid-attention decoder generates sequential CoT with causal attention and then switches to bidirectional attention for fast, parallel decoding of action vectors. This design is complemented by a two-stage training pipeline: we first use Supervised Fine-Tuning (SFT) to teach the model foundational reasoning, then apply Reinforcement Learning (RL) with task-success rewards to causally align the full reasoning-action sequence with desired outcomes. This synergy leads to state-of-the-art performance, achieving a 97.0% success rate on the LIBERO benchmark. Our ablations confirm the design's effectiveness: the hybrid architecture alone outperforms standard decoders by 15.5%, and the final RL stage provides a crucial 2% boost to secure top performance.

Self-supervised learning (SSL) has revolutionized visual representation learning, but has not achieved the robustness of human vision. A reason for this could be that SSL does not leverage all the data available to humans during learning. When learning about an object, humans often purposefully turn or move around objects and research suggests that these interactions can substantially enhance their learning. Here we explore whether such object-related actions can boost SSL. For this, we extract the actions performed to change from one ego-centric view of an object to another in four video datasets. We then introduce a new loss function to learn visual and action embeddings by aligning the performed action with the representations of two images extracted from the same clip. This permits the performed actions to structure the latent visual representation. Our experiments show that our method consistently outperforms previous methods on downstream category recognition. In our analysis, we find that the observed improvement is associated with a better viewpoint-wise alignment of different objects from the same category. Overall, our work demonstrates that embodied interactions with objects can improve SSL of object categories.

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the Pin(p,q,r) group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable geometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

Although Vision-Language Models (VLM) have demonstrated impressive planning and reasoning capabilities, translating these abilities into the physical world introduces significant challenges. Conventional Vision-Language-Action (VLA) models, which integrate reasoning and action into a monolithic architecture, generalize poorly because they are constrained by scarce, narrow-domain data. While recent dual-system approaches attempt to decouple "thinking" from "acting", they are often constrained by semantic ambiguities within the action module. This ambiguity makes large-scale, cross-task training infeasible. Consequently, these systems typically necessitate fine-tuning on newly collected data when deployed to novel environments, and the cooperation mechanism between the two systems remains ill-defined. To address these limitations, we introduce, for the first time, a framework centered around a generalizable action expert. Our approach utilizes sparse 3D trajectories as an intermediate representation, effectively bridging the high-level planning capabilities of the VLM with the low-level physical action module. During the planning phase, the VLM is only required to generate coarse 3D waypoints. These waypoints are then processed by our generalizable action expert, which refines them into dense, executable action sequences by sampling real-time point cloud observations of the environment. To promote training efficiency and robust generalization, we introduce a novel "Action Pre-training, Pointcloud Fine-tuning" paradigm. Our method combines the broad generalization capabilities of VLMs in visual understanding and planning with the fine-grained, action-level generalization of action expert.

In our work we not explicitly hint that it is a misconception to think that humans learn fast. Learning process takes time. Babies start learning to move in the restricted liquid area called placenta. Children often are limited by underdeveloped body. Even adults are not allowed to participate in complex competitions right away. However, with robots, when learning from scratch, we often don't have the privilege of waiting for dozen millions of steps. "Swaddling" regularization is responsible for restraining an agent in rapid but unstable development penalizing action strength in a specific way not affecting actions directly. The Symphony, Transitional-policy Deterministic Actor and Critic algorithm, is a concise combination of different ideas for possibility of training humanoid robots from scratch with Sample Efficiency, Sample Proximity and Safety of Actions in mind. It is no secret that continuous increase in Gaussian noise without appropriate smoothing is harmful for motors and gearboxes. Compared to Stochastic algorithms, we set a limited parametric noise and promote a reduced strength of actions, safely increasing entropy, since the actions are kind of immersed in weaker noise. When actions require more extreme values, actions rise above the weak noise. Training becomes empirically much safer for both the environment around and the robot's mechanisms. We use Fading Replay Buffer: using a fixed formula containing the hyperbolic tangent, we adjust the batch sampling probability: the memory contains a recent memory and a long-term memory trail. Fading Replay Buffer allows us to use Temporal Advantage when we improve the current Critic Network prediction compared to the exponential moving average. Temporal Advantage allows us to update Actor and Critic in one pass, as well as combine Actor and Critic in one Object and implement their Losses in one line.

Role-based learning holds the promise of achieving scalable multi-agent learning by decomposing complex tasks using roles. However, it is largely unclear how to efficiently discover such a set of roles. To solve this problem, we propose to first decompose joint action spaces into restricted role action spaces by clustering actions according to their effects on the environment and other agents. Learning a role selector based on action effects makes role discovery much easier because it forms a bi-level learning hierarchy -- the role selector searches in a smaller role space and at a lower temporal resolution, while role policies learn in significantly reduced primitive action-observation spaces. We further integrate information about action effects into the role policies to boost learning efficiency and policy generalization. By virtue of these advances, our method (1) outperforms the current state-of-the-art MARL algorithms on 10 of the 14 scenarios that comprise the challenging StarCraft II micromanagement benchmark and (2) achieves rapid transfer to new environments with three times the number of agents. Demonstrative videos are available at https://sites.google.com/view/rode-marl .

Despite strong results on recognition and segmentation, current 3D visual pre-training methods often underperform on robotic manipulation. We attribute this gap to two factors: the lack of state-action-state dynamics modeling and the unnecessary redundancy of explicit geometric reconstruction. We introduce AFRO, a self-supervised framework that learns dynamics-aware 3D representations without action or reconstruction supervision. AFRO casts state prediction as a generative diffusion process and jointly models forward and inverse dynamics in a shared latent space to capture causal transition structure. To prevent feature leakage in action learning, we employ feature differencing and inverse-consistency supervision, improving the quality and stability of visual features. When combined with Diffusion Policy, AFRO substantially increases manipulation success rates across 16 simulated and 4 real-world tasks, outperforming existing pre-training approaches. The framework also scales favorably with data volume and task complexity. Qualitative visualizations indicate that AFRO learns semantically rich, discriminative features, offering an effective pre-training solution for 3D representation learning in robotics. Project page: https://kolakivy.github.io/AFRO/

We present a framework for visual action planning of complex manipulation tasks with high-dimensional state spaces, focusing on manipulation of deformable objects. We propose a Latent Space Roadmap (LSR) for task planning which is a graph-based structure globally capturing the system dynamics in a low-dimensional latent space. Our framework consists of three parts: (1) a Mapping Module (MM) that maps observations given in the form of images into a structured latent space extracting the respective states as well as generates observations from the latent states, (2) the LSR which builds and connects clusters containing similar states in order to find the latent plans between start and goal states extracted by MM, and (3) the Action Proposal Module that complements the latent plan found by the LSR with the corresponding actions. We present a thorough investigation of our framework on simulated box stacking and rope/box manipulation tasks, and a folding task executed on a real robot.

We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general manifold latent spaces using training strategies related to Variational Autoencoders (VAEs). Our methods are referred to as Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders and decoders for the system states and evolution based on deep neural network architectures that include general Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and other architectures. Motivated by problems arising in parameterized PDEs and physics, we investigate the performance of our methods on tasks for learning reduced dimensional representations of the nonlinear Burgers Equations, Constrained Mechanical Systems, and spatial fields of Reaction-Diffusion Systems. GD-VAEs provide methods that can be used to obtain representations in manifold latent spaces for diverse learning tasks involving dynamics.

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

Exploration is a key problem in reinforcement learning, since agents can only learn from data they acquire in the environment. With that in mind, maintaining a population of agents is an attractive method, as it allows data be collected with a diverse set of behaviors. This behavioral diversity is often boosted via multi-objective loss functions. However, those approaches typically leverage mean field updates based on pairwise distances, which makes them susceptible to cycling behaviors and increased redundancy. In addition, explicitly boosting diversity often has a detrimental impact on optimizing already fruitful behaviors for rewards. As such, the reward-diversity trade off typically relies on heuristics. Finally, such methods require behavioral representations, often handcrafted and domain specific. In this paper, we introduce an approach to optimize all members of a population simultaneously. Rather than using pairwise distance, we measure the volume of the entire population in a behavioral manifold, defined by task-agnostic behavioral embeddings. In addition, our algorithm Diversity via Determinants (DvD), adapts the degree of diversity during training using online learning techniques. We introduce both evolutionary and gradient-based instantiations of DvD and show they effectively improve exploration without reducing performance when better exploration is not required.

Vision-language-action (VLA) models aim to understand natural language instructions and visual observations and to execute corresponding actions as an embodied agent. Recent work integrates future images into the understanding-acting loop, yielding unified VLAs that jointly understand, generate, and act -- reading text and images and producing future images and actions. However, these models either rely on external experts for modality unification or treat image generation and action prediction as separate processes, limiting the benefits of direct synergy between these tasks. Our core philosophy is to optimize generation and action jointly through a synchronous denoising process, where the iterative refinement enables actions to evolve from initialization, under constant and sufficient visual guidance. We ground this philosophy in our proposed Unified Diffusion VLA and Joint Discrete Denoising Diffusion Process (JD3P), which is a joint diffusion process that integrates multiple modalities into a single denoising trajectory to serve as the key mechanism enabling understanding, generation, and acting to be intrinsically synergistic. Our model and theory are built on a unified tokenized space of all modalities and a hybrid attention mechanism. We further propose a two-stage training pipeline and several inference-time techniques that optimize performance and efficiency. Our approach achieves state-of-the-art performance on benchmarks such as CALVIN, LIBERO, and SimplerEnv with 4times faster inference than autoregressive methods, and we demonstrate its effectiveness through in-depth analysis and real-world evaluations. Our project page is available at https://irpn-eai.github.io/UD-VLA.github.io/.

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.

Latent Action Models (LAMs) enable the learning of world models from unlabeled video by inferring abstract actions between consecutive frames. However, LAMs face a fundamental trade-off between action abstraction and generation fidelity. Existing methods typically circumvent this issue by using two-stage training with pre-trained world models or by limiting predictions to optical flow. In this paper, we introduce DiLA, a novel Disentangled Latent Action world model that aims to resolve this trade-off via content-structure disentanglement. Our key insight is that disentanglement and latent action learning are co-evolving: the predictive bottleneck inherent in latent action learning serves as a driving force for disentanglement, compelling the model to distill spatial layouts into the structure pathway while offloading visual details to a separate content pathway for generation. This synergy yields a continuous, semantically structured latent action space without compromising generative quality. DiLA achieves superior results in video generation quality, action transfer, visual planning, and manifold interpretability. These findings establish DiLA as a unified framework that simultaneously achieves high-level action abstraction and high-fidelity generation, advancing the frontier of self-supervised world model learning.

Teaching robots to autonomously complete everyday tasks remains a challenge. Imitation Learning (IL) is a powerful approach that imbues robots with skills via demonstrations, but is limited by the labor-intensive process of collecting teleoperated robot data. Human videos offer a scalable alternative, but it remains difficult to directly train IL policies from them due to the lack of robot action labels. To address this, we propose to represent actions as short-horizon 2D trajectories on an image. These actions, or motion tracks, capture the predicted direction of motion for either human hands or robot end-effectors. We instantiate an IL policy called Motion Track Policy (MT-pi) which receives image observations and outputs motion tracks as actions. By leveraging this unified, cross-embodiment action space, MT-pi completes tasks with high success given just minutes of human video and limited additional robot demonstrations. At test time, we predict motion tracks from two camera views, recovering 6DoF trajectories via multi-view synthesis. MT-pi achieves an average success rate of 86.5% across 4 real-world tasks, outperforming state-of-the-art IL baselines which do not leverage human data or our action space by 40%, and generalizes to scenarios seen only in human videos. Code and videos are available on our website https://portal-cornell.github.io/motion_track_policy/.

Sequential recommendation increasingly employs latent multi-step reasoning to enhance test-time computation. Despite empirical gains, existing approaches largely drive intermediate reasoning states via target-dominant objectives without imposing explicit feasibility constraints. This results in latent drift, where reasoning trajectories deviate into implausible regions. We argue that effective recommendation reasoning should instead be viewed as navigation on a collaborative manifold rather than free-form latent refinement. To this end, we propose ManCAR (Manifold-Constrained Adaptive Reasoning), a principled framework that grounds reasoning within the topology of a global interaction graph. ManCAR constructs a local intent prior from the collaborative neighborhood of a user's recent actions, represented as a distribution over the item simplex. During training, the model progressively aligns its latent predictive distribution with this prior, forcing the reasoning trajectory to remain within the valid manifold. At test time, reasoning proceeds adaptively until the predictive distribution stabilizes, avoiding over-refinement. We provide a variational interpretation of ManCAR to theoretically validate its drift-prevention and adaptive test-time stopping mechanisms. Experiments on seven benchmarks demonstrate that ManCAR consistently outperforms state-of-the-art baselines, achieving up to a 46.88% relative improvement w.r.t. NDCG@10. Our code is available at https://github.com/FuCongResearchSquad/ManCAR.

Real-time execution is crucial for deploying Vision-Language-Action (VLA) models in the physical world. Existing asynchronous inference methods primarily optimize trajectory smoothness, but neglect the critical latency in reacting to environmental changes. By rethinking the notion of reaction in action chunking policies, this paper presents a systematic analysis of the factors governing reaction time. We show that reaction time follows a uniform distribution determined jointly by the Time to First Action (TTFA) and the execution horizon. Moreover, we reveal that the standard practice of applying a constant schedule in flow-based VLAs can be inefficient and forces the system to complete all sampling steps before any movement can start, forming the bottleneck in reaction latency. To overcome this issue, we propose Fast Action Sampling for ImmediaTE Reaction (FASTER). By introducing a Horizon-Aware Schedule, FASTER adaptively prioritizes near-term actions during flow sampling, compressing the denoising of the immediate reaction by tenfold (e.g., in π_{0.5} and X-VLA) into a single step, while preserving the quality of long-horizon trajectory. Coupled with a streaming client-server pipeline, FASTER substantially reduces the effective reaction latency on real robots, especially when deployed on consumer-grade GPUs. Real-world experiments, including a highly dynamic table tennis task, prove that FASTER unlocks unprecedented real-time responsiveness for generalist policies, enabling rapid generation of accurate and smooth trajectories.

We study the variance of stochastic policy gradients (SPGs) with many action samples per state. We derive a many-actions optimality condition, which determines when many-actions SPG yields lower variance as compared to a single-action agent with proportionally extended trajectory. We propose Model-Based Many-Actions (MBMA), an approach leveraging dynamics models for many-actions sampling in the context of SPG. MBMA addresses issues associated with existing implementations of many-actions SPG and yields lower bias and comparable variance to SPG estimated from states in model-simulated rollouts. We find that MBMA bias and variance structure matches that predicted by theory. As a result, MBMA achieves improved sample efficiency and higher returns on a range of continuous action environments as compared to model-free, many-actions, and model-based on-policy SPG baselines.

A hallmark of life on Earth is the ability of agents to exert causal power and be drivers of subsequent events. This is key to cognition at all scales. Causal emergence, measuring the degree to which an agent exerts unique predictive power on its future, is one consequence of causal power. Indeed, recent discoveries have shown that biological agents, even minimal ones, increase their causal emergence after learning new memories. However, there is a major knowledge gap regarding how causally emergent artificial agents are. We focused on Reinforcement Learning (RL) of neural-network agents across an array of environmental conditions, encompassing different algorithms, agent architectures, and six environments arranged on a complexity spectrum. For consistency, we computed the causal emergence of their latent-space representations over their lifetimes. We used the recently proposed ΦID to estimate causal emergence and tested how it related to learning performance. Our results suggested a Causally Emergent Alignment Hypothesis: successful agents exhibited causal emergence that was consistently predictive of final reward early in training and whose representational dynamics aligned with reward improvement in most tasks. This idea suggests that causal emergence may be a previously undisclosed axis of reorganization of neural representations in RL agents, with the potential to establish causal relationships and interventions that will lead to better RL agents. Our work also highlights the alignment between causal emergence and learning as another way biological and artificial creatures compare.

Leveraging diverse robotic data for pretraining remains a critical challenge. Existing methods typically model the dataset's action distribution using simple observations as inputs. However, these inputs are often incomplete, resulting in a dispersed conditional action distribution-an issue we refer to as coordinate system chaos and state chaos. This inconsistency significantly hampers pretraining efficiency. To address this, we propose 4D-VLA, a novel approach that effectively integrates 4D information into the input to mitigate these sources of chaos. Our model introduces depth and temporal information into visual features with sequential RGB-D inputs, aligning the coordinate systems of the robot and the scene. This alignment endows the model with strong spatiotemporal reasoning capabilities while minimizing training overhead. Additionally, we introduce memory bank sampling, a frame sampling strategy designed to extract informative frames from historical images, further improving effectiveness and efficiency. Experimental results demonstrate that our pretraining method and architectural components substantially enhance model performance. In both simulated and real-world experiments, our model achieves a significant increase in success rate over OpenVLA. To further assess spatial perception and generalization to novel views, we introduce MV-Bench, a multi-view simulation benchmark. Our model consistently outperforms existing methods, demonstrating stronger spatial understanding and adaptability.

The free energy principle, and its corollary active inference, constitute a bio-inspired theory that assumes biological agents act to remain in a restricted set of preferred states of the world, i.e., they minimize their free energy. Under this principle, biological agents learn a generative model of the world and plan actions in the future that will maintain the agent in an homeostatic state that satisfies its preferences. This framework lends itself to being realized in silico, as it comprehends important aspects that make it computationally affordable, such as variational inference and amortized planning. In this work, we investigate the tool of deep learning to design and realize artificial agents based on active inference, presenting a deep-learning oriented presentation of the free energy principle, surveying works that are relevant in both machine learning and active inference areas, and discussing the design choices that are involved in the implementation process. This manuscript probes newer perspectives for the active inference framework, grounding its theoretical aspects into more pragmatic affairs, offering a practical guide to active inference newcomers and a starting point for deep learning practitioners that would like to investigate implementations of the free energy principle.

Agentic AI systems increasingly operate in shared social environments where they exchange information, instructions, and behavioral cues. However, little empirical evidence exists on how such agents regulate one another in the absence of human participants or centralized moderation. In this work, we present an empirical analysis of OpenClaw agents interacting on Moltbook, an agent-only social network. Analyzing 39,026 posts and 5,712 comments produced by 14,490 agents, we quantify the prevalence of action-inducing instruction sharing using a lexicon-based Action-Inducing Risk Score (AIRS), and examine how other agents respond to such content. We find that 18.4% of posts contain action-inducing language, indicating that instruction sharing is a routine behavior in this environment. While most social responses are neutral, posts containing actionable instructions are significantly more likely to elicit norm-enforcing replies that caution against unsafe or risky behavior, compared to non-instructional posts. Importantly, toxic responses remain rare across both conditions. These results suggest that OpenClaw agents exhibit selective social regulation, whereby potentially risky instructions are more likely to be challenged than neutral content, despite the absence of human oversight. Our findings provide early empirical evidence of emergent normative behavior in agent-only social systems and highlight the importance of studying social dynamics alongside technical safeguards in agentic AI ecosystems.

Latent Action Models (LAMs) learn to extract action-relevant representations solely from raw observations, enabling reinforcement learning from unlabelled videos and significantly scaling available training data. However, LAMs face a critical challenge in disentangling action-relevant features from action-correlated noise (e.g., background motion). Failing to filter these distractors causes LAMs to capture spurious correlations and build sub-optimal latent action spaces. In this paper, we introduce MaskLAM -- a lightweight modification to LAM training to mitigate this issue by incorporating visual agent segmentation. MaskLAM utilises segmentation masks from pretrained foundation models to weight the LAM reconstruction loss, thereby prioritising salient information over background elements while requiring no architectural modifications. We demonstrate the effectiveness of our method on continuous-control MuJoCo tasks, modified with action-correlated background noise. Our approach yields up to a 4x increase in accrued rewards compared to standard baselines and a 3x improvement in the latent action quality, as evidenced by linear probe evaluation.

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances in the theoretical understanding of neural networks, we study how a randomly initialized neural network with piece-wise linear activation splits the data manifold into regions where the neural network behaves as a linear function. We derive bounds on the density of boundary of linear regions and the distance to these boundaries on the data manifold. This leads to insights into the expressivity of randomly initialized deep neural networks on non-Euclidean data sets. We empirically corroborate our theoretical results using a toy supervised learning problem. Our experiments demonstrate that number of linear regions varies across manifolds and the results hold with changing neural network architectures. We further demonstrate how the complexity of linear regions is different on the low dimensional manifold of images as compared to the Euclidean space, using the MetFaces dataset.

We revisit a basic question in sequence modeling: is explicit self-attention actually necessary for strong performance and reasoning? We argue that standard multi-head attention is best seen as a form of tensor lifting: hidden vectors are mapped into a high-dimensional space of pairwise interactions, and learning proceeds by constraining this lifted tensor through gradient descent. This mechanism is extremely expressive but mathematically opaque, because after many layers it becomes very hard to describe the model with a small family of explicit invariants. To explore an alternative, we propose an attention-free architecture based on Grassmann flows. Instead of forming an L by L attention matrix, our Causal Grassmann layer (i) linearly reduces token states, (ii) encodes local token pairs as two-dimensional subspaces on a Grassmann manifold via Plucker coordinates, and (iii) fuses these geometric features back into the hidden states through gated mixing. Information therefore propagates by controlled deformations of low-rank subspaces over multi-scale local windows, so the core computation lives on a finite-dimensional manifold rather than in an unstructured tensor space. On the Wikitext-2 language modeling benchmark, purely Grassmann-based models with 13 to 18 million parameters achieve validation perplexities within about 10 to 15 percent of size-matched Transformers. On the SNLI natural language inference task, a Grassmann-Plucker head on top of DistilBERT slightly outperforms a Transformer head, with best validation and test accuracies of 0.8550 and 0.8538 compared to 0.8545 and 0.8511. We analyze the complexity of Grassmann mixing, show linear scaling in sequence length for fixed rank, and argue that such manifold-based designs offer a more structured route toward geometric and invariant-based interpretations of neural reasoning.

How does the brain predict physical outcomes while acting in the world? Machine learning world models compress visual input into latent spaces, discarding the spatial structure that characterizes sensory cortex. We propose isomorphic world models: architectures preserving sensory topology so that physics prediction becomes geometric propagation rather than abstract state transition. We implement this using neural fields with motor-gated channels, where activity evolves through local lateral connectivity and motor commands multiplicatively modulate specific populations. Three experiments support this approach: (1) local connectivity is sufficient to learn ballistic physics, with predictions traversing intermediate locations rather than "teleporting"; (2) policies trained entirely in imagination transfer to real physics at nearly twice the rate of latent-space alternatives; and (3) motor-gated channels spontaneously develop body-selective encoding through visuomotor prediction alone. These findings suggest intuitive physics and body schema may share a common origin in spatially structured neural dynamics.

Scaling action-controllable world models is limited by the scarcity of action labels. While latent action learning promises to extract control interfaces from unlabeled video, learned latents often fail to transfer across contexts: they entangle scene-specific cues and lack a shared coordinate system. This occurs because standard objectives operate only within each clip, providing no mechanism to align action semantics across contexts. Our key insight is that although actions are unobserved, their semantic effects are observable and can serve as a shared reference. We introduce SeqΔ-REPA, a sequence-level control-effect alignment objective that anchors integrated latent action to temporal feature differences from a frozen, self-supervised video encoder. Building on this, we present Olaf-World, a pipeline that pretrains action-conditioned video world models from large-scale passive video. Extensive experiments demonstrate that our method learns a more structured latent action space, leading to stronger zero-shot action transfer and more data-efficient adaptation to new control interfaces than state-of-the-art baselines.

Learning to predict agent motions with relationship reasoning is important for many applications. In motion prediction tasks, maintaining motion equivariance under Euclidean geometric transformations and invariance of agent interaction is a critical and fundamental principle. However, such equivariance and invariance properties are overlooked by most existing methods. To fill this gap, we propose EqMotion, an efficient equivariant motion prediction model with invariant interaction reasoning. To achieve motion equivariance, we propose an equivariant geometric feature learning module to learn a Euclidean transformable feature through dedicated designs of equivariant operations. To reason agent's interactions, we propose an invariant interaction reasoning module to achieve a more stable interaction modeling. To further promote more comprehensive motion features, we propose an invariant pattern feature learning module to learn an invariant pattern feature, which cooperates with the equivariant geometric feature to enhance network expressiveness. We conduct experiments for the proposed model on four distinct scenarios: particle dynamics, molecule dynamics, human skeleton motion prediction and pedestrian trajectory prediction. Experimental results show that our method is not only generally applicable, but also achieves state-of-the-art prediction performances on all the four tasks, improving by 24.0/30.1/8.6/9.2%. Code is available at https://github.com/MediaBrain-SJTU/EqMotion.

Vision-Language-Action (VLA) models are driving a revolution in robotics, enabling machines to understand instructions and interact with the physical world. This field is exploding with new models and datasets, making it both exciting and challenging to keep pace with. This survey offers a clear and structured guide to the VLA landscape. We design it to follow the natural learning path of a researcher: we start with the basic Modules of any VLA model, trace the history through key Milestones, and then dive deep into the core Challenges that define recent research frontier. Our main contribution is a detailed breakdown of the five biggest challenges in: (1) Representation, (2) Execution, (3) Generalization, (4) Safety, and (5) Dataset and Evaluation. This structure mirrors the developmental roadmap of a generalist agent: establishing the fundamental perception-action loop, scaling capabilities across diverse embodiments and environments, and finally ensuring trustworthy deployment-all supported by the essential data infrastructure. For each of them, we review existing approaches and highlight future opportunities. We position this paper as both a foundational guide for newcomers and a strategic roadmap for experienced researchers, with the dual aim of accelerating learning and inspiring new ideas in embodied intelligence. A live version of this survey, with continuous updates, is maintained on our https://suyuz1.github.io/Survery/{project page}.

Modeling and generating human reactions poses a significant challenge with broad applications for computer vision and human-computer interaction. Existing methods either treat multiple individuals as a single entity, directly generating interactions, or rely solely on one person's motion to generate the other's reaction, failing to integrate the rich semantic information that underpins human interactions. Yet, these methods often fall short in adaptive responsiveness, i.e., the ability to accurately respond to diverse and dynamic interaction scenarios. Recognizing this gap, our work introduces an approach tailored to address the limitations of existing models by focusing on text-driven human reaction generation. Our model specifically generates realistic motion sequences for individuals that responding to the other's actions based on a descriptive text of the interaction scenario. The goal is to produce motion sequences that not only complement the opponent's movements but also semantically fit the described interactions. To achieve this, we present MoReact, a diffusion-based method designed to disentangle the generation of global trajectories and local motions sequentially. This approach stems from the observation that generating global trajectories first is crucial for guiding local motion, ensuring better alignment with given action and text. Furthermore, we introduce a novel interaction loss to enhance the realism of generated close interactions. Our experiments, utilizing data adapted from a two-person motion dataset, demonstrate the efficacy of our approach for this novel task, which is capable of producing realistic, diverse, and controllable reactions that not only closely match the movements of the counterpart but also adhere to the textual guidance. Please find our webpage at https://xiyan-xu.github.io/MoReactWebPage.

Can we turn a video prediction model into a robot policy? Videos, including those of humans or teleoperated robots, capture rich physical interactions. However, most of them lack labeled actions, which limits their use in robot learning. We present Video Prediction for Robot Actions (ViPRA), a simple pretraining-finetuning framework that learns continuous robot control from these actionless videos. Instead of directly predicting actions, we train a video-language model to predict both future visual observations and motion-centric latent actions, which serve as intermediate representations of scene dynamics. We train these latent actions using perceptual losses and optical flow consistency to ensure they reflect physically grounded behavior. For downstream control, we introduce a chunked flow matching decoder that maps latent actions to robot-specific continuous action sequences, using only 100 to 200 teleoperated demonstrations. This approach avoids expensive action annotation, supports generalization across embodiments, and enables smooth, high-frequency continuous control upto 22 Hz via chunked action decoding. Unlike prior latent action works that treat pretraining as autoregressive policy learning, explicitly models both what changes and how. Our method outperforms strong baselines, with a 16% gain on the SIMPLER benchmark and a 13% improvement across real world manipulation tasks. We will release models and code at https://vipra-project.github.io

Detecting the anomaly of human behavior is paramount to timely recognizing endangering situations, such as street fights or elderly falls. However, anomaly detection is complex since anomalous events are rare and because it is an open set recognition task, i.e., what is anomalous at inference has not been observed at training. We propose COSKAD, a novel model that encodes skeletal human motion by a graph convolutional network and learns to COntract SKeletal kinematic embeddings onto a latent hypersphere of minimum volume for Video Anomaly Detection. We propose three latent spaces: the commonly-adopted Euclidean and the novel spherical and hyperbolic. All variants outperform the state-of-the-art on the most recent UBnormal dataset, for which we contribute a human-related version with annotated skeletons. COSKAD sets a new state-of-the-art on the human-related versions of ShanghaiTech Campus and CUHK Avenue, with performance comparable to video-based methods. Source code and dataset will be released upon acceptance.

Vision-Language-Action (VLA) models are a promising path toward embodied intelligence, yet they often overlook the predictive and temporal-causal structure underlying visual dynamics. World-model VLAs address this by predicting future frames, but waste capacity reconstructing redundant backgrounds. Latent-action VLAs encode frame-to-frame transitions compactly, but lack temporally continuous dynamic modeling and world knowledge. To overcome these limitations, we introduce CoWVLA (Chain-of-World VLA), a new "Chain of World" paradigm that unifies world-model temporal reasoning with a disentangled latent motion representation. First, a pretrained video VAE serves as a latent motion extractor, explicitly factorizing video segments into structure and motion latents. Then, during pre-training, the VLA learns from an instruction and an initial frame to infer a continuous latent motion chain and predict the segment's terminal frame. Finally, during co-fine-tuning, this latent dynamic is aligned with discrete action prediction by jointly modeling sparse keyframes and action sequences in a unified autoregressive decoder. This design preserves the world-model benefits of temporal reasoning and world knowledge while retaining the compactness and interpretability of latent actions, enabling efficient visuomotor learning. Extensive experiments on robotic simulation benchmarks show that CoWVLA outperforms existing world-model and latent-action approaches and achieves moderate computational efficiency, highlighting its potential as a more effective VLA pretraining paradigm. The project website can be found at https://fx-hit.github.io/cowvla-io.

Recent advances in diffusion/flow-matching policies have enabled imitation learning of complex, multi-modal action trajectories. However, they are computationally expensive because they sample a trajectory of trajectories: a diffusion/flow trajectory of action trajectories. They discard intermediate action trajectories, and must wait for the sampling process to complete before any actions can be executed on the robot. We simplify diffusion/flow policies by treating action trajectories as flow trajectories. Instead of starting from pure noise, our algorithm samples from a narrow Gaussian around the last action. Then, it incrementally integrates a velocity field learned via flow matching to produce a sequence of actions that constitute a single trajectory. This enables actions to be streamed to the robot on-the-fly during the flow sampling process, and is well-suited for receding horizon policy execution. Despite streaming, our method retains the ability to model multi-modal behavior. We train flows that stabilize around demonstration trajectories to reduce distribution shift and improve imitation learning performance. Streaming flow policy outperforms prior methods while enabling faster policy execution and tighter sensorimotor loops for learning-based robot control. Project website: https://streaming-flow-policy.github.io/