Daily Papers

Remote photoplethysmography (rPPG), enabling non-contact physiological monitoring through facial light reflection analysis, faces critical computational bottlenecks as deep learning introduces performance gains at the cost of prohibitive resource demands. This paper proposes ME-rPPG, a memory-efficient algorithm built on temporal-spatial state space duality, which resolves the trilemma of model scalability, cross-dataset generalization, and real-time constraints. Leveraging a transferable state space, ME-rPPG efficiently captures subtle periodic variations across facial frames while maintaining minimal computational overhead, enabling training on extended video sequences and supporting low-latency inference. Achieving cross-dataset MAEs of 5.38 (MMPD), 0.70 (VitalVideo), and 0.25 (PURE), ME-rPPG outperforms all baselines with improvements ranging from 21.3% to 60.2%. Our solution enables real-time inference with only 3.6 MB memory usage and 9.46 ms latency -- surpassing existing methods by 19.5%-49.7% accuracy and 43.2% user satisfaction gains in real-world deployments. The code and demos are released for reproducibility on https://health-hci-group.github.io/ME-rPPG-demo/.

Vision transformers have significantly advanced the field of computer vision, offering robust modeling capabilities and global receptive field. However, their high computational demands limit their applicability in processing long sequences. To tackle this issue, State Space Models (SSMs) have gained prominence in vision tasks as they offer linear computational complexity. Recently, State Space Duality (SSD), an improved variant of SSMs, was introduced in Mamba2 to enhance model performance and efficiency. However, the inherent causal nature of SSD/SSMs restricts their applications in non-causal vision tasks. To address this limitation, we introduce Visual State Space Duality (VSSD) model, which has a non-causal format of SSD. Specifically, we propose to discard the magnitude of interactions between the hidden state and tokens while preserving their relative weights, which relieves the dependencies of token contribution on previous tokens. Together with the involvement of multi-scan strategies, we show that the scanning results can be integrated to achieve non-causality, which not only improves the performance of SSD in vision tasks but also enhances its efficiency. We conduct extensive experiments on various benchmarks including image classification, detection, and segmentation, where VSSD surpasses existing state-of-the-art SSM-based models. Code and weights are available at https://github.com/YuHengsss/VSSD.

Video diffusion models have recently shown promise for world modeling through autoregressive frame prediction conditioned on actions. However, they struggle to maintain long-term memory due to the high computational cost associated with processing extended sequences in attention layers. To overcome this limitation, we propose a novel architecture leveraging state-space models (SSMs) to extend temporal memory without compromising computational efficiency. Unlike previous approaches that retrofit SSMs for non-causal vision tasks, our method fully exploits the inherent advantages of SSMs in causal sequence modeling. Central to our design is a block-wise SSM scanning scheme, which strategically trades off spatial consistency for extended temporal memory, combined with dense local attention to ensure coherence between consecutive frames. We evaluate the long-term memory capabilities of our model through spatial retrieval and reasoning tasks over extended horizons. Experiments on Memory Maze and Minecraft datasets demonstrate that our approach surpasses baselines in preserving long-range memory, while maintaining practical inference speeds suitable for interactive applications.

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

Sequential Recommendation (SR) models infer user preferences from interaction histories. While transferable Multi-modal SR models outperform traditional ID-based approaches, existing methods struggle with slow fine-tuning convergence due to complex optimization requirements and negative transfer effects. We propose MMM4Rec (Multi-Modal Mamba for Sequential Recommendation), a novel Multi-modal SR framework that incorporates a dedicated algebraic constraint mechanism for efficient transfer learning. By combining State Space Duality (SSD)'s temporal decay properties with a globally-aware temporal modeling design, our model dynamically prioritizes key modality information, overcoming limitations of Transformer-based approaches. The framework implements a constrained two-stage process: (1) sequence-level cross-modal alignment via shared projection matrices, followed by (2) temporal fusion using our newly designed Cross-SSD module and dual-channel Fourier adaptive filtering. This architecture maintains semantic consistency while suppressing noise propagation. MMM4Rec achieves rapid fine-tuning convergence with simple cross-entropy loss, significantly improving Multi-modal recommendation accuracy while maintaining strong transferability. Extensive experiments demonstrate MMM4Rec's state-of-the-art performance, achieving strong multi-modal retrieval capability and exhibiting 10x faster average convergence speed when transferring to large-scale downstream datasets. The implementation is available at https://github.com/AlwaysFHao/MMM4Rec .

Selective state space models (SSMs), such as Mamba, highly excel at capturing long-range dependencies in 1D sequential data, while their applications to 2D vision tasks still face challenges. Current visual SSMs often convert images into 1D sequences and employ various scanning patterns to incorporate local spatial dependencies. However, these methods are limited in effectively capturing the complex image spatial structures and the increased computational cost caused by the lengthened scanning paths. To address these limitations, we propose Spatial-Mamba, a novel approach that establishes neighborhood connectivity directly in the state space. Instead of relying solely on sequential state transitions, we introduce a structure-aware state fusion equation, which leverages dilated convolutions to capture image spatial structural dependencies, significantly enhancing the flow of visual contextual information. Spatial-Mamba proceeds in three stages: initial state computation in a unidirectional scan, spatial context acquisition through structure-aware state fusion, and final state computation using the observation equation. Our theoretical analysis shows that Spatial-Mamba unifies the original Mamba and linear attention under the same matrix multiplication framework, providing a deeper understanding of our method. Experimental results demonstrate that Spatial-Mamba, even with a single scan, attains or surpasses the state-of-the-art SSM-based models in image classification, detection and segmentation. Source codes and trained models can be found at https://github.com/EdwardChasel/Spatial-Mamba.

Temporal knowledge graphs represent temporal facts (s,p,o,tau) relating a subject s and an object o via a relation label p at time tau, where tau could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.

State-Space Models (SSMs) have recently emerged as a powerful and efficient alternative to the long-standing transformer architecture. However, existing SSM conceptualizations retain deeply rooted biases from their roots in natural language processing. This constrains their ability to appropriately model the spatially-dependent characteristics of visual inputs. In this paper, we address these limitations by re-deriving modern selective state-space techniques, starting from a natively multidimensional formulation. Currently, prior works attempt to apply natively 1D SSMs to 2D data (i.e. images) by relying on arbitrary combinations of 1D scan directions to capture spatial dependencies. In contrast, Mamba2D improves upon this with a single 2D scan direction that factors in both dimensions of the input natively, effectively modelling spatial dependencies when constructing hidden states. Mamba2D shows comparable performance to prior adaptations of SSMs for vision tasks, on standard image classification evaluations with the ImageNet-1K dataset. Source code is available at https://github.com/cocoalex00/Mamba2D.

We present SpaceTimePilot, a video diffusion model that disentangles space and time for controllable generative rendering. Given a monocular video, SpaceTimePilot can independently alter the camera viewpoint and the motion sequence within the generative process, re-rendering the scene for continuous and arbitrary exploration across space and time. To achieve this, we introduce an effective animation time-embedding mechanism in the diffusion process, allowing explicit control of the output video's motion sequence with respect to that of the source video. As no datasets provide paired videos of the same dynamic scene with continuous temporal variations, we propose a simple yet effective temporal-warping training scheme that repurposes existing multi-view datasets to mimic temporal differences. This strategy effectively supervises the model to learn temporal control and achieve robust space-time disentanglement. To further enhance the precision of dual control, we introduce two additional components: an improved camera-conditioning mechanism that allows altering the camera from the first frame, and CamxTime, the first synthetic space-and-time full-coverage rendering dataset that provides fully free space-time video trajectories within a scene. Joint training on the temporal-warping scheme and the CamxTime dataset yields more precise temporal control. We evaluate SpaceTimePilot on both real-world and synthetic data, demonstrating clear space-time disentanglement and strong results compared to prior work. Project page: https://zheninghuang.github.io/Space-Time-Pilot/ Code: https://github.com/ZheningHuang/spacetimepilot

While Transformers have been the main architecture behind deep learning's success in language modeling, state-space models (SSMs) such as Mamba have recently been shown to match or outperform Transformers at small to medium scale. We show that these families of models are actually quite closely related, and develop a rich framework of theoretical connections between SSMs and variants of attention, connected through various decompositions of a well-studied class of structured semiseparable matrices. Our state space duality (SSD) framework allows us to design a new architecture (Mamba-2) whose core layer is an a refinement of Mamba's selective SSM that is 2-8X faster, while continuing to be competitive with Transformers on language modeling.

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.

State Space Models (SSMs)-most notably RNNs-have historically played a central role in sequential modeling. Although attention mechanisms such as Transformers have since dominated due to their ability to model global context, their quadratic complexity and limited scalability make them less suited for long sequences. Video super-resolution (VSR) methods have traditionally relied on recurrent architectures to propagate features across frames. However, such approaches suffer from well-known issues including vanishing gradients, lack of parallelism, and slow inference speed. Recent advances in selective SSMs like Mamba offer a compelling alternative: by enabling input-dependent state transitions with linear-time complexity, Mamba mitigates these issues while maintaining strong long-range modeling capabilities. Despite this potential, Mamba alone struggles to capture fine-grained spatial dependencies due to its causal nature and lack of explicit context aggregation. To address this, we propose a hybrid architecture that combines shifted window self-attention for spatial context aggregation with Mamba-based selective scanning for efficient temporal propagation. Furthermore, we introduce Gather-Scatter Mamba (GSM), an alignment-aware mechanism that warps features toward a center anchor frame within the temporal window before Mamba propagation and scatters them back afterward, effectively reducing occlusion artifacts and ensuring effective redistribution of aggregated information across all frames. The official implementation is provided at: https://github.com/Ko-Lani/GSMamba.

Autoregressive (AR) diffusion enables streaming, interactive long-video generation by producing frames causally, yet maintaining coherence over minute-scale horizons remains challenging due to accumulated errors, motion drift, and content repetition. We approach this problem from a memory perspective, treating video synthesis as a recurrent dynamical process that requires coordinated short- and long-term context. We propose VideoSSM, a Long Video Model that unifies AR diffusion with a hybrid state-space memory. The state-space model (SSM) serves as an evolving global memory of scene dynamics across the entire sequence, while a context window provides local memory for motion cues and fine details. This hybrid design preserves global consistency without frozen, repetitive patterns, supports prompt-adaptive interaction, and scales in linear time with sequence length. Experiments on short- and long-range benchmarks demonstrate state-of-the-art temporal consistency and motion stability among autoregressive video generator especially at minute-scale horizons, enabling content diversity and interactive prompt-based control, thereby establishing a scalable, memory-aware framework for long video generation.

Spatiotemporal forecasting techniques are significant for various domains such as transportation, energy, and weather. Accurate prediction of spatiotemporal series remains challenging due to the complex spatiotemporal heterogeneity. In particular, current end-to-end models are limited by input length and thus often fall into spatiotemporal mirage, i.e., similar input time series followed by dissimilar future values and vice versa. To address these problems, we propose a novel self-supervised pre-training framework Spatial-Temporal-Decoupled Masked Pre-training (STD-MAE) that employs two decoupled masked autoencoders to reconstruct spatiotemporal series along the spatial and temporal dimensions. Rich-context representations learned through such reconstruction could be seamlessly integrated by downstream predictors with arbitrary architectures to augment their performances. A series of quantitative and qualitative evaluations on six widely used benchmarks (PEMS03, PEMS04, PEMS07, PEMS08, METR-LA, and PEMS-BAY) are conducted to validate the state-of-the-art performance of STD-MAE. Codes are available at https://github.com/Jimmy-7664/STD-MAE.

The capabilities of large language models (LLMs) have sparked debate over whether such systems just learn an enormous collection of superficial statistics or a coherent model of the data generating process -- a world model. We find evidence for the latter by analyzing the learned representations of three spatial datasets (world, US, NYC places) and three temporal datasets (historical figures, artworks, news headlines) in the Llama-2 family of models. We discover that LLMs learn linear representations of space and time across multiple scales. These representations are robust to prompting variations and unified across different entity types (e.g. cities and landmarks). In addition, we identify individual ``space neurons'' and ``time neurons'' that reliably encode spatial and temporal coordinates. Our analysis demonstrates that modern LLMs acquire structured knowledge about fundamental dimensions such as space and time, supporting the view that they learn not merely superficial statistics, but literal world models.

Temporal Point Processes (TPP) are probabilistic generative frameworks. They model discrete event sequences localized in continuous time. Generally, real-life events reveal descriptive information, known as marks. Marked TPPs model time and marks of the event together for practical relevance. Conditioned on past events, marked TPPs aim to learn the joint distribution of the time and the mark of the next event. For simplicity, conditionally independent TPP models assume time and marks are independent given event history. They factorize the conditional joint distribution of time and mark into the product of individual conditional distributions. This structural limitation in the design of TPP models hurt the predictive performance on entangled time and mark interactions. In this work, we model the conditional inter-dependence of time and mark to overcome the limitations of conditionally independent models. We construct a multivariate TPP conditioning the time distribution on the current event mark in addition to past events. Besides the conventional intensity-based models for conditional joint distribution, we also draw on flexible intensity-free TPP models from the literature. The proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks. Our experimentation on various datasets with multiple evaluation metrics highlights the merit of the proposed approach.

While Vision-Language-Action (VLA) models have revolutionized autonomous driving by unifying perception and planning, their reliance on explicit textual Chain-of-Thought (CoT) leads to semantic-perceptual decoupling and perceptual-symbolic conflicts. Recent shifts toward latent reasoning attempt to bypass these bottlenecks by thinking in continuous hidden space. However, without explicit intermediate constraints, standard latent CoT often operates as a physics-agnostic representation. To address this, we propose the Latent Spatio-Temporal VLA (LaST-VLA), a framework shifting the reasoning paradigm from discrete symbolic processing into a physically grounded Latent Spatio-Temporal CoT. By implementing a dual-feature alignment mechanism, we distill geometric constraints from 3D foundation models and dynamic foresight from world models directly into the latent space. Coupled with a progressive SFT training strategy that transitions from feature alignment to trajectory generation, and refined via Reinforcement Learning with Group Relative Policy Optimization (GRPO) to ensure safety and rule compliance. \method~setting a new record on NAVSIM v1 (91.3 PDMS) and NAVSIM v2 (87.1 EPDMS), while excelling in spatial-temporal reasoning on SURDS and NuDynamics benchmarks.

Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually incompatible coarse-grained modes of observation. We show that this structure arises in a range of social-science settings by constructing six explicit examples from personnel assessment, survey framing, clinical diagnosis, espionage coordination, legal pluralism, and organizational auditing. For each case we identify the latent state space, the observational contexts as partitions, and the shared atoms that intertwine contexts, yielding instances of the L_{12} bowtie, triangle, pentagon, and automaton partition logics. These examples make precise a notion of social complementarity: different modes of inquiry can be incompatible even though the underlying system remains fully value-definite. Complementarity in this sense does not entail contextuality or ontic indeterminacy. We further compare the classical probabilities generated by convex mixtures of dispersion-free states with the quantum-like Born probabilities available when the same exclusivity graph admits a faithful orthogonal representation. The framework thus separates logical structure from probabilistic realization and suggests empirically testable benchmarks for quantum-cognition models.

World models aim to simulate environments and enable effective agent behavior. However, modeling real-world environments presents unique challenges as they dynamically change across both space and, crucially, time. To capture these composed dynamics, we introduce a Spatio-Temporal Road Image Dataset for Exploration (STRIDE) permuting 360-degree panoramic imagery into rich interconnected observation, state and action nodes. Leveraging this structure, we can simultaneously model the relationship between egocentric views, positional coordinates, and movement commands across both space and time. We benchmark this dataset via TARDIS, a transformer-based generative world model that integrates spatial and temporal dynamics through a unified autoregressive framework trained on STRIDE. We demonstrate robust performance across a range of agentic tasks such as controllable photorealistic image synthesis, instruction following, autonomous self-control, and state-of-the-art georeferencing. These results suggest a promising direction towards sophisticated generalist agents--capable of understanding and manipulating the spatial and temporal aspects of their material environments--with enhanced embodied reasoning capabilities. Training code, datasets, and model checkpoints are made available at https://huggingface.co/datasets/Tera-AI/STRIDE.

Effectively modeling long spatiotemporal sequences is challenging due to the need to model complex spatial correlations and long-range temporal dependencies simultaneously. ConvLSTMs attempt to address this by updating tensor-valued states with recurrent neural networks, but their sequential computation makes them slow to train. In contrast, Transformers can process an entire spatiotemporal sequence, compressed into tokens, in parallel. However, the cost of attention scales quadratically in length, limiting their scalability to longer sequences. Here, we address the challenges of prior methods and introduce convolutional state space models (ConvSSM) that combine the tensor modeling ideas of ConvLSTM with the long sequence modeling approaches of state space methods such as S4 and S5. First, we demonstrate how parallel scans can be applied to convolutional recurrences to achieve subquadratic parallelization and fast autoregressive generation. We then establish an equivalence between the dynamics of ConvSSMs and SSMs, which motivates parameterization and initialization strategies for modeling long-range dependencies. The result is ConvS5, an efficient ConvSSM variant for long-range spatiotemporal modeling. ConvS5 significantly outperforms Transformers and ConvLSTM on a long horizon Moving-MNIST experiment while training 3X faster than ConvLSTM and generating samples 400X faster than Transformers. In addition, ConvS5 matches or exceeds the performance of state-of-the-art methods on challenging DMLab, Minecraft and Habitat prediction benchmarks and enables new directions for modeling long spatiotemporal sequences.

Spatio-temporal predictive learning is a learning paradigm that enables models to learn spatial and temporal patterns by predicting future frames from given past frames in an unsupervised manner. Despite remarkable progress in recent years, a lack of systematic understanding persists due to the diverse settings, complex implementation, and difficult reproducibility. Without standardization, comparisons can be unfair and insights inconclusive. To address this dilemma, we propose OpenSTL, a comprehensive benchmark for spatio-temporal predictive learning that categorizes prevalent approaches into recurrent-based and recurrent-free models. OpenSTL provides a modular and extensible framework implementing various state-of-the-art methods. We conduct standard evaluations on datasets across various domains, including synthetic moving object trajectory, human motion, driving scenes, traffic flow and weather forecasting. Based on our observations, we provide a detailed analysis of how model architecture and dataset properties affect spatio-temporal predictive learning performance. Surprisingly, we find that recurrent-free models achieve a good balance between efficiency and performance than recurrent models. Thus, we further extend the common MetaFormers to boost recurrent-free spatial-temporal predictive learning. We open-source the code and models at https://github.com/chengtan9907/OpenSTL.

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

Humans perceive and understand real-world spaces through a stream of visual observations. Therefore, the ability to streamingly maintain and update spatial evidence from potentially unbounded video streams is essential for spatial intelligence. The core challenge is not simply longer context windows but how spatial information is selected, organized, and retained over time. In this paper, we propose Spatial-TTT towards streaming visual-based spatial intelligence with test-time training (TTT), which adapts a subset of parameters (fast weights) to capture and organize spatial evidence over long-horizon scene videos. Specifically, we design a hybrid architecture and adopt large-chunk updates parallel with sliding-window attention for efficient spatial video processing. To further promote spatial awareness, we introduce a spatial-predictive mechanism applied to TTT layers with 3D spatiotemporal convolution, which encourages the model to capture geometric correspondence and temporal continuity across frames. Beyond architecture design, we construct a dataset with dense 3D spatial descriptions, which guides the model to update its fast weights to memorize and organize global 3D spatial signals in a structured manner. Extensive experiments demonstrate that Spatial-TTT improves long-horizon spatial understanding and achieves state-of-the-art performance on video spatial benchmarks. Project page: https://liuff19.github.io/Spatial-TTT.

Spatio-temporal forecasting is essential for real-world applications such as traffic management and urban computing. Although recent methods have shown improved accuracy, they often fail to account for dynamic deviations between current inputs and historical patterns. These deviations contain critical signals that can significantly affect model performance. To fill this gap, we propose ST-SSDL, a Spatio-Temporal time series forecasting framework that incorporates a Self-Supervised Deviation Learning scheme to capture and utilize such deviations. ST-SSDL anchors each input to its historical average and discretizes the latent space using learnable prototypes that represent typical spatio-temporal patterns. Two auxiliary objectives are proposed to refine this structure: a contrastive loss that enhances inter-prototype discriminability and a deviation loss that regularizes the distance consistency between input representations and corresponding prototypes to quantify deviation. Optimized jointly with the forecasting objective, these components guide the model to organize its hidden space and improve generalization across diverse input conditions. Experiments on six benchmark datasets show that ST-SSDL consistently outperforms state-of-the-art baselines across multiple metrics. Visualizations further demonstrate its ability to adaptively respond to varying levels of deviation in complex spatio-temporal scenarios. Our code and datasets are available at https://github.com/Jimmy-7664/ST-SSDL.

Satellite image time-series analysis demands fine-grained spatial-temporal reasoning, which remains a challenge for existing multimodal large language models (MLLMs). In this work, we study the capabilities of MLLMs on a novel task that jointly targets temporal change understanding and future scene generation, aiming to assess their potential for modeling complex multimodal dynamics over time. We propose TAMMs, a Temporal-Aware Multimodal Model for satellite image change understanding and forecasting, which enhances frozen MLLMs with lightweight temporal modules for structured sequence encoding and contextual prompting. To guide future image generation, TAMMs introduces a Semantic-Fused Control Injection (SFCI) mechanism that adaptively combines high-level semantic reasoning and structural priors within an enhanced ControlNet. This dual-path conditioning enables temporally consistent and semantically grounded image synthesis. Experiments demonstrate that TAMMs outperforms strong MLLM baselines in both temporal change understanding and future image forecasting tasks, highlighting how carefully designed temporal reasoning and semantic fusion can unlock the full potential of MLLMs for spatio-temporal understanding.

Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of domains, at a reduced training and inference cost compared to attention-based transformers. Recent developments show that if the linear recurrence powering SSMs allows for multiplicative interactions between inputs and hidden states (e.g. GateLoop, Mamba, GLA), then the resulting architecture can surpass in both in accuracy and efficiency attention-powered foundation models trained on text, at scales of billion parameters. In this paper, we give theoretical grounding to this recent finding using tools from Rough Path Theory: we show that when random linear recurrences are equipped with simple input-controlled transitions (selectivity mechanism), then the hidden state is provably a low-dimensional projection of a powerful mathematical object called the signature of the input -- capturing non-linear interactions between tokens at distinct timescales. Our theory not only motivates the success of modern selective state-space models such as Mamba but also provides a solid framework to understand the expressive power of future SSM variants.

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

We provide an optimization-based framework to perform counterfactual analysis in a dynamic model with hidden states. Our framework is grounded in the ``abduction, action, and prediction'' approach to answer counterfactual queries and handles two key challenges where (1) the states are hidden and (2) the model is dynamic. Recognizing the lack of knowledge on the underlying causal mechanism and the possibility of infinitely many such mechanisms, we optimize over this space and compute upper and lower bounds on the counterfactual quantity of interest. Our work brings together ideas from causality, state-space models, simulation, and optimization, and we apply it on a breast cancer case study. To the best of our knowledge, we are the first to compute lower and upper bounds on a counterfactual query in a dynamic latent-state model.

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

Recent successes in autoregressive (AR) generation models, such as the GPT series in natural language processing, have motivated efforts to replicate this success in visual tasks. Some works attempt to extend this approach to autonomous driving by building video-based world models capable of generating realistic future video sequences and predicting ego states. However, prior works tend to produce unsatisfactory results, as the classic GPT framework is designed to handle 1D contextual information, such as text, and lacks the inherent ability to model the spatial and temporal dynamics essential for video generation. In this paper, we present DrivingWorld, a GPT-style world model for autonomous driving, featuring several spatial-temporal fusion mechanisms. This design enables effective modeling of both spatial and temporal dynamics, facilitating high-fidelity, long-duration video generation. Specifically, we propose a next-state prediction strategy to model temporal coherence between consecutive frames and apply a next-token prediction strategy to capture spatial information within each frame. To further enhance generalization ability, we propose a novel masking strategy and reweighting strategy for token prediction to mitigate long-term drifting issues and enable precise control. Our work demonstrates the ability to produce high-fidelity and consistent video clips of over 40 seconds in duration, which is over 2 times longer than state-of-the-art driving world models. Experiments show that, in contrast to prior works, our method achieves superior visual quality and significantly more accurate controllable future video generation. Our code is available at https://github.com/YvanYin/DrivingWorld.

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.

World simulation has gained increasing popularity due to its ability to model virtual environments and predict the consequences of actions. However, the limited temporal context window often leads to failures in maintaining long-term consistency, particularly in preserving 3D spatial consistency. In this work, we present WorldMem, a framework that enhances scene generation with a memory bank consisting of memory units that store memory frames and states (e.g., poses and timestamps). By employing a memory attention mechanism that effectively extracts relevant information from these memory frames based on their states, our method is capable of accurately reconstructing previously observed scenes, even under significant viewpoint or temporal gaps. Furthermore, by incorporating timestamps into the states, our framework not only models a static world but also captures its dynamic evolution over time, enabling both perception and interaction within the simulated world. Extensive experiments in both virtual and real scenarios validate the effectiveness of our approach.

Goal representation affects the performance of Hierarchical Reinforcement Learning (HRL) algorithms by decomposing the complex learning problem into easier subtasks. Recent studies show that representations that preserve temporally abstract environment dynamics are successful in solving difficult problems and provide theoretical guarantees for optimality. These methods however cannot scale to tasks where environment dynamics increase in complexity i.e. the temporally abstract transition relations depend on larger number of variables. On the other hand, other efforts have tried to use spatial abstraction to mitigate the previous issues. Their limitations include scalability to high dimensional environments and dependency on prior knowledge. In this paper, we propose a novel three-layer HRL algorithm that introduces, at different levels of the hierarchy, both a spatial and a temporal goal abstraction. We provide a theoretical study of the regret bounds of the learned policies. We evaluate the approach on complex continuous control tasks, demonstrating the effectiveness of spatial and temporal abstractions learned by this approach.

One of the primary objectives of satellite remote sensing is to capture the complex dynamics of the Earth environment, which encompasses tasks such as reconstructing continuous cloud-free time series images, detecting land cover changes, and forecasting future surface evolution. However, existing methods typically require specialized models tailored to different tasks, lacking unified modeling of spatiotemporal features across multiple time series tasks. In this paper, we propose a Unified Time Series Generative Model (UniTS), a general framework applicable to various time series tasks, including time series reconstruction, time series cloud removal, time series semantic change detection, and time series forecasting. Based on the flow matching generative paradigm, UniTS constructs a deterministic evolution path from noise to targets under the guidance of task-specific conditions, achieving unified modeling of spatiotemporal representations for multiple tasks. The UniTS architecture consists of a diffusion transformer with spatio-temporal blocks, where we design an Adaptive Condition Injector (ACor) to enhance the model's conditional perception of multimodal inputs, enabling high-quality controllable generation. Additionally, we design a Spatiotemporal-aware Modulator (STM) to improve the ability of spatio-temporal blocks to capture complex spatiotemporal dependencies. Furthermore, we construct two high-quality multimodal time series datasets, TS-S12 and TS-S12CR, filling the gap of benchmark datasets for time series cloud removal and forecasting tasks. Extensive experiments demonstrate that UniTS exhibits exceptional generative and cognitive capabilities in both low-level and high-level time series tasks. It significantly outperforms existing methods, particularly when facing challenges such as severe cloud contamination, modality absence, and forecasting phenological variations.

Dynamic spatial reasoning from monocular video is essential for bridging visual intelligence and the physical world, yet remains challenging for vision-language models (VLMs). Prior approaches either verbalize spatial-temporal reasoning entirely as text, which is inherently verbose and imprecise for complex dynamics, or rely on external geometric modules that increase inference complexity without fostering intrinsic model capability. In this paper, we present 4DThinker, the first framework that enables VLMs to "think with 4D" through dynamic latent mental imagery, i.e., internally simulating how scenes evolve within the continuous hidden space. Specifically, we first introduce a scalable, annotation-free data generation pipeline that synthesizes 4D reasoning data from raw videos. We then propose Dynamic-Imagery Fine-Tuning (DIFT), which jointly supervises textual tokens and 4D latents to ground the model in dynamic visual semantics. Building on this, 4D Reinforcement Learning (4DRL) further tackles complex reasoning tasks via outcome-based rewards, restricting policy gradients to text tokens to ensure stable optimization. Extensive experiments across multiple dynamic spatial reasoning benchmarks demonstrate that 4DThinker consistently outperforms strong baselines and offers a new perspective toward 4D reasoning in VLMs. Our code is available at https://github.com/zhangquanchen/4DThinker.

Large-scale video generation models have demonstrated emergent physical coherence, positioning them as potential world models. However, a gap remains between contemporary "stateless" video architectures and classic state-centric world model theories. This work bridges this gap by proposing a novel taxonomy centered on two pillars: State Construction and Dynamics Modeling. We categorize state construction into implicit paradigms (context management) and explicit paradigms (latent compression), while dynamics modeling is analyzed through knowledge integration and architectural reformulation. Furthermore, we advocate for a transition in evaluation from visual fidelity to functional benchmarks, testing physical persistence and causal reasoning. We conclude by identifying two critical frontiers: enhancing persistence via data-driven memory and compressed fidelity, and advancing causality through latent factor decoupling and reasoning-prior integration. By addressing these challenges, the field can evolve from generating visually plausible videos to building robust, general-purpose world simulators.

Knowledge about the hidden factors that determine particular system dynamics is crucial for both explaining them and pursuing goal-directed interventions. Inferring these factors from time series data without supervision remains an open challenge. Here, we focus on spatiotemporal processes, including wave propagation and weather dynamics, for which we assume that universal causes (e.g. physics) apply throughout space and time. A recently introduced DIstributed SpatioTemporal graph Artificial Neural network Architecture (DISTANA) is used and enhanced to learn such processes, requiring fewer parameters and achieving significantly more accurate predictions compared to temporal convolutional neural networks and other related approaches. We show that DISTANA, when combined with a retrospective latent state inference principle called active tuning, can reliably derive location-respective hidden causal factors. In a current weather prediction benchmark, DISTANA infers our planet's land-sea mask solely by observing temperature dynamics and, meanwhile, uses the self inferred information to improve its own future temperature predictions.

Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in W_infty. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle.

We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma showing that lifting to sets or distributions yields a deterministic global dynamic, an ordinal stabilization theorem sending operator transforms to the fixed subspace by stage omega under normal spectral contraction, and a product of Riesz projections theorem for commuting layers. We establish a compositionality law for lifted maps, show closure of Phi packings, and present a quantitative application to sensory depletion that models tissue removal as a projection and derives strict decreases in the attainable fixed point under minimal monotonicity and positivity assumptions. We also state measurable conditions for probabilistic lifts, give explicit non normal and non commuting counterexamples, and provide finite dimensional and stochastic witnesses together with per theorem scope tables and a small reproducible code appendix.

The Sequential Recommendation modeling paradigm is shifting from Transformer to Mamba architecture, which comprises two generations: Mamba1, based on the State Space Model (SSM), and Mamba2, based on State Space Duality (SSD). Although SSD offers superior computational efficiency compared to SSM, it suffers performance degradation in sequential recommendation tasks, especially in low-dimensional scenarios that are critical for these tasks. Considering that time-aware enhancement methods are commonly employed to mitigate performance loss, our analysis reveals that the performance decline of SSD can similarly be fundamentally compensated by leveraging mechanisms in time-aware methods. Thus, we propose integrating time-awareness into the SSD framework to address these performance issues. However, integrating current time-aware methods, modeled after TiSASRec, into SSD faces the following challenges: 1) the complexity of integrating these transformer-based mechanisms with the SSD architecture, and 2) the computational inefficiency caused by the need for dimensionality expansion of time-difference modeling. To overcome these challenges, we introduce a novel Time-aware Structured Masked Matrix that efficiently incorporates time-aware capabilities into SSD. Building on this, we propose Time-Aware Mamba for Recommendation (TiM4Rec), which mitigates performance degradation in low-dimensional SSD contexts while preserving computational efficiency. This marks the inaugural application of a time-aware enhancement method specifically tailored for the Mamba architecture within the domain of sequential recommendation. Extensive experiments conducted on three real-world datasets demonstrate the superiority of our approach. The code for our model is accessible at https://github.com/AlwaysFHao/TiM4Rec.

Spatial embodied intelligence requires agents to act to acquire information under partial observability. While multimodal foundation models excel at passive perception, their capacity for active, self-directed exploration remains understudied. We propose Theory of Space, defined as an agent's ability to actively acquire information through self-directed, active exploration and to construct, revise, and exploit a spatial belief from sequential, partial observations. We evaluate this through a benchmark where the goal is curiosity-driven exploration to build an accurate cognitive map. A key innovation is spatial belief probing, which prompts models to reveal their internal spatial representations at each step. Our evaluation of state-of-the-art models reveals several critical bottlenecks. First, we identify an Active-Passive Gap, where performance drops significantly when agents must autonomously gather information. Second, we find high inefficiency, as models explore unsystematically compared to program-based proxies. Through belief probing, we diagnose that while perception is an initial bottleneck, global beliefs suffer from instability that causes spatial knowledge to degrade over time. Finally, using a false belief paradigm, we uncover Belief Inertia, where agents fail to update obsolete priors with new evidence. This issue is present in text-based agents but is particularly severe in vision-based models. Our findings suggest that current foundation models struggle to maintain coherent, revisable spatial beliefs during active exploration.

This study explores the interference in temporal processing within a dual-task paradigm from an artificial intelligence (AI) perspective. In this context, the dual-task setup is implemented as a simplified version of the Overcooked environment with two variations, single task (T) and dual task (T+N). Both variations involve an embedded time production task, but the dual task (T+N) additionally involves a concurrent number comparison task. Two deep reinforcement learning (DRL) agents were separately trained for each of these tasks. These agents exhibited emergent behavior consistent with human timing research. Specifically, the dual task (T+N) agent exhibited significant overproduction of time relative to its single task (T) counterpart. This result was consistent across four target durations. Preliminary analysis of neural dynamics in the agents' LSTM layers did not reveal any clear evidence of a dedicated or intrinsic timer. Hence, further investigation is needed to better understand the underlying time-keeping mechanisms of the agents and to provide insights into the observed behavioral patterns. This study is a small step towards exploring parallels between emergent DRL behavior and behavior observed in biological systems in order to facilitate a better understanding of both.

Modern neural recording techniques allow neuroscientists to obtain spiking activity of multiple neurons from different brain regions over long time periods, which requires new statistical methods to be developed for understanding structure of the large-scale data. In this paper, we develop a bi-clustering method to cluster the neural spiking activity spatially and temporally, according to their low-dimensional latent structures. The spatial (neuron) clusters are defined by the latent trajectories within each neural population, while the temporal (state) clusters are defined by (populationally) synchronous local linear dynamics shared with different periods. To flexibly extract the bi-clustering structure, we build the model non-parametrically, and develop an efficient Markov chain Monte Carlo (MCMC) algorithm to sample the posterior distributions of model parameters. Validating our proposed MCMC algorithm through simulations, we find the method can recover unknown parameters and true bi-clustering structures successfully. We then apply the proposed bi-clustering method to multi-regional neural recordings under different experiment settings, where we find that simultaneously considering latent trajectories and spatial-temporal clustering structures can provide us with a more accurate and interpretable result. Overall, the proposed method provides scientific insights for large-scale (counting) time series with elongated recording periods, and it can potentially have application beyond neuroscience.

Humans inhabit a physical 4D world where geometric structure and semantic content evolve over time, constituting a dynamic 4D reality (spatial with temporal dimension). While current Multimodal Large Language Models (MLLMs) excel in static visual understanding, can they also be adept at "thinking in dynamics", i.e., perceive, track and reason about spatio-temporal dynamics in evolving scenes? To systematically assess their spatio-temporal reasoning and localized dynamics perception capabilities, we introduce Dyn-Bench, a large-scale benchmark built from diverse real-world and synthetic video datasets, enabling robust and scalable evaluation of spatio-temporal understanding. Through multi-stage filtering from massive 2D and 4D data sources, Dyn-Bench provides a high-quality collection of dynamic scenes, comprising 1k videos, 7k visual question answering (VQA) pairs, and 3k dynamic object grounding pairs. We probe general, spatial and region-level MLLMs to express how they think in dynamics both linguistically and visually, and find that existing models cannot simultaneously maintain strong performance in both spatio-temporal reasoning and dynamic object grounding, often producing inconsistent interpretations of motion and interaction. Notably, conventional prompting strategies (e.g., chain-of-thought or caption-based hints) provide limited improvement, whereas structured integration approaches, including Mask-Guided Fusion and Spatio-Temporal Textual Cognitive Map (ST-TCM), significantly enhance MLLMs' dynamics perception and spatio-temporal reasoning in the physical 4D world. Code and benchmark are available at https://dyn-bench.github.io/.

State Space Models (SSMs) have recently emerged as efficient alternatives to Transformer-Based Models (TBMs) for long-sequence processing, offering linear scaling and lower memory use. Yet, how contextual information flows across layers and tokens in these architectures remains understudied. We present the first unified, token- and layer-level analysis of representation propagation in SSMs and TBMs. Using centered kernel alignment, stability metrics, and probing, we characterize how representations evolve within and across layers. We find a key divergence: TBMs rapidly homogenize token representations, with diversity reemerging only in later layers, while SSMs preserve token uniqueness early but converge to homogenization deeper. Theoretical analysis and parameter randomization further reveal that oversmoothing in TBMs stems from architectural design, whereas in SSMs it arises mainly from training dynamics. These insights clarify the inductive biases of both architectures and inform future model and training designs for long-context reasoning.

Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pattern of a specific series with multivariate exogenous series, and then the attention layer learns the spatial correlative weight and obtains the global representations simultaneously. The results show that the new approach can capture the temporal-spatial dynamics of household leverage well and get more accurate and solid predictive results. More, the simulation also studies show that clustering and choosing correlative series are necessary to obtain accurate forecasting results.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

We present a large-scale study on unsupervised spatiotemporal representation learning from videos. With a unified perspective on four recent image-based frameworks, we study a simple objective that can easily generalize all these methods to space-time. Our objective encourages temporally-persistent features in the same video, and in spite of its simplicity, it works surprisingly well across: (i) different unsupervised frameworks, (ii) pre-training datasets, (iii) downstream datasets, and (iv) backbone architectures. We draw a series of intriguing observations from this study, e.g., we discover that encouraging long-spanned persistency can be effective even if the timespan is 60 seconds. In addition to state-of-the-art results in multiple benchmarks, we report a few promising cases in which unsupervised pre-training can outperform its supervised counterpart. Code is made available at https://github.com/facebookresearch/SlowFast

Existing Multivariate Time Series Anomaly Detection (MTSAD) frameworks increasingly rely on integrating Graph Neural Networks (GNNs) with sequence models to capture complex spatio-temporal dependencies. However, less attention is paid to the spatial over-generalization problem, where unconstrained structural modeling indiscriminately reconstructs anomalies, inevitably degrading detection recall. To tackle this problem, we propose a novel framework that unifies spatio-temporal modeling through a joint prior-observation adversarial learning paradigm. In the spatial dimension, the model alternately learns adjacency matrices as structural prior and models the association discrepancy between prior and data-driven observation in a minimax manner during training. Such adversarial optimization not only improves the model sensitivity for time-wise detection, but also enables the model to localize anomalies to specific channels. To systematically evaluate this anomaly localization capability, we further construct a synthetic benchmark equipped with precise channel-wise annotations. Extensive experiments across public datasets and our dedicated benchmark demonstrate that the proposed framework establishes a new state-of-the-art in both time-wise detection and spatial localization tasks. Our code, pre-trained models, and benchmark are publicly available at https://github.com/anocodetest1/POST.

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

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling recovery of mechanism trajectories at test time. This formulation generalizes to intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and space. Central to our approach is a combination of continuous-time neural networks with two novel neural architectures, i.e., Jump and Attentive Continuous-time Normalizing Flows. This approach allows us to learn complex distributions for both the spatial and temporal domain and to condition non-trivially on the observed event history. We validate our models on data sets from a wide variety of contexts such as seismology, epidemiology, urban mobility, and neuroscience.

LWM-Temporal is a new member of the Large Wireless Models (LWM) family that targets the spatiotemporal nature of wireless channels. Designed as a task-agnostic foundation model, LWM-Temporal learns universal channel embeddings that capture mobility-induced evolution and are reusable across various downstream tasks. To achieve this objective, LWM-Temporal operates in the angle-delay-time domain and introduces Sparse Spatio-Temporal Attention (SSTA), a propagation-aligned attention mechanism that restricts interactions to physically plausible neighborhoods, reducing attention complexity by an order of magnitude while preserving geometry-consistent dependencies. LWM-Temporal is pretrained in a self-supervised manner using a physics-informed masking curriculum that emulates realistic occlusions, pilot sparsity, and measurement impairments. Experimental results on channel prediction across multiple mobility regimes show consistent improvements over strong baselines, particularly under long horizons and limited fine-tuning data, highlighting the importance of geometry-aware architectures and geometry-consistent pretraining for learning transferable spatiotemporal wireless representations.

Recent advances in deep learning have mainly relied on Transformers due to their data dependency and ability to learn at scale. The attention module in these architectures, however, exhibits quadratic time and space in input size, limiting their scalability for long-sequence modeling. Despite recent attempts to design efficient and effective architecture backbone for multi-dimensional data, such as images and multivariate time series, existing models are either data independent, or fail to allow inter- and intra-dimension communication. Recently, State Space Models (SSMs), and more specifically Selective State Space Models, with efficient hardware-aware implementation, have shown promising potential for long sequence modeling. Motivated by the success of SSMs, we present MambaMixer, a new architecture with data-dependent weights that uses a dual selection mechanism across tokens and channels, called Selective Token and Channel Mixer. MambaMixer connects selective mixers using a weighted averaging mechanism, allowing layers to have direct access to early features. As a proof of concept, we design Vision MambaMixer (ViM2) and Time Series MambaMixer (TSM2) architectures based on the MambaMixer block and explore their performance in various vision and time series forecasting tasks. Our results underline the importance of selective mixing across both tokens and channels. In ImageNet classification, object detection, and semantic segmentation tasks, ViM2 achieves competitive performance with well-established vision models and outperforms SSM-based vision models. In time series forecasting, TSM2 achieves outstanding performance compared to state-of-the-art methods while demonstrating significantly improved computational cost. These results show that while Transformers, cross-channel attention, and MLPs are sufficient for good performance in time series forecasting, neither is necessary.

Koopman representations aim to learn features of nonlinear dynamical systems (NLDS) which lead to linear dynamics in the latent space. Theoretically, such features can be used to simplify many problems in modeling and control of NLDS. In this work we study autoencoder formulations of this problem, and different ways they can be used to model dynamics, specifically for future state prediction over long horizons. We discover several limitations of predicting future states in the latent space and propose an inference-time mechanism, which we refer to as Periodic Reencoding, for faithfully capturing long term dynamics. We justify this method both analytically and empirically via experiments in low and high dimensional NLDS.

Geo-temporal understanding, the ability to infer location, time, and contextual properties from visual input alone, underpins applications such as disaster management, traffic planning, embodied navigation, world modeling, and geography education. Although recent vision-language models (VLMs) have advanced image geo-localization using cues like landmarks and road signs, their ability to reason about temporal signals and physically grounded spatial cues remains limited. To address this gap, we introduce TimeSpot, a benchmark for evaluating real-world geo-temporal reasoning in VLMs. TimeSpot comprises 1,455 ground-level images from 80 countries and requires structured prediction of temporal attributes (season, month, time of day, daylight phase) and geographic attributes (continent, country, climate zone, environment type, latitude-longitude) directly from visual evidence. It also includes spatial-temporal reasoning tasks that test physical plausibility under real-world uncertainty. Evaluations of state-of-the-art open- and closed-source VLMs show low performance, particularly for temporal inference. While supervised fine-tuning yields improvements, results remain insufficient, highlighting the need for new methods to achieve robust, physically grounded geo-temporal understanding. TimeSpot is available at: https://TimeSpot-GT.github.io.

Multimodal large language models (MLLMs) have made remarkable progress in either temporal or spatial localization. However, they struggle to perform spatio-temporal video grounding. This limitation stems from two major challenges. Firstly, it is difficult to extract accurate spatio-temporal information of each frame in the video. Secondly, the substantial number of visual tokens makes it challenging to precisely map visual tokens of each frame to their corresponding spatial coordinates. To address these issues, we introduce SpaceVLLM, a MLLM endowed with spatio-temporal video grounding capability. Specifically, we adopt a set of interleaved Spatio-Temporal Aware Queries to capture temporal perception and dynamic spatial information. Moreover, we propose a Query-Guided Space Decoder to establish a corresponding connection between the queries and spatial coordinates. Additionally, due to the lack of spatio-temporal datasets, we construct the Unified Spatio-Temporal Grounding (Uni-STG) dataset, comprising 480K instances across three tasks. This dataset fully exploits the potential of MLLM to simultaneously facilitate localization in both temporal and spatial dimensions. Extensive experiments demonstrate that SpaceVLLM achieves the state-of-the-art performance across 11 benchmarks covering temporal, spatial, spatio-temporal and video understanding tasks, highlighting the effectiveness of our approach. Our code, datasets and model will be released at https://github.com/Jayce1kk/SpaceVLLM.

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.

Finding multiple temporal relationships among locations can benefit a bunch of urban applications, such as dynamic offline advertising and smart public transport planning. While some efforts have been made on finding static relationships among locations, little attention is focused on studying time-aware location relationships. Indeed, abundant location-based human activities are time-varying and the availability of these data enables a new paradigm for understanding the dynamic relationships in a period among connective locations. To this end, we propose to study a new problem, namely multi-Temporal relationship inference among locations (Trial for short), where the major challenge is how to integrate dynamic and geographical influence under the relationship sparsity constraint. Specifically, we propose a solution to Trial with a graph learning scheme, which includes a spatially evolving graph neural network (SEENet) with two collaborative components: spatially evolving graph convolution module (SEConv) and spatially evolving self-supervised learning strategy (SE-SSL). SEConv performs the intra-time aggregation and inter-time propagation to capture the multifaceted spatially evolving contexts from the view of location message passing. In addition, SE-SSL designs time-aware self-supervised learning tasks in a global-local manner with additional evolving constraint to enhance the location representation learning and further handle the relationship sparsity. Finally, experiments on four real-world datasets demonstrate the superiority of our method over several state-of-the-art approaches.

Current model-based reinforcement learning (MBRL) agents struggle with long-term dependencies. This limits their ability to effectively solve tasks involving extended time gaps between actions and outcomes, or tasks demanding the recalling of distant observations to inform current actions. To improve temporal coherence, we integrate a new family of state space models (SSMs) in world models of MBRL agents to present a new method, Recall to Imagine (R2I). This integration aims to enhance both long-term memory and long-horizon credit assignment. Through a diverse set of illustrative tasks, we systematically demonstrate that R2I not only establishes a new state-of-the-art for challenging memory and credit assignment RL tasks, such as BSuite and POPGym, but also showcases superhuman performance in the complex memory domain of Memory Maze. At the same time, it upholds comparable performance in classic RL tasks, such as Atari and DMC, suggesting the generality of our method. We also show that R2I is faster than the state-of-the-art MBRL method, DreamerV3, resulting in faster wall-time convergence.

Building world models with spatial consistency and real-time interactivity remains a fundamental challenge in computer vision. Current video generation paradigms often struggle with a lack of spatial persistence and insufficient visual realism, making it difficult to support seamless navigation in complex environments. To address these challenges, we propose INSPATIO-WORLD, a novel real-time framework capable of recovering and generating high-fidelity, dynamic interactive scenes from a single reference video. At the core of our approach is a Spatiotemporal Autoregressive (STAR) architecture, which enables consistent and controllable scene evolution through two tightly coupled components: Implicit Spatiotemporal Cache aggregates reference and historical observations into a latent world representation, ensuring global consistency during long-horizon navigation; Explicit Spatial Constraint Module enforces geometric structure and translates user interactions into precise and physically plausible camera trajectories. Furthermore, we introduce Joint Distribution Matching Distillation (JDMD). By using real-world data distributions as a regularizing guide, JDMD effectively overcomes the fidelity degradation typically caused by over-reliance on synthetic data. Extensive experiments demonstrate that INSPATIO-WORLD significantly outperforms existing state-of-the-art (SOTA) models in spatial consistency and interaction precision, ranking first among real-time interactive methods on the WorldScore-Dynamic benchmark, and establishing a practical pipeline for navigating 4D environments reconstructed from monocular videos.

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

In order to make the foundation model more efficient and effective, our idea is combining sequence transformation and state transformation. First, we prove the availability of rotary position embedding in the state space duality algorithm, which reduces the perplexity of the hybrid quadratic causal self-attention and state space duality by more than 4%, to ensure that the combining sequence transformation unifies position encoding. Second, we propose dynamic mask attention, which maintains 100% accuracy in the more challenging multi-query associative recall task, improving by more than 150% compared to quadratic causal self-attention and state space duality, to ensure that the combining sequence transformation selectively filters relevant information. Third, we design cross domain mixture of experts, which makes the computational speed of expert retrieval with more than 1024 experts 8 to 10 times faster than the mixture of experts, to ensure that the combining state transformation quickly retrieval mixture. Finally, we summarize these matrix algorithms that can form the foundation model: Wonderful Matrices, which can be a competitor to popular model architectures.

Integrating CNNs and RNNs to capture spatiotemporal dependencies is a prevalent strategy for spatiotemporal prediction tasks. However, the property of CNNs to learn local spatial information decreases their efficiency in capturing spatiotemporal dependencies, thereby limiting their prediction accuracy. In this paper, we propose a new recurrent cell, SwinLSTM, which integrates Swin Transformer blocks and the simplified LSTM, an extension that replaces the convolutional structure in ConvLSTM with the self-attention mechanism. Furthermore, we construct a network with SwinLSTM cell as the core for spatiotemporal prediction. Without using unique tricks, SwinLSTM outperforms state-of-the-art methods on Moving MNIST, Human3.6m, TaxiBJ, and KTH datasets. In particular, it exhibits a significant improvement in prediction accuracy compared to ConvLSTM. Our competitive experimental results demonstrate that learning global spatial dependencies is more advantageous for models to capture spatiotemporal dependencies. We hope that SwinLSTM can serve as a solid baseline to promote the advancement of spatiotemporal prediction accuracy. The codes are publicly available at https://github.com/SongTang-x/SwinLSTM.

Offline reinforcement learning (RL) holds promise as a means to learn high-reward policies from a static dataset, without the need for further environment interactions. However, a key challenge in offline RL lies in effectively stitching portions of suboptimal trajectories from the static dataset while avoiding extrapolation errors arising due to a lack of support in the dataset. Existing approaches use conservative methods that are tricky to tune and struggle with multi-modal data (as we show) or rely on noisy Monte Carlo return-to-go samples for reward conditioning. In this work, we propose a novel approach that leverages the expressiveness of latent diffusion to model in-support trajectory sequences as compressed latent skills. This facilitates learning a Q-function while avoiding extrapolation error via batch-constraining. The latent space is also expressive and gracefully copes with multi-modal data. We show that the learned temporally-abstract latent space encodes richer task-specific information for offline RL tasks as compared to raw state-actions. This improves credit assignment and facilitates faster reward propagation during Q-learning. Our method demonstrates state-of-the-art performance on the D4RL benchmarks, particularly excelling in long-horizon, sparse-reward tasks.

State space models have shown to be effective at modeling long range dependencies, specially on sequence classification tasks. In this work we focus on autoregressive sequence modeling over English books, Github source code and ArXiv mathematics articles. Based on recent developments around the effectiveness of gated activation functions, we propose a new layer named Gated State Space (GSS) and show that it trains significantly faster than the diagonal version of S4 (i.e. DSS) on TPUs, is fairly competitive with several well-tuned Transformer-based baselines and exhibits zero-shot generalization to longer inputs while being straightforward to implement. Finally, we show that leveraging self-attention to model local dependencies improves the performance of GSS even further.

This paper presents a new exploration into a category of diffusion models built upon state space architecture. We endeavor to train diffusion models for image data, wherein the traditional U-Net backbone is supplanted by a state space backbone, functioning on raw patches or latent space. Given its notable efficacy in accommodating long-range dependencies, Diffusion State Space Models (DiS) are distinguished by treating all inputs including time, condition, and noisy image patches as tokens. Our assessment of DiS encompasses both unconditional and class-conditional image generation scenarios, revealing that DiS exhibits comparable, if not superior, performance to CNN-based or Transformer-based U-Net architectures of commensurate size. Furthermore, we analyze the scalability of DiS, gauged by the forward pass complexity quantified in Gflops. DiS models with higher Gflops, achieved through augmentation of depth/width or augmentation of input tokens, consistently demonstrate lower FID. In addition to demonstrating commendable scalability characteristics, DiS-H/2 models in latent space achieve performance levels akin to prior diffusion models on class-conditional ImageNet benchmarks at the resolution of 256times256 and 512times512, while significantly reducing the computational burden. The code and models are available at: https://github.com/feizc/DiS.

Humans excel at spatio-temporal reasoning, effortlessly interpreting dynamic visual events from an egocentric viewpoint. However, whether multimodal large language models (MLLMs) can similarly comprehend the 4D world remains uncertain. This paper explores multimodal spatio-temporal reasoning from an egocentric perspective, aiming to equip MLLMs with human-like reasoning capabilities. To support this objective, we introduce Ego-ST Bench, a novel benchmark containing over 5,000 question-answer pairs across four categories, systematically evaluating spatial, temporal, and integrated spatio-temporal reasoning. Additionally, we propose the ST-R1 Video model, a video-based reasoning model that incorporates reverse thinking into its reinforcement learning process, significantly enhancing performance. We combine long-chain-of-thought (long-CoT) supervised fine-tuning with Group Relative Policy Optimization (GRPO) reinforcement learning, achieving notable improvements with limited high-quality data. Ego-ST Bench and ST-R1 provide valuable insights and resources for advancing video-based spatio-temporal reasoning research.

Seeking high-quality representations with latent variable models (LVMs) to reveal the intrinsic correlation between neural activity and behavior or sensory stimuli has attracted much interest. In the study of the biological visual system, naturalistic visual stimuli are inherently high-dimensional and time-dependent, leading to intricate dynamics within visual neural activity. However, most work on LVMs has not explicitly considered neural temporal relationships. To cope with such conditions, we propose Time-Evolving Visual Dynamical System (TE-ViDS), a sequential LVM that decomposes neural activity into low-dimensional latent representations that evolve over time. To better align the model with the characteristics of visual neural activity, we split latent representations into two parts and apply contrastive learning to shape them. Extensive experiments on synthetic datasets and real neural datasets from the mouse visual cortex demonstrate that TE-ViDS achieves the best decoding performance on naturalistic scenes/movies, extracts interpretable latent trajectories that uncover clear underlying neural dynamics, and provides new insights into differences in visual information processing between subjects and between cortical regions. In summary, TE-ViDS is markedly competent in extracting stimulus-relevant embeddings from visual neural activity and contributes to the understanding of visual processing mechanisms. Our codes are available at https://github.com/Grasshlw/Time-Evolving-Visual-Dynamical-System.

Recent advances in vision-language models (VLMs) have made impressive strides in understanding spatio-temporal relationships in videos. However, when spatial information is obscured, these models struggle to capture purely temporal patterns. We introduce SpookyBench, a benchmark where information is encoded solely in temporal sequences of noise-like frames, mirroring natural phenomena from biological signaling to covert communication. Interestingly, while humans can recognize shapes, text, and patterns in these sequences with over 98% accuracy, state-of-the-art VLMs achieve 0% accuracy. This performance gap highlights a critical limitation: an over-reliance on frame-level spatial features and an inability to extract meaning from temporal cues. Furthermore, when trained in data sets with low spatial signal-to-noise ratios (SNR), temporal understanding of models degrades more rapidly than human perception, especially in tasks requiring fine-grained temporal reasoning. Overcoming this limitation will require novel architectures or training paradigms that decouple spatial dependencies from temporal processing. Our systematic analysis shows that this issue persists across model scales and architectures. We release SpookyBench to catalyze research in temporal pattern recognition and bridge the gap between human and machine video understanding. Dataset and code has been made available on our project website: https://timeblindness.github.io/.

Spatio-temporal reasoning is essential in understanding real-world environments in various fields, eg, autonomous driving and sports analytics. Recent advances have improved the spatial reasoning ability of Vision-Language Models (VLMs) by introducing large-scale data, but these models still struggle to analyze kinematic elements like traveled distance and speed of moving objects. To bridge this gap, we construct a spatio-temporal reasoning dataset and benchmark involving kinematic instruction tuning, referred to as STKit and STKit-Bench. They consist of real-world videos with 3D annotations, detailing object motion dynamics: traveled distance, speed, movement direction, inter-object distance comparisons, and relative movement direction. To further scale such data construction to videos without 3D labels, we propose an automatic pipeline to generate pseudo-labels using 4D reconstruction in real-world scale. With our kinematic instruction tuning data for spatio-temporal reasoning, we present ST-VLM, a VLM enhanced for spatio-temporal reasoning, which exhibits outstanding performance on STKit-Bench. Furthermore, we show that ST-VLM generalizes robustly across diverse domains and tasks, outperforming baselines on other spatio-temporal benchmarks (eg, ActivityNet, TVQA+). Finally, by integrating learned spatio-temporal reasoning with existing abilities, ST-VLM enables complex multi-step reasoning. Project page: https://ikodoh.github.io/ST-VLM.

World models serve as essential building blocks toward Artificial General Intelligence (AGI), enabling intelligent agents to predict future states and plan actions by simulating complex physical interactions. However, existing interactive models primarily predict visual observations, thereby neglecting crucial hidden states like geometric structures and spatial coherence. This leads to rapid error accumulation and temporal inconsistency. To address these limitations, we introduce DeepVerse, a novel 4D interactive world model explicitly incorporating geometric predictions from previous timesteps into current predictions conditioned on actions. Experiments demonstrate that by incorporating explicit geometric constraints, DeepVerse captures richer spatio-temporal relationships and underlying physical dynamics. This capability significantly reduces drift and enhances temporal consistency, enabling the model to reliably generate extended future sequences and achieve substantial improvements in prediction accuracy, visual realism, and scene rationality. Furthermore, our method provides an effective solution for geometry-aware memory retrieval, effectively preserving long-term spatial consistency. We validate the effectiveness of DeepVerse across diverse scenarios, establishing its capacity for high-fidelity, long-horizon predictions grounded in geometry-aware dynamics.

Next-generation AI companions must go beyond general video understanding to resolve spatial and temporal references in dynamic, real-world environments. Existing Video Large Language Models (Video LLMs), while capable of coarse-level comprehension, struggle with fine-grained, spatiotemporal reasoning, especially when user queries rely on time-based event references for temporal anchoring, or gestural cues for spatial anchoring to clarify object references and positions. To bridge this critical gap, we introduce Strefer, a synthetic instruction data generation framework designed to equip Video LLMs with spatiotemporal referring and reasoning capabilities. Strefer produces diverse instruction-tuning data using a data engine that pseudo-annotates temporally dense, fine-grained video metadata, capturing rich spatial and temporal information in a structured manner, including subjects, objects, their locations as masklets, and their action descriptions and timelines. Our approach enhances the ability of Video LLMs to interpret spatial and temporal references, fostering more versatile, space-time-aware reasoning essential for real-world AI companions. Without using proprietary models, costly human annotation, or the need to annotate large volumes of new videos, experimental evaluations show that models trained with data produced by Strefer outperform baselines on tasks requiring spatial and temporal disambiguation. Additionally, these models exhibit enhanced space-time-aware reasoning, establishing a new foundation for perceptually grounded, instruction-tuned Video LLMs.

Intelligent systems across physics, language and perception often exhibit factorisable structure, yet are typically modelled by monolithic neural architectures that do not explicitly exploit this structure. The separable neural architecture (SNA) addresses this by formalising a representational class that unifies additive, quadratic and tensor-decomposed neural models. By constraining interaction order and tensor rank, SNAs impose a structural inductive bias that factorises high-dimensional mappings into low-arity components. Separability need not be a property of the system itself: it often emerges in the coordinates or representations through which the system is expressed. Crucially, this coordinate-aware formulation reveals a structural analogy between chaotic spatiotemporal dynamics and linguistic autoregression. By treating continuous physical states as smooth, separable embeddings, SNAs enable distributional modelling of chaotic systems. This approach mitigates the nonphysical drift characteristics of deterministic operators whilst remaining applicable to discrete sequences. The compositional versatility of this approach is demonstrated across four domains: autonomous waypoint navigation via reinforcement learning, inverse generation of multifunctional microstructures, distributional modelling of turbulent flow and neural language modelling. These results establish the separable neural architecture as a domain-agnostic primitive for predictive and generative intelligence, capable of unifying both deterministic and distributional representations.

Traffic forecasting has emerged as a core component of intelligent transportation systems. However, timely accurate traffic forecasting, especially long-term forecasting, still remains an open challenge due to the highly nonlinear and dynamic spatial-temporal dependencies of traffic flows. In this paper, we propose a novel paradigm of Spatial-Temporal Transformer Networks (STTNs) that leverages dynamical directed spatial dependencies and long-range temporal dependencies to improve the accuracy of long-term traffic forecasting. Specifically, we present a new variant of graph neural networks, named spatial transformer, by dynamically modeling directed spatial dependencies with self-attention mechanism to capture realtime traffic conditions as well as the directionality of traffic flows. Furthermore, different spatial dependency patterns can be jointly modeled with multi-heads attention mechanism to consider diverse relationships related to different factors (e.g. similarity, connectivity and covariance). On the other hand, the temporal transformer is utilized to model long-range bidirectional temporal dependencies across multiple time steps. Finally, they are composed as a block to jointly model the spatial-temporal dependencies for accurate traffic prediction. Compared to existing works, the proposed model enables fast and scalable training over a long range spatial-temporal dependencies. Experiment results demonstrate that the proposed model achieves competitive results compared with the state-of-the-arts, especially forecasting long-term traffic flows on real-world PeMS-Bay and PeMSD7(M) datasets.

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.

Visual Model-Based Reinforcement Learning (MBRL) promises to encapsulate agent's knowledge about the underlying dynamics of the environment, enabling learning a world model as a useful planner. However, top MBRL agents such as Dreamer often struggle with visual pixel-based inputs in the presence of exogenous or irrelevant noise in the observation space, due to failure to capture task-specific features while filtering out irrelevant spatio-temporal details. To tackle this problem, we apply a spatio-temporal masking strategy, a bisimulation principle, combined with latent reconstruction, to capture endogenous task-specific aspects of the environment for world models, effectively eliminating non-essential information. Joint training of representations, dynamics, and policy often leads to instabilities. To further address this issue, we develop a Hybrid Recurrent State-Space Model (HRSSM) structure, enhancing state representation robustness for effective policy learning. Our empirical evaluation demonstrates significant performance improvements over existing methods in a range of visually complex control tasks such as Maniskill gu2023maniskill2 with exogenous distractors from the Matterport environment. Our code is avaliable at https://github.com/bit1029public/HRSSM.

As video diffusion models (VDMs) advance toward world models, a key question arises: do they truly understand causality, or merely overfit to statistical temporal patterns? Existing benchmarks mostly rely on synthetic data, limiting real-world generalization due to the sim-to-real gap. We present YoCausal, a two-level benchmark inspired by the Violation of Expectation (VoE) paradigm from cognitive science. By temporally reversing real-world videos at zero cost as natural counterfactual samples, YoCausal establishes an arbitrarily extensible evaluation protocol. Level 1 introduces the Reverse Surprise Index (RSI), quantifying arrow-of-time perception via denoising loss. Level 2 introduces the Causality Cognition Index (CCI), which leverages a VLM to stratify datasets into causal and non-causal subsets, disentangling genuine causal reasoning from temporal bias. Evaluation of 13 state-of-the-art VDMs reveals that perceiving the arrow of time does not imply understanding causality, and a significant gap persists relative to human-level causal cognition.

Foundational world models must be both interactive and preserve spatiotemporal coherence for effective future planning with action choices. However, present models for long video generation have limited inherent world modeling capabilities due to two main challenges: compounding errors and insufficient memory mechanisms. We enhance image-to-video models with interactive capabilities through additional action conditioning and autoregressive framework, and reveal that compounding error is inherently irreducible in autoregressive video generation, while insufficient memory mechanism leads to incoherence of world models. We propose video retrieval augmented generation (VRAG) with explicit global state conditioning, which significantly reduces long-term compounding errors and increases spatiotemporal consistency of world models. In contrast, naive autoregressive generation with extended context windows and retrieval-augmented generation prove less effective for video generation, primarily due to the limited in-context learning capabilities of current video models. Our work illuminates the fundamental challenges in video world models and establishes a comprehensive benchmark for improving video generation models with internal world modeling capabilities.

Episodic memory plays a crucial role in various cognitive processes, such as the ability to mentally recall past events. While cognitive science emphasizes the significance of spatial context in the formation and retrieval of episodic memory, the current primary approach to implementing episodic memory in AI systems is through transformers that store temporally ordered experiences, which overlooks the spatial dimension. As a result, it is unclear how the underlying structure could be extended to incorporate the spatial axis beyond temporal order alone and thereby what benefits can be obtained. To address this, this paper explores the use of Spatially-Aware Transformer models that incorporate spatial information. These models enable the creation of place-centric episodic memory that considers both temporal and spatial dimensions. Adopting this approach, we demonstrate that memory utilization efficiency can be improved, leading to enhanced accuracy in various place-centric downstream tasks. Additionally, we propose the Adaptive Memory Allocator, a memory management method based on reinforcement learning that aims to optimize efficiency of memory utilization. Our experiments demonstrate the advantages of our proposed model in various environments and across multiple downstream tasks, including prediction, generation, reasoning, and reinforcement learning. The source code for our models and experiments will be available at https://github.com/junmokane/spatially-aware-transformer.

The ability to reason about spatial dynamics is a cornerstone of intelligence, yet current research overlooks the human intent behind spatial changes. To address these limitations, we introduce Teleo-Spatial Intelligence (TSI), a new paradigm that unifies two critical pillars: Physical-Dynamic Reasoning--understanding the physical principles of object interactions--and Intent-Driven Reasoning--inferring the human goals behind these actions. To catalyze research in TSI, we present EscherVerse, consisting of a large-scale, open-world benchmark (Escher-Bench), a dataset (Escher-35k), and models (Escher series). Derived from real-world videos, EscherVerse moves beyond constrained settings to explicitly evaluate an agent's ability to reason about object permanence, state transitions, and trajectory prediction in dynamic, human-centric scenarios. Crucially, it is the first benchmark to systematically assess Intent-Driven Reasoning, challenging models to connect physical events to their underlying human purposes. Our work, including a novel data curation pipeline, provides a foundational resource to advance spatial intelligence from passive scene description toward a holistic, purpose-driven understanding of the world.

Current advancements in reinforcement learning (RL) have predominantly focused on learning step-based policies that generate actions for each perceived state. While these methods efficiently leverage step information from environmental interaction, they often ignore the temporal correlation between actions, resulting in inefficient exploration and unsmooth trajectories that are challenging to implement on real hardware. Episodic RL (ERL) seeks to overcome these challenges by exploring in parameters space that capture the correlation of actions. However, these approaches typically compromise data efficiency, as they treat trajectories as opaque black boxes. In this work, we introduce a novel ERL algorithm, Temporally-Correlated Episodic RL (TCE), which effectively utilizes step information in episodic policy updates, opening the 'black box' in existing ERL methods while retaining the smooth and consistent exploration in parameter space. TCE synergistically combines the advantages of step-based and episodic RL, achieving comparable performance to recent ERL methods while maintaining data efficiency akin to state-of-the-art (SoTA) step-based RL.

Inferring music time structures has a broad range of applications in music production, processing and analysis. Scholars have proposed various methods to analyze different aspects of time structures, such as beat, downbeat, tempo and meter. Many state-of-the-art (SOFA) methods, however, are computationally expensive. This makes them inapplicable in real-world industrial settings where the scale of the music collections can be millions. This paper proposes a new state space and a semi-Markov model for music time structure analysis. The proposed approach turns the commonly used 2D state spaces into a 1D model through a jump-back reward strategy. It reduces the state spaces size drastically. We then utilize the proposed method for causal, joint beat, downbeat, tempo, and meter tracking, and compare it against several previous methods. The proposed method delivers similar performance with the SOFA joint causal models with a much smaller state space and a more than 30 times speedup.

Given time series data, how can we answer questions like "what will happen in the future?" and "how did we get here?" These sorts of probabilistic inference questions are challenging when observations are high-dimensional. In this paper, we show how these questions can have compact, closed form solutions in terms of learned representations. The key idea is to apply a variant of contrastive learning to time series data. Prior work already shows that the representations learned by contrastive learning encode a probability ratio. By extending prior work to show that the marginal distribution over representations is Gaussian, we can then prove that joint distribution of representations is also Gaussian. Taken together, these results show that representations learned via temporal contrastive learning follow a Gauss-Markov chain, a graphical model where inference (e.g., prediction, planning) over representations corresponds to inverting a low-dimensional matrix. In one special case, inferring intermediate representations will be equivalent to interpolating between the learned representations. We validate our theory using numerical simulations on tasks up to 46-dimensions.

Forecasting future events based on evidence of current conditions is an innate skill of human beings, and key for predicting the outcome of any decision making. In artificial vision for example, we would like to predict the next human action before it happens, without observing the future video frames associated to it. Computer vision models for action anticipation are expected to collect the subtle evidence in the preamble of the target actions. In prior studies recurrence modeling often leads to better performance, the strong temporal inference is assumed to be a key element for reasonable prediction. To this end, we propose a unified recurrence modeling for video action anticipation via message passing framework. The information flow in space-time can be described by the interaction between vertices and edges, and the changes of vertices for each incoming frame reflects the underlying dynamics. Our model leverages self-attention as the building blocks for each of the message passing functions. In addition, we introduce different edge learning strategies that can be end-to-end optimized to gain better flexibility for the connectivity between vertices. Our experimental results demonstrate that our proposed method outperforms previous works on the large-scale EPIC-Kitchen dataset.

Spatial reasoning in 3D space is central to human cognition and indispensable for embodied tasks such as navigation and manipulation. However, state-of-the-art vision-language models (VLMs) struggle frequently with tasks as simple as anticipating how a scene will look after an egocentric motion: they perceive 2D images but lack an internal model of 3D dynamics. We therefore propose MindJourney, a test-time scaling framework that grants a VLM with this missing capability by coupling it to a controllable world model based on video diffusion. The VLM iteratively sketches a concise camera trajectory, while the world model synthesizes the corresponding view at each step. The VLM then reasons over this multi-view evidence gathered during the interactive exploration. Without any fine-tuning, our MindJourney achieves over an average 8% performance boost on the representative spatial reasoning benchmark SAT, showing that pairing VLMs with world models for test-time scaling offers a simple, plug-and-play route to robust 3D reasoning. Meanwhile, our method also improves upon the test-time inference VLMs trained through reinforcement learning, which demonstrates the potential of our method that utilizes world models for test-time scaling.

Spatial and temporal resource constraints are critical for both biological and artificial intelligent systems. Here we define differentiable cost terms for breadth, depth, and time within a recurrent convolutional neural network conceived as a finite subset of an infinite lattice. We optimize these costs jointly with task errors via backpropagation. We set different pressures on breadth, depth, and time, which leads to diverse computational graphs emerging organically through training. We find that all three resources can be traded off against each other to achieve a given level of accuracy. Networks grow in all three dimensions with task complexity and spontaneously take more recurrent steps when inputs are occluded. Surprisingly, time used by the model correlates with human reaction times in an object recognition task. Our framework provides a normative account of how resource constraints shape neural architectures, connecting to questions about brain design in neuroscience, and may help illuminate the diversity of neural solutions found in nature.

Most existing spatial reasoning benchmarks focus on static or globally observable environments, failing to capture the challenges of long-horizon reasoning and memory utilization under partial observability and dynamic changes. We introduce two dynamic spatial benchmarks, locally observable maze navigation and match-2 elimination that systematically evaluate models' abilities in spatial understanding and adaptive planning when local perception, environment feedback, and global objectives are tightly coupled. Each action triggers structural changes in the environment, requiring continuous update of cognition and strategy. We further propose a subjective experience-based memory mechanism for cross-task experience transfer and validation. Experiments show that our benchmarks reveal key limitations of mainstream models in dynamic spatial reasoning and long-term memory, providing a comprehensive platform for future methodological advances. Our code and data are available at https://anonymous.4open.science/r/EvoEmpirBench-143C/.

Recent Video Large Language Models (Video-LLMs) have shown strong multimodal reasoning capabilities, yet remain challenged by video understanding tasks that require consistent temporal ordering and causal coherence. Many parameter-efficient Video-LLMs rely on unconstrained bidirectional projectors to model inter-frame interactions, which can blur temporal ordering by allowing later frames to influence earlier representations, without explicit architectural mechanisms to respect the directional nature of video reasoning. To address this limitation, we propose V-CORE, a parameter-efficient framework that introduces explicit temporal ordering constraints for video understanding. V-CORE consists of two key components: (1) Learnable Spatial Aggregation (LSA), which adaptively selects salient spatial tokens to reduce redundancy, and (2) a Causality-Aware Temporal Projector (CATP), which enforces structured unidirectional information flow via block-causal attention and a terminal dynamic summary token acting as a causal sink. This design preserves intra-frame spatial interactions while ensuring that temporal information is aggregated in a strictly ordered manner. With 4-bit QLoRA and a frozen LLM backbone, V-CORE can be trained efficiently on a single consumer GPU. Experiments show that V-CORE achieves strong performance on the challenging NExT-QA benchmark, reaching 61.2% accuracy, and remains competitive across MSVD-QA, MSRVTT-QA, and TGIF-QA, with gains concentrated in temporal and causal reasoning subcategories (+3.5% and +5.2% respectively), directly validating the importance of explicit temporal ordering constraints.

Spatiotemporal reasoning plays a key role in Cyber-Physical Systems (CPS). Despite advances in Large Language Models (LLMs) and Large Reasoning Models (LRMs), their capacity to reason about complex spatiotemporal signals remains underexplored. This paper proposes a hierarchical SpatioTemporal reAsoning benchmaRK, STARK, to systematically evaluate LLMs across three levels of reasoning complexity: state estimation (e.g., predicting field variables, localizing and tracking events in space and time), spatiotemporal reasoning over states (e.g., inferring spatial-temporal relationships), and world-knowledge-aware reasoning that integrates contextual and domain knowledge (e.g., intent prediction, landmark-aware navigation). We curate 26 distinct spatiotemporal tasks with diverse sensor modalities, comprising 14,552 challenges where models answer directly or by Python Code Interpreter. Evaluating 3 LRMs and 8 LLMs, we find LLMs achieve limited success in tasks requiring geometric reasoning (e.g., multilateration or triangulation), particularly as complexity increases. Surprisingly, LRMs show robust performance across tasks with various levels of difficulty, often competing or surpassing traditional first-principle-based methods. Our results show that in reasoning tasks requiring world knowledge, the performance gap between LLMs and LRMs narrows, with some LLMs even surpassing LRMs. However, the LRM o3 model continues to achieve leading performance across all evaluated tasks, a result attributed primarily to the larger size of the reasoning models. STARK motivates future innovations in model architectures and reasoning paradigms for intelligent CPS by providing a structured framework to identify limitations in the spatiotemporal reasoning of LLMs and LRMs.

Humans are born with vision-based 4D spatial-temporal intelligence, which enables us to perceive and reason about the evolution of 3D space over time from purely visual inputs. Despite its importance, this capability remains a significant bottleneck for current multimodal large language models (MLLMs). To tackle this challenge, we introduce MLLM-4D, a comprehensive framework designed to bridge the gaps in training data curation and model post-training for spatiotemporal understanding and reasoning. On the data front, we develop a cost-efficient data curation pipeline that repurposes existing stereo video datasets into high-quality 4D spatiotemporal instructional data. This results in the MLLM4D-2M and MLLM4D-R1-30k datasets for Supervised Fine-Tuning (SFT) and Reinforcement Fine-Tuning (RFT), alongside MLLM4D-Bench for comprehensive evaluation. Regarding model training, our post-training strategy establishes a foundational 4D understanding via SFT and further catalyzes 4D reasoning capabilities by employing Group Relative Policy Optimization (GRPO) with specialized Spatiotemporal Chain of Thought (ST-CoT) prompting and Spatiotemporal reward functions (ST-reward) without involving the modification of architecture. Extensive experiments demonstrate that MLLM-4D achieves state-of-the-art spatial-temporal understanding and reasoning capabilities from purely 2D RGB inputs. Project page: https://github.com/GVCLab/MLLM-4D.

Activity difference based learning algorithms-such as contrastive Hebbian learning and equilibrium propagation-have been proposed as biologically plausible alternatives to error back-propagation. However, on traditional digital chips these algorithms suffer from having to solve a costly inference problem twice, making these approaches more than two orders of magnitude slower than back-propagation. In the analog realm equilibrium propagation may be promising for fast and energy efficient learning, but states still need to be inferred and stored twice. Inspired by lifted neural networks and compartmental neuron models we propose a simple energy based compartmental neuron model, termed dual propagation, in which each neuron is a dyad with two intrinsic states. At inference time these intrinsic states encode the error/activity duality through their difference and their mean respectively. The advantage of this method is that only a single inference phase is needed and that inference can be solved in layerwise closed-form. Experimentally we show on common computer vision datasets, including Imagenet32x32, that dual propagation performs equivalently to back-propagation both in terms of accuracy and runtime.

The growing interest in embodied agents increases the demand for spatiotemporal video understanding, yet existing benchmarks largely emphasize extractive reasoning, where answers can be explicitly presented within spatiotemporal events. It remains unclear whether multimodal large language models can instead perform abstractive spatiotemporal reasoning, which requires integrating observations over time, combining dispersed cues, and inferring implicit spatial and contextual structure. To address this gap, we formalize abstractive spatiotemporal reasoning from videos by introducing a structured evaluation taxonomy that systematically targets its core dimensions and construct a controllable, scenario-driven synthetic egocentric video dataset tailored to evaluate abstractive spatiotemporal reasoning capabilities, spanning object-, room-, and floor-plan-level scenarios. Based on this framework, we present VAEX-BENCH, a benchmark comprising five abstractive reasoning tasks together with their extractive counterparts. Our extensive experiments compare the performance of state-of-the-art MLLMs under extractive and abstractive settings, exposing their limitations on abstractive tasks and providing a fine-grained analysis of the underlying bottlenecks. The dataset will be released soon.

Recently, large-scale pre-trained language-image models like CLIP have shown extraordinary capabilities for understanding spatial contents, but naively transferring such models to video recognition still suffers from unsatisfactory temporal modeling capabilities. Existing methods insert tunable structures into or in parallel with the pre-trained model, which either requires back-propagation through the whole pre-trained model and is thus resource-demanding, or is limited by the temporal reasoning capability of the pre-trained structure. In this work, we present DiST, which disentangles the learning of spatial and temporal aspects of videos. Specifically, DiST uses a dual-encoder structure, where a pre-trained foundation model acts as the spatial encoder, and a lightweight network is introduced as the temporal encoder. An integration branch is inserted between the encoders to fuse spatio-temporal information. The disentangled spatial and temporal learning in DiST is highly efficient because it avoids the back-propagation of massive pre-trained parameters. Meanwhile, we empirically show that disentangled learning with an extra network for integration benefits both spatial and temporal understanding. Extensive experiments on five benchmarks show that DiST delivers better performance than existing state-of-the-art methods by convincing gaps. When pre-training on the large-scale Kinetics-710, we achieve 89.7% on Kinetics-400 with a frozen ViT-L model, which verifies the scalability of DiST. Codes and models can be found in https://github.com/alibaba-mmai-research/DiST.

Vision-Language-Action (VLA) models have recently shown strong generalization, with some approaches seeking to explicitly generate linguistic reasoning traces or predict future observations prior to execution. However, explicit reasoning typically incurs non-negligible inference latency, which constrains the temporal resolution required for robotic manipulation. Moreover, such reasoning is confined to the linguistic space, imposing a representational bottleneck that struggles to faithfully capture ineffable physical attributes. To mitigate these limitations, we propose LaST_0, a framework that enables efficient reasoning before acting through a Latent Spatio-Temporal Chain-of-Thought (CoT), capturing fine-grained physical and robotic dynamics that are often difficult to verbalize. Specifically, we introduce a token-efficient latent CoT space that models future visual dynamics, 3D structural information, and robot proprioceptive states, and further extends these representations across time to enable temporally consistent implicit reasoning trajectories. Furthermore, LaST_0 adopts a dual-system architecture implemented via a Mixture-of-Transformers design, where a reasoning expert conducts low-frequency latent inference and an acting expert generates high-frequency actions conditioned on robotics-oriented latent representations. To facilitate coordination, LaST_0 is trained with heterogeneous operation frequencies, enabling adaptive switching during deployment. Across 10 real-world tasks spanning tabletop, mobile, and dexterous hand manipulation, LaST_0 improves mean success rates by 13%, 14% and 14% over prior SOTA VLA methods, respectively.

State-space model releases are typically coupled to fused CUDA and Triton kernels, inheriting a hard dependency on NVIDIA hardware. We show that Mamba-2's state space duality algorithm -- diagonal state structure, chunkable recurrence, and einsum-dominated compute with static control flow -- maps cleanly onto what XLA's fusion and tiling passes actually optimise, making custom kernels optional rather than required. We implement the full inference path (prefill, cached autoregressive decoding) as shaped standard primitives under XLA, without hand-written kernels, and realise the architecture's theoretical O(1) state management as a compiled on-device cache requiring no host synchronisation during generation. The implementation runs unmodified on CPU, NVIDIA GPU, and Google Cloud TPU from a single JAX source. On TPU v6e across five model scales (130M--2.7B parameters), XLA-generated code reaches approximately 140 TFLOPS on single-stream prefill (15% MFU) and up to 64% bandwidth utilisation on decode. Greedy decoding matches the PyTorch/CUDA reference token-for-token across 64 steps, with hidden-state agreement within float32 rounding tolerance. The pattern transfers to any SSM recurrence satisfying the same structural conditions, on any platform with a mature XLA backend. The implementation is publicly available at https://github.com/CosmoNaught/mamba2-jax and merged into the Bonsai JAX model library.

Spatio-Temporal Graph (STG) forecasting is a fundamental task in many real-world applications. Spatio-Temporal Graph Neural Networks have emerged as the most popular method for STG forecasting, but they often struggle with temporal out-of-distribution (OoD) issues and dynamic spatial causation. In this paper, we propose a novel framework called CaST to tackle these two challenges via causal treatments. Concretely, leveraging a causal lens, we first build a structural causal model to decipher the data generation process of STGs. To handle the temporal OoD issue, we employ the back-door adjustment by a novel disentanglement block to separate invariant parts and temporal environments from input data. Moreover, we utilize the front-door adjustment and adopt the Hodge-Laplacian operator for edge-level convolution to model the ripple effect of causation. Experiments results on three real-world datasets demonstrate the effectiveness and practicality of CaST, which consistently outperforms existing methods with good interpretability.

Vision-Language-Action (VLA) models have recently enabled robotic manipulation by grounding visual and linguistic cues into actions. However, most VLAs assume the Markov property, relying only on the current observation and thus suffering from temporal myopia that degrades long-horizon coherence. In this work, we view motion as a more compact and informative representation of temporal context and world dynamics, capturing inter-state changes while filtering static pixel-level noise. Building on this idea, we propose HiF-VLA (Hindsight, Insight, and Foresight for VLAs), a unified framework that leverages motion for bidirectional temporal reasoning. HiF-VLA encodes past dynamics through hindsight priors, anticipates future motion via foresight reasoning, and integrates both through a hindsight-modulated joint expert to enable a ''think-while-acting'' paradigm for long-horizon manipulation. As a result, HiF-VLA surpasses strong baselines on LIBERO-Long and CALVIN ABC-D benchmarks, while incurring negligible additional inference latency. Furthermore, HiF-VLA achieves substantial improvements in real-world long-horizon manipulation tasks, demonstrating its broad effectiveness in practical robotic settings.

Embodied AI requires agents that perceive, act, and anticipate how actions reshape future world states. World models serve as internal simulators that capture environment dynamics, enabling forward and counterfactual rollouts to support perception, prediction, and decision making. This survey presents a unified framework for world models in embodied AI. Specifically, we formalize the problem setting and learning objectives, and propose a three-axis taxonomy encompassing: (1) Functionality, Decision-Coupled vs. General-Purpose; (2) Temporal Modeling, Sequential Simulation and Inference vs. Global Difference Prediction; (3) Spatial Representation, Global Latent Vector, Token Feature Sequence, Spatial Latent Grid, and Decomposed Rendering Representation. We systematize data resources and metrics across robotics, autonomous driving, and general video settings, covering pixel prediction quality, state-level understanding, and task performance. Furthermore, we offer a quantitative comparison of state-of-the-art models and distill key open challenges, including the scarcity of unified datasets and the need for evaluation metrics that assess physical consistency over pixel fidelity, the trade-off between model performance and the computational efficiency required for real-time control, and the core modeling difficulty of achieving long-horizon temporal consistency while mitigating error accumulation. Finally, we maintain a curated bibliography at https://github.com/Li-Zn-H/AwesomeWorldModels.

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.

Grounding events in videos serves as a fundamental capability in video analysis. While Vision Language Models (VLMs) are increasingly employed for this task, existing approaches predominantly train models to associate events with timestamps in the forward video only. This paradigm hinders VLMs from capturing the inherent temporal structure and directionality of events, thereby limiting robustness and generalization. To address this limitation, inspired by the arrow of time in physics, which characterizes the intrinsic directionality of temporal processes, we propose ArrowGEV, a reinforcement learning framework that explicitly models temporal directionality in events to improve both event grounding and temporal directionality understanding in VLMs. Specifically, we categorize events into time-sensitive (e.g., putting down a bag) and time-insensitive (e.g., holding a towel in the left hand). The former denote events whose reversal substantially alters their meaning, while the latter remain semantically unchanged under reversal. For time-sensitive events, ArrowGEV introduces a reward that encourages VLMs to discriminate between forward and backward videos, whereas for time-insensitive events, it enforces consistent grounding across both directions. Extensive experiments demonstrate that ArrowGEV not only improves grounding precision and temporal directionality recognition, but also enhances general video understanding and reasoning ability.

Vision-language-action (VLA) models show potential for general robotic tasks, but remain challenging in spatiotemporally coherent manipulation, which requires fine-grained representations. Typically, existing methods embed 3D positions into visual representations to enhance the spatial precision of actions. However, these methods struggle to achieve temporally coherent control over action execution. In this work, we propose VLA-4D, a general VLA model with 4D awareness for spatiotemporally coherent robotic manipulation. Our model is guided by two key designs: 1) 4D-aware visual representation. We extract visual features, embed 1D time into 3D positions for 4D embeddings, and fuse them into a unified visual representation via a cross-attention mechanism. 2) Spatiotemporal action representation. We extend conventional spatial action representations with temporal information to enable the spatiotemporal planning, and align the multimodal representations into the LLM for spatiotemporal action prediction. Within this unified framework, the designed visual and action representations jointly make robotic manipulation spatially-smooth and temporally-coherent. In addition, we extend the VLA dataset with temporal action annotations for fine-tuning our model. Extensive experiments have been conducted to verify the superiority of our method across different tasks of robotic manipulation.

State-space models (SSMs) are a new class of foundation models that have emerged as a compelling alternative to Transformers and their attention mechanisms for sequence processing tasks. This paper provides a detailed theoretical analysis of selective SSMs, the core components of the Mamba and Mamba-2 architectures. We leverage the connection between selective SSMs and the self-attention mechanism to highlight the fundamental similarities between these models. Building on this connection, we establish a length independent covering number-based generalization bound for selective SSMs, providing a deeper understanding of their theoretical performance guarantees. We analyze the effects of state matrix stability and input-dependent discretization, shedding light on the critical role played by these factors in the generalization capabilities of selective SSMs. Finally, we empirically demonstrate the sequence length independence of the derived bounds on two tasks.

Temporal credit assignment in reinforcement learning has long been a central challenge. Inspired by the multi-timescale encoding of the dopamine system in neurobiology, recent research has sought to introduce multiple discount factors into Actor-Critic architectures, such as Proximal Policy Optimization (PPO), to balance short-term responses with long-term planning. However, this paper reveals that blindly fusing multi-timescale signals in complex delayed-reward tasks can lead to severe algorithmic pathologies. We systematically demonstrate that exposing a temporal attention routing mechanism to policy gradients results in surrogate objective hacking, while adopting gradient-free uncertainty weighting triggers irreversible myopic degeneration, a phenomenon we term the Paradox of Temporal Uncertainty. To address these issues, we propose a Target Decoupling architecture: on the Critic side, we retain multi-timescale predictions to enforce auxiliary representation learning, while on the Actor side, we strictly isolate short-term signals and update the policy based solely on long-term advantages. Rigorous empirical evaluations across multiple independent random seeds in the LunarLander-v2 environment demonstrate that our proposed architecture achieves statistically significant performance improvements. Without relying on hyperparameter hacking, it consistently surpasses the ''Environment Solved'' threshold with minimal variance, completely eliminates policy collapse, and escapes the hovering local optima that trap single-timescale baselines. The source code to reproduce our experiments is publicly available at https://github.com/ben-dlwlrma/Representation-Over-Routing.

Spatio-temporal prediction is a pivotal task with broad applications in traffic management, climate monitoring, energy scheduling, etc. However, existing methodologies often struggle to balance model expressiveness and computational efficiency, especially when scaling to large real-world datasets. To tackle these challenges, we propose STH-SepNet (Spatio-Temporal Hypergraph Separation Networks), a novel framework that decouples temporal and spatial modeling to enhance both efficiency and precision. Therein, the temporal dimension is modeled using lightweight large language models, which effectively capture low-rank temporal dynamics. Concurrently, the spatial dimension is addressed through an adaptive hypergraph neural network, which dynamically constructs hyperedges to model intricate, higher-order interactions. A carefully designed gating mechanism is integrated to seamlessly fuse temporal and spatial representations. By leveraging the fundamental principles of low-rank temporal dynamics and spatial interactions, STH-SepNet offers a pragmatic and scalable solution for spatio-temporal prediction in real-world applications. Extensive experiments on large-scale real-world datasets across multiple benchmarks demonstrate the effectiveness of STH-SepNet in boosting predictive performance while maintaining computational efficiency. This work may provide a promising lightweight framework for spatio-temporal prediction, aiming to reduce computational demands and while enhancing predictive performance. Our code is avaliable at https://github.com/SEU-WENJIA/ST-SepNet-Lightweight-LLMs-Meet-Adaptive-Hypergraphs.

Fine-grained spatio-temporal understanding is essential for video reasoning and embodied AI. Yet, while Multimodal Large Language Models (MLLMs) master static semantics, their grasp of temporal dynamics remains brittle. We present TimeBlind, a diagnostic benchmark for compositional spatio-temporal understanding. Inspired by cognitive science, TimeBlind categorizes fine-grained temporal understanding into three levels: recognizing atomic events, characterizing event properties, and reasoning about event interdependencies. Unlike benchmarks that conflate recognition with temporal reasoning, TimeBlind leverages a minimal-pairs paradigm: video pairs share identical static visual content but differ solely in temporal structure, utilizing complementary questions to neutralize language priors. Evaluating over 20 state-of-the-art MLLMs (e.g., GPT-5, Gemini 3 Pro) on 600 curated instances (2400 video-question pairs), reveals that the Instance Accuracy (correctly distinguishing both videos in a pair) of the best performing MLLM is only 48.2%, far below the human performance (98.2%). These results demonstrate that even frontier models rely heavily on static visual shortcuts rather than genuine temporal logic, positioning TimeBlind as a vital diagnostic tool for next-generation video understanding. Dataset and code are available at https://baiqi-li.github.io/timeblind_project/ .

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

Current multimodal models aim to transcend the limitations of single-modality representations by unifying understanding and generation, often using text-to-image (T2I) tasks to calibrate semantic consistency. However, their reliance on static, single-image generation in training and evaluation leads to overfitting to static pattern matching and semantic fusion, while fundamentally hindering their ability to model dynamic processes that unfold over time. To address these constraints, we propose Envision-a causal event progression benchmark for chained text-to-multi-image generation. Grounded in world knowledge and structured by spatiotemporal causality, it reorganizes existing evaluation dimensions and includes 1,000 four-stage prompts spanning six scientific and humanities domains. To transition evaluation from single images to sequential frames and assess whether models truly internalize world knowledge while adhering to causal-temporal constraints, we introduce Envision-Score, a holistic metric integrating multi-dimensional consistency, physicality, and aesthetics. Comprehensive evaluation of 15 models (10 specialized T2I models, 5 unified models) uncovers: specialized T2I models demonstrate proficiency in aesthetic rendering yet lack intrinsic world knowledge. Unified multimodal models bridge this gap, consistently outperforming specialized counterparts in causal narrative coherence. However, even these unified architectures remain subordinate to closed-source models and struggle to overcome the core challenge of spatiotemporal consistency. This demonstrates that a focus on causally-isolated single images impedes multi-frame reasoning and generation, promoting static pattern matching over dynamic world modeling-ultimately limiting world knowledge internalization, generation.

Given a dataset on actions and resulting long-term rewards, a direct estimation approach fits value functions that minimize prediction error on the training data. Temporal difference learning (TD) methods instead fit value functions by minimizing the degree of temporal inconsistency between estimates made at successive time-steps. Focusing on finite state Markov chains, we provide a crisp asymptotic theory of the statistical advantages of this approach. First, we show that an intuitive inverse trajectory pooling coefficient completely characterizes the percent reduction in mean-squared error of value estimates. Depending on problem structure, the reduction could be enormous or nonexistent. Next, we prove that there can be dramatic improvements in estimates of the difference in value-to-go for two states: TD's errors are bounded in terms of a novel measure - the problem's trajectory crossing time - which can be much smaller than the problem's time horizon.

LLM-for-time series (TS) methods typically treat time shallowly, injecting positional or prompt-based cues once at the input of a largely frozen decoder, which limits temporal reasoning as this information degrades through the layers. We introduce Temporal-Prior Conditioning (TPC), which elevates time to a first-class modality that conditions the model at multiple depths. TPC attaches a small set of learnable time series tokens to the patch stream; at selected layers these tokens cross-attend to temporal embeddings derived from compact, human-readable temporal descriptors encoded by the same frozen LLM, then feed temporal context back via self-attention. This disentangles time series signal and temporal information while maintaining a low parameter budget. We show that by training only the cross-attention modules and explicitly disentangling time series signal and temporal information, TPC consistently outperforms both full fine-tuning and shallow conditioning strategies, achieving state-of-the-art performance in long-term forecasting across diverse datasets. Code available at: https://github.com/fil-mp/Deep_tpc

Vision-centric hierarchical embodied models have demonstrated strong potential for long-horizon robotic control. However, existing methods lack spatial awareness capabilities, limiting their effectiveness in bridging visual plans to actionable control in complex environments. To address this problem, we propose Spatial Policy (SP), a unified spatial-aware visuomotor robotic manipulation framework via explicit spatial modeling and reasoning. Specifically, we first design a spatial-conditioned embodied video generation module to model spatially guided predictions through a spatial plan table. Then, we propose a spatial-based action prediction module to infer executable actions with coordination. Finally, we propose a spatial reasoning feedback policy to refine the spatial plan table via dual-stage replanning. Extensive experiments show that SP significantly outperforms state-of-the-art baselines, achieving a 33.0% average improvement over the best baseline. With an 86.7% average success rate across 11 diverse tasks, SP substantially enhances the practicality of embodied models for robotic control applications. Code and checkpoints are maintained at https://plantpotatoonmoon.github.io/SpatialPolicy/.

Traffic prediction is a typical spatio-temporal data mining task and has great significance to the public transportation system. Considering the demand for its grand application, we recognize key factors for an ideal spatio-temporal prediction method: efficient, lightweight, and effective. However, the current deep model-based spatio-temporal prediction solutions generally own intricate architectures with cumbersome optimization, which can hardly meet these expectations. To accomplish the above goals, we propose an intuitive and novel framework, MLPST, a pure multi-layer perceptron architecture for traffic prediction. Specifically, we first capture spatial relationships from both local and global receptive fields. Then, temporal dependencies in different intervals are comprehensively considered. Through compact and swift MLP processing, MLPST can well capture the spatial and temporal dependencies while requiring only linear computational complexity, as well as model parameters that are more than an order of magnitude lower than baselines. Extensive experiments validated the superior effectiveness and efficiency of MLPST against advanced baselines, and among models with optimal accuracy, MLPST achieves the best time and space efficiency.

We introduce EnerVerse, a comprehensive framework for embodied future space generation specifically designed for robotic manipulation tasks. EnerVerse seamlessly integrates convolutional and bidirectional attention mechanisms for inner-chunk space modeling, ensuring low-level consistency and continuity. Recognizing the inherent redundancy in video data, we propose a sparse memory context combined with a chunkwise unidirectional generative paradigm to enable the generation of infinitely long sequences. To further augment robotic capabilities, we introduce the Free Anchor View (FAV) space, which provides flexible perspectives to enhance observation and analysis. The FAV space mitigates motion modeling ambiguity, removes physical constraints in confined environments, and significantly improves the robot's generalization and adaptability across various tasks and settings. To address the prohibitive costs and labor intensity of acquiring multi-camera observations, we present a data engine pipeline that integrates a generative model with 4D Gaussian Splatting (4DGS). This pipeline leverages the generative model's robust generalization capabilities and the spatial constraints provided by 4DGS, enabling an iterative enhancement of data quality and diversity, thus creating a data flywheel effect that effectively narrows the sim-to-real gap. Finally, our experiments demonstrate that the embodied future space generation prior substantially enhances policy predictive capabilities, resulting in improved overall performance, particularly in long-range robotic manipulation tasks.

Spatio-temporal reasoning is a core capability for Multimodal Large Language Models (MLLMs) operating in the real world. As such, evaluating it precisely has become an essential challenge. However, existing spatio-temporal reasoning benchmark datasets primarily rely on static image sets or passively curated video data, which limits the evaluation of fine-grained reasoning capabilities. In this paper, we introduce VGenST-Bench, a video benchmark that employs generative models to actively synthesize highly controlled and diverse evaluation scenarios. To construct VGenST-Bench, we propose a multi-agent pipeline incorporating a human quality control stage, ensuring the quality of all generated videos and QA pairs. We establish a comprehensive 3x2x2 video taxonomy, encompassing Spatial Scale, Perspective, and Scene Dynamics to span diverse scenarios. Furthermore, we design a hierarchical task suite that decouples low-level visual perception from high-level spatio-temporal reasoning. By shifting the paradigm from passive curation to active synthesis, VGenST-Bench enables fine-grained diagnosis of spatio-temporal understanding in MLLMs.

Current end-to-end autonomous driving systems are fundamentally limited by a mismatch between temporal causal reasoning and global trajectory consistency. Autoregressive (AR) models capture interaction-aware temporal dependencies via causal factorization, but their step-wise decoding leads to error accumulation and suboptimal global structure. In contrast, diffusion models optimize trajectories globally but lack explicit causal constraints, making them unreliable in interactive and safety-critical scenarios. This dichotomy reveals a deeper issue: existing methods treat causal modeling and global optimization as separate paradigms, without a principled way to unify them within a single trajectory distribution. To address this, we propose ChainFlow-VLA, which unifies causal generation and global refinement within a unified probabilistic framework. We formulate planning as a mixture over AR-induced modes and learn Vision-Language Model (VLM)-conditioned residual distributions over these modes. An autoregressive generator (Chain) produces a discrete set of causal trajectory modes, followed by a diffusion-based refiner (Flow) that leverages VLM hidden states as semantic priors to perform mode-conditioned correction in residual space while preserving causal structure. This straightforward conditioning seamlessly injects high-level scene understanding into fine-grained trajectory adjustments. Experiments demonstrate that ChainFlow-VLA achieves robust planning in ambiguous and long-tail scenarios, achieving a state-of-the-art score of 94.85 on the NAVSIM v1 leaderboard, matching human-level performance (94.8). Code will be available at https://github.com/AFARI-Research/ChainFlow-VLA.

We study pre-training representations for decision-making using video data, which is abundantly available for tasks such as game agents and software testing. Even though significant empirical advances have been made on this problem, a theoretical understanding remains absent. We initiate the theoretical investigation into principled approaches for representation learning and focus on learning the latent state representations of the underlying MDP using video data. We study two types of settings: one where there is iid noise in the observation, and a more challenging setting where there is also the presence of exogenous noise, which is non-iid noise that is temporally correlated, such as the motion of people or cars in the background. We study three commonly used approaches: autoencoding, temporal contrastive learning, and forward modeling. We prove upper bounds for temporal contrastive learning and forward modeling in the presence of only iid noise. We show that these approaches can learn the latent state and use it to do efficient downstream RL with polynomial sample complexity. When exogenous noise is also present, we establish a lower bound result showing that the sample complexity of learning from video data can be exponentially worse than learning from action-labeled trajectory data. This partially explains why reinforcement learning with video pre-training is hard. We evaluate these representational learning methods in two visual domains, yielding results that are consistent with our theoretical findings.

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

Autoregressive video diffusion models have proved effective for world modeling and interactive scene generation, with Minecraft gameplay as a representative application. To faithfully simulate play, a model must generate natural content while exploring new scenes and preserve spatial consistency when revisiting explored areas. Under limited computation budgets, it must compress and exploit historical cues within a finite context window, which exposes a trade-off: Temporal-only memory lacks long-term spatial consistency, whereas adding spatial memory strengthens consistency but may degrade new scene generation quality when the model over-relies on insufficient spatial context. We present Memory Forcing, a learning framework that pairs training protocols with a geometry-indexed spatial memory. Hybrid Training exposes distinct gameplay regimes, guiding the model to rely on temporal memory during exploration and incorporate spatial memory for revisits. Chained Forward Training extends autoregressive training with model rollouts, where chained predictions create larger pose variations and encourage reliance on spatial memory for maintaining consistency. Point-to-Frame Retrieval efficiently retrieves history by mapping currently visible points to their source frames, while Incremental 3D Reconstruction maintains and updates an explicit 3D cache. Extensive experiments demonstrate that Memory Forcing achieves superior long-term spatial consistency and generative quality across diverse environments, while maintaining computational efficiency for extended sequences.

We address causal reasoning in multivariate time series data generated by stochastic processes. Existing approaches are largely restricted to static settings, ignoring the continuity and emission of variations across time. In contrast, we propose a learning paradigm that directly establishes causation between events in the course of time. We present two key lemmas to compute causal contributions and frame them as reinforcement learning problems. Our approach offers formal and computational tools for uncovering and quantifying causal relationships in diffusion processes, subsuming various important settings such as discrete-time Markov decision processes. Finally, in fairly intricate experiments and through sheer learning, our framework reveals and quantifies causal links, which otherwise seem inexplicable.