Latent Dynamics Modeling

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35 papers in the last four weeks, up 483% on the four weeks before. 0.3% of all new papers.

Jul 13Week of Sep 28

Latest papers 172

Sep 17, 2026cs.LG

Seismic Site Response Prediction from Sparse Observations Using Finite-Element-Pretrained Latent Dynamics

Numerical site-response predictions often deviate from observations, yet correcting these discrepancies is difficult because records are limited in both sensor coverage and number of events. This study proposes the Transfer-Enabled Forced Latent Autoencoder for Response Equations (FLARE-T) to improve these predictions by learning and calibrating low-dimensional latent dynamics that connect the base acceleration input to acceleration outputs at multiple depths. FLARE-T learns a low-dimensional response manifold and input-driven dynamics from dense finite-element simulations. It then trains a sparse encoder to map simulated sensor responses into the learned coordinates and uses limited records to calibrate the dynamics within them. A short response window initializes each prediction, while the complete base motion drives the response. The framework was evaluated using a layered-soil centrifuge test and the Lotung field vertical array. Test-set results show that FLARE-T improved multi-depth acceleration histories and 5%-damped pseudoacceleration response spectra relative to the original finite-element models, reducing errors at every evaluated sensor for motions of different intensities and, at Lotung, for both horizontal components. Two Lotung source models with different constitutive parameters achieved comparable test-set accuracy, indicating reduced dependence on precise prior calibration. FLARE-T therefore provides a data-efficient means of combining dense numerical response information with limited field records to improve future site-response predictions.

Yi Zhu, Su Chen, Xiaojun Li

State Key Laboratory of Bridge Safety and Resilience, Beijing University of Technology Beijing 100124, China

Neural Surrogate Modeling Latent Dynamics Modeling Seismology

Sep 15, 2026cs.LG

Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds

Generative modeling of time-dependent data is typically formulated on a discrete temporal grid, restricting supervision to the observed timestamps in the training data. We instead frame generation as continuous-time evolution on a learned data manifold. To this end, we leverage pretrained score-based models as geometric priors and learn a vector field that evolves data along score-induced interpolation paths. Because these dynamics follow transitions that respect the geometry learned by the score model, they support generation at arbitrary timestamps and temporal super-resolution beyond the discretization of the training data. Moreover, this geometric formulation allows us to train the vector field simulation-free through a regression objective. To improve long-horizon rollout robustness, we introduce an objective that promotes path-relative transverse exponential stability. While motivated by stability theory, it admits a practical interpretation as denoising score matching transverse to the interpolation path. Further, we extend the framework to a probabilistic setting that models a distribution over plausible future trajectories. We demonstrate the method on natural video and scientific dynamical data, including temporal super-resolution, PDE-based spatiotemporal fields, and molecular dynamics. Our results show that score-based priors provide a strong foundation for learning stochastic continuous-time generative dynamics.

Jan Tauberschmidt, Brian B. Moser, Stanislav Frolov +3

DFKI Kaiserslautern · RPTU Kaiserslautern · Imperial College London

Dynamical Systems Latent Dynamics Modeling Generative Modeling Score-Based Generative Modeling

Sep 15, 2026cs.LG

Stable by Construction: Variational Latent Markov Operators for Long-Horizon PDE Prediction

Neural PDE solvers provide efficient surrogates for time-dependent physical systems, but autoregressive prediction over long horizons remains challenging because local errors can induce distribution shift and accumulate under recursive deployment. We develop a variational approach to this problem by introducing latent Markov dynamics in which physical states are represented by latent distributions and evolved through probabilistic transitions. The framework is formulated directly on function spaces and specialized to functional Gaussian models, where structured latent perturbations induce a spectral geometry and variational transition alignment regularizes the learned dynamics. We further analyze how these mechanisms affect autoregressive error propagation, providing a theoretical connection between variational training and long-horizon prediction. We instantiate the framework as the Variational Autoencoding Markov Operator (VAMO), which combines spatially resolved latent fields, structured Gaussian perturbations, and a neural-operator transition. Empirically, we demonstrate the effectiveness of VAMO on several fluid-dynamics benchmarks with prediction horizons extending substantially beyond those represented during training, where it consistently reduces error accumulation and improves rollout stability over several deterministic and noise-injection baselines. Overall, these results highlight variational modeling as a complementary approach to robust long-horizon neural PDE dynamics.

Junyi Liao, Johann Guilleminot, Vahid Tarokh

†Department of Electrical and Computer Engineering, Duke University · ‡Department of Mechanical Engineering and Materials Science, Duke University

Variational Autoencoders Latent Dynamics Modeling PDE Operator Learning Spatiotemporal Forecasting Neural Operators

Sep 14, 2026cs.CV

Reconstructing Is Not Acting: Action-Centric Latent Dynamics Modeling

Latent action models (LAMs) learn action representations from unlabeled videos by inferring latent actions from visual transitions and reconstructing future states. However, we identify a fundamental

\textbf{reconstruction-action mismatch}

: lower reconstruction error does not necessarily yield better latent dynamics or downstream performance. We attribute this mismatch to two underconstrained aspects of reconstruction-based latent dynamics modeling: (i) the inverse dynamics model (IDM) is not explicitly encouraged to distinguish action-related transitions from nuisance appearance, and (ii) the forward dynamics model (FDM) can underutilize the inferred latent action by exploiting predictive shortcuts from the current state. To address both limitations, we propose

\textbf{ACT-LAM}

, a lightweight action-centric framework that strengthens both action extraction and action utilization. Specifically, its Action Query IDM (AQ-IDM) employs learnable action queries and gated aggregation to selectively extract rich action-related transition cues without strong information bottlenecks. And its Action Token FDM (AT-FDM) projects latent actions into action tokens that progressively interact with evolving state representations, enabling continuous state-aware action conditioning. ACT-LAM further streamlines feature processing to concentrate model capacity on latent dynamics modeling. Extensive experiments on several robotic datasets and the VP

^2

benchmark demonstrate stronger latent action consistency, forward dynamics, and downstream visual planning performance with fewer trainable parameters and lower computational overhead. In particular, ACT-LAM surpasses the previous state of the art by

\textbf{7.6%}

on the aggregated VP

^2

success rate. Codes at

[url](https://github.com/DingjieFu/ACT-LAM)

.

Dingjie Fu, Dianxing Shi, Yangyang Xu +1

Harbin Institute of Technology (Shenzhen) · Beihang University

Latent Action Learning Latent Dynamics Modeling Action-Conditioned World Models Robotics

Sep 9, 2026cs.LG

Semigroup-JEPA: Latent Dynamics Consistency for Zero-Shot Physics Generalization

Joint-Embedding Predictive Architecture (JEPA) world models learn a compact latent representation of the world that supports prediction and planning, but their capability to learn physics and generate physically realistic dynamics remains hitherto untested. In this work, we introduce SemiGroup-JEPA (SG-JEPA), which extends the LeWorldModel framework by supplying the parameter governing the physics to the temporal model via action-conditioning and jointly training an encoder and predictor through an autoregressive latent rollout. To evaluate the model's ability to generalize out of distribution, we design dynamical tasks under different gravitational fields that, despite obeying the same physical law, exhibit qualitatively different dynamics, ranging from floating motion in weak gravitational fields to rapid bouncing in strong ones. In contrast to DINO-WM, SG-JEPA reduces open-loop prediction error by up to 2 times on two-dimensional datasets, and increases control success rate up to 2.5 times for three-dimensional robotic datasets, for which we train independent diffusion policies. To explain this advantage, we develop a linear feature model that separates local law-conditioned error from its recursive amplification under rollout. Guided by this model, we find that back-propagating the multi-step rollout loss into the representation trains the encoder to keep the features that the predictor can carry forward, and that those are the features the dynamics depend on, so most of the gain comes from the encoder learning better features rather than from the predictor learning better dynamics. See project page at https://sg-jepa.github.io.

Andy Zeyi Liu, Haoran Sun, Lucas Baker +2

Yale University · Jump Trading · Brown University

World Models for Robotics Latent Dynamics Modeling Joint-Embedding Predictive Architecture

Sep 9, 2026stat.ME

Dynamical Non-compensatory Multidimensional IRT Model Using Variational Approximation

Multidimensional item response theory (MIRT) is a statistical test theory that precisely estimates multiple latent skills of learners from the responses in a test. Both compensatory and non-compensatory models have been proposed for MIRT: the former assumes that each skill can complement other skills, whereas the latter assumes they cannot. This non-compensatory assumption is convincing in many tests that measure multiple skills; therefore, applying non-compensatory models to such data is crucial for achieving unbiased and accurate estimation. In contrast to tests, latent skills will change over time in daily learning. To monitor the growth of skills, dynamical extensions of MIRT models have been investigated. However, most of them assumed compensatory models, and a model that can reproduce continuous latent states of skills under the non-compensatory assumption has not been proposed thus far. To enable accurate skill tracing under the non-compensatory assumption, we propose a dynamical extension of non-compensatory MIRT models by combining a linear dynamical system and a non-compensatory model. This results in a complicated posterior of skills, which we approximate with a Gaussian distribution by minimizing the Kullback-Leibler divergence between the approximated posterior and the true posterior. The learning algorithm for the model parameters is derived through Monte Carlo expectation maximization. Simulation studies verify that the proposed method is able to reproduce latent skills accurately, whereas the dynamical compensatory model suffers from significant underestimation errors. Furthermore, experiments on an actual data set demonstrate that our dynamical non-compensatory model can infer practical skill tracing and clarify differences in skill tracing between non-compensatory and compensatory models.

Hiroshi Tamano, Daichi Mochihashi

the graduate university for advanced studies, sokendai · the institute of statistical mathematics

Latent Dynamics Modeling Knowledge Tracing Item Response Theory

Aug 31, 2026cs.LG

Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains

Solving multiphysics partial differential equations (PDEs) remains a major challenge in scientific computing, especially for highly complex

μ

m-scale tortuous geometries critical to energy and chemical engineering. We address this challenge by proposing a Geometry-aware Latent Autoregressive generative Model for PDEs (GeoLAMP), which solves physics within highly irregular and tortuous structures by decoupling flow and transport physics. GeoLAMP introduces a dual-encoder architecture on graph representations to jointly capture global topology and fine-scale geometric features, enabling an effective transition from real-space fields to compact latent representations. In the latent space, we propose a causal self-attention transformer with flow matching to model temporal dynamics, allowing stable and scalable block-wise autoregressive prediction. In addition, we propose a grid-graph data fusion scheme that projects low-resolution grid-based approximate priors onto graph representations, improving prediction of flow in tortuous structures. We establish three multiphysics benchmark datasets in complex geometries, covering reactive flow, heat convection, and elasticity. GeoLAMP consistently achieves the most stable autoregression performance on these datasets. Our results provide a systematic study of geometry-aware learning for PDEs in

μ

m-scale complex geometries and offer new insights into block-wise time marching of latent autoregressive PDE modeling via a flow matching framework.

Zi Wang, Minghui Xu, Tapan Mukerji

Department of Energy Science and Engineering Stanford University Stanford, CA 94305

Graph Neural Networks Neural PDE Solvers Latent Dynamics Modeling PDE Surrogate Modeling Autoregressive Generation

Aug 29, 2026cs.LG

Flow-JEPA: Robust Latent Dynamics for JEPA World Models via Flow Matching

Joint-Embedding Predictive Architectures (JEPAs) provide a powerful framework for latent world modeling and planning in a reconstruction-free manner. Although numerous JEPA-based approaches have been proposed to mitigate representation collapse, our experiments on localized, out-of-distribution visual noise reveal that performance degradation remains pronounced and unresolved. We propose Flow-JEPA (F-JEPA), a flow-based latent dynamics model that jointly generates a sequence of future latent states conditioned on the current observation and actions. A Gaussian distribution serves as the flow source, exposing the vector field to perturbed latent trajectories as it learns to transport them toward clean future representations. This formulation retains the reconstruction-free JEPA framework while switching from pointwise transition regression to stochastic trajectory-level prediction. F-JEPA raises mean success from

86\%

to

92\%

under clean observations and from

67\%

to

86\%

under noisy conditions. Further evaluations over varying perturbation severity and inference settings show that the performance advantage persists across a broad range of conditions. These results suggest that conditional flow matching provides a promising alternative to deterministic autoregressive prediction as a dynamics formulation in JEPA world models.

Yanchen Huo, Ziying Song, Yadan Luo

Nanyang Technological University · The University of Queensland

Flow Matching Latent Dynamics Modeling Joint-Embedding Predictive Architecture Latent World Models Flow-Based Generative Modeling

Aug 17, 2026cs.CV

LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splatting

We present LaGSplat (Latent Lagrangian Gaussian Splatting), a framework that infers interactive, physics-governed dynamics from one or a few monocular videos. At inference it lets a user push on the filmed object, rigid or deformable, with an external force that was never measured, annotated, or seen during training. This is possible because a low-dimensional latent state

\mathbf{q} \in \mathbb{R}^d

plays two roles at once: it is the generalised coordinate of a learned dissipative Lagrangian and the conditioning variable of a Gaussian Splatting decoder. The inductive bias of this decoder, whose primitives are explicit points

μ_i(\mathbf{q})

that move with the object, is what lets a force

f

applied in the image pull back into a latent generalised force

J(\mathbf{q})^\top f

and enter the equations of motion, which pixel-space (CNN) or neural-field (NeRF) decoders cannot do. We validate LaGSplat on test cases of increasing difficulty, from rigid to deformable and from autonomous to forced real systems, combining monocular video and sensor measurements. We further demonstrate interactive use: forces of arbitrary magnitude and direction can be applied to the reconstructed object at any time, its response rendered in real time, in 2D or 3D. Assuming a dissipative Euler-Lagrange equation over a few generalised coordinates trades generality for a bounded, plausible response to unseen forces, where an unconstrained predictor diverges.

Louen Pottier

Université Paris-Saclay, CEA, List, F-91120 Palaiseau, France

3D Gaussian Splatting Latent Dynamics Modeling Dynamic Scene Reconstruction Physical Reasoning in Video Deformable Object Simulation

Aug 13, 2026cs.LG

History-informed Lagrangian Neural Networks

Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously. Although physics-guided neural networks like Lagrangian Neural Networks (LNNs) guarantee physical plausibility, they generally require complete state inputs and lack adaptability to changing system parameters. To break these limitations, we introduce History-informed Lagrangian Neural Networks (HiLNN). Grounded in the insight that temporal position sequences implicitly encode underlying dynamics, HiLNN employs a recurrent encoder to extract a latent context from history. This context not only reconstructs the unobserved initial velocity but also adaptively modulates the mass matrix, potential energy, and damping coefficients of a structured Lagrangian system. By leveraging a differentiable RK4 rollout scheme, the entire pipeline is optimized end-to-end under multi-step trajectory supervision and energy-consistency regularization. Empirical evaluations across conservative, dissipative, and heterogeneous variable-parameter systems show that HiLNN delivers superior long-term prediction accuracy and maintains precise energy profiles compared to state-of-the-art baselines. The source code is publicly available at https://github.com/yingtian22/History-informed-LNN.

Tianshuo Zhang, Xianglei Xing, Wenzhe Zhai +2

College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150001, China

Latent Dynamics Modeling Physics-Informed ML

Aug 10, 2026cs.CV

Learning How the World Evolves: Extrapolative Video World Models via Latent Dynamics Reasoning

The world evolves following its dynamics, i.e., its laws of motion. However, leading video diffusion models largely fit the pixels without modeling how the pixels transit over time. Thus, they render visually plausible frames but may not accurately obey the laws. To capture the dynamics purely from pixels, we introduce Latent Dynamics Reasoning (LDR). LDR casts the latent transition as an explicit kinematic integration, where the lower-order dynamics are integrated numerically and the model regresses only the third- and higher-order residual that drives the rollout. For this integration to extrapolate better, LDR runs it on a structured latent rather than dense convolutional features. Following PhyWorld, we validate LDR on a controlled white-box physics benchmark spanning five tasks (uniform motion, parabola, collision, bouncing, looming), focusing on out-of-distribution scenarios that reveal whether a model has truly learned the underlying dynamics. LDR extrapolates the learned dynamics far better: the gap between its in- and out-of-distribution error is over 20

\times

smaller than the video diffusion baseline's, under both single- and joint-task training at 256

^2

resolution, while using 26

\times

fewer parameters and running 143

\times

faster. LDR can even generalize under severe shift: for example, trained only on red balls moving left-to-right, it correctly predicts the motion of a blue square moving right-to-left. To our knowledge, this is the first video world model that extrapolates learned dynamics beyond its training distribution. Project page: https://lat-dyn-reason.github.io/

Haodong Li, Shaoteng Liu, Tianyu Wang +7

1UCSD 2Adobe

Physical Consistency in Video Generation Physical Reasoning Latent Dynamics Modeling OOD Generalization Video World Models

Aug 10, 2026cs.RO

SLIM-0.5B: Learning Action-Grounded Predictive Latents for Robot Manipulation

Vision-language-action policies rely on large multimodal backbones to jointly perform perception, language conditioning, and action generation at every control step. Much of this capacity supports open-domain semantics, whereas continuous robot manipulation primarily requires compact representations of observations, actions, and the transitions induced by actions. Pixel-level world models provide another route, but predicting visual details irrelevant to control can be unnecessarily expensive. We propose SLIM (Self-supervised Latent Interaction Model), a compact 0.5B-parameter latent interaction policy. SLIM learns action-grounded predictive latents that capture both action-conditioned future transitions and the actions that explain observed changes. SLIM learns these representations through self-supervised masked trajectory prediction, combining action reconstruction with future-latent prediction. A compact Mixture-of-Transformers (MoT) backbone models interactions between observation latents and action tokens. The resulting policy is trained with flow matching for language-conditioned action generation. Across simulation benchmarks and real-world evaluation, SLIM matches or exceeds representative large-scale VLA and world-action-model baselines with fewer parameters, no additional embodied pretraining, lower inference latency, and substantially lower GPU memory usage.

Jingkai Wang, Zihan Tang, Gu Zhang +7

1Fudan University · 2Beijing Academy of Artificial Intelligence · 3Tsinghua University +1

Latent Dynamics Modeling Language-Conditioned Robot Manipulation Vision-Language-Action Models Latent World Models

Aug 9, 2026cs.LG

Path-dependent Discrete Amortized Inference

We consider the problem of sampling compositional and discrete objects from a given unnormalized posterior distribution. Notably, recent studies have shown that this problem can be efficiently solved by learning a deterministic Markov Decision Process (MDP) that progressively builds each object in proportion to the posterior. In this work, however, we demonstrate that the Markovian assumption can both hamper signal propagation during training and catastrophically reduce the learned sampler's expressivity due to state aliasing. To address these issues, we propose lifting the MDP with a learnable latent dynamical system that allows the underlying policy to depend on the entire past trajectory---and not only on the current state. In view of this, we refer to the resulting method as path-dependent discrete amortized inference. Importantly, we provably extend existing learning algorithms for discrete amortized samplers to our setting. In experiments on standard benchmark problems, we also show that our approach often leads to faster learning convergence and improved state space exploration relatively to prior techniques.

Tiago da Silva, Esmeralda S. Whitammer, Salem Lahlou

1MBZUAI · University of Edinburgh · 3CIFAR Fellow

Markov Decision Processes Latent Dynamics Modeling Amortized Inference Posterior Sampling

Aug 6, 2026cs.LG

Flowing Through States: Neural ODE Regularization for Reinforcement Learning

Neural networks applied to sequential decision-making tasks typically rely on latent representations of environment states. While environment dynamics dictate how semantic states evolve, the corresponding latent transitions are usually left implicit, creating a potential misalignment between the two. We propose to model latent dynamics explicitly by drawing an analogy between Markov decision process (MDP) trajectories and ordinary differential equation (ODE) flows: in both cases, the current state fully determines its successors. Building on this view, we introduce a neural ODE-based regularization method that enforces latent embeddings to follow consistent ODE flows, thereby aligning representation learning with environment dynamics. Although broadly applicable to deep learning agents, we demonstrate its effectiveness in reinforcement learning by integrating it into Actor-Critic algorithms. Our approach yields major performance gains across various standard Atari benchmarks for A2C and gridworld environments for PPO.

Mohamed Ghanem, Bernd Finkbeiner

CISPA Helmholtz Center for Information Security · Technical University of Munich

Latent Dynamics Modeling Representation Learning for RL State Representation Learning Neural ODEs

Aug 5, 2026cs.LG

Quantum-Structured World Models (QSWMs) for Predictive Latent Dynamics

World models learn latent states that summarize interaction histories, evolve over time, and support prediction, simulation, or planning. Most existing world models represent these states using classical vectors, probability distributions, recurrent hidden states, or transformer activations. In this paper, we introduce Quantum-Structured World Models (QSWMs), a quantum-inspired framework for predictive world modeling with structured latent states, latent transition operators, and measurement-inspired decoding maps. We study whether mathematical structures inspired by quantum theory, such as complex-valued representations and density-matrix-like latents, provide useful inductive biases for world modeling. We establish three foundational properties: classical inclusion, predictive sufficiency, and structured compactness. We then instantiate complex-valued and density-matrix-like QSWM variants and evaluate them on elementary cellular automata against strong classical baselines. Results show promising local predictive potential for complex-valued QSWMs, while also revealing limitations in long-horizon rollout, density-matrix variants

Hailong Jiang, Emran Hossain, Feng Yu +3

Youngstown State University, Youngstown, OH, USA · Kent State University · George Washington University

Latent Dynamics Modeling Quantum-Inspired ML Latent World Models

Aug 5, 2026cs.LG

Beyond Linear Dynamics: Neural Bilinear Dynamical Models for Time Series Forecasting

Time series in real-world applications are often generated by nonlinear dynamical systems, making accurate forecasting challenging. Existing approaches that explicitly model system dynamics typically rely on linear assumptions or Koopman-based linearizations, which may inadequately capture complex nonlinear behaviors and lead to error accumulation in long-horizon prediction. To address this limitation, we propose the Neural Bilinear Dynamical Model (NBDM), which models nonlinear system dynamics through a bilinear latent dynamical formulation. Specifically, NBDM leverages Koopman theory to lift the original nonlinear dynamics into a higher-dimensional latent space, where a bilinear dynamical model is constructed to characterize state evolution. To mitigate the approximation error introduced by bilinear representations, we further incorporate a parameterized error compensation term. Within this formulation, control inputs are explicitly integrated into the dynamics, using auxiliary variables when available and learned feedback signals otherwise. To handle scenarios with missing control inputs, we design a memory-enhanced controller that infers latent controls through multiplicative interactions between historical states and control signals. Experiments on five real-world datasets demonstrate that NBDM consistently outperforms competitive baselines in both given-control and missing-control settings, particularly for multi-step and long-horizon forecasting.

Mengzhou Gao, Huangqian Yu, Pengfei Jiao

Hangzhou Dianzi University Hangzhou, China

Dynamical Systems Long-Term Time Series Forecasting Latent Dynamics Modeling Time Series Forecasting

Aug 4, 2026cs.LG

SJEPA: Learning Elegant Latent Dynamics with Hybrid Symbolic-Neural Predictors

Joint-embedding predictive architectures learn abstract states by predicting target embeddings from context embeddings, but their transition models are typically opaque neural maps. We introduce SJEPA, a reconstruction-free JEPA framework that learns predictive representations whose induced dynamics admit compact symbolic descriptions. Its hybrid transition combines a symbolic law with a regularised neural correction for dynamics outside the selected grammar. The central principle is to learn the simplest adequate dynamics: representation constraints preserve informative, non-collapsed predictive coordinates, while operator compression favours low-complexity symbolic-neural transitions that remain predictively adequate. We formalise this principle through induced-dynamics complexity, analyse predictive-coordinate non-identifiability, and show that unconstrained operator compression creates a direct shortcut to representation collapse. The framework supports both alternating representation-equation learning and symbolic dynamics fitted to fixed representations. In controlled pendulum experiments, joint learning discovers substantially simpler symbolic dynamics with lower long-horizon rollout error and divergence than post-hoc fitting, while an unconstrained one-step diagnostic realises the predicted collapse shortcut. Under grammar misspecification, correction regularisation preserves the representable symbolic mechanism and directs the neural component towards residual dynamics. The results expose a controllable trade-off among predictive fidelity, representation quality, symbolic parsimony, and symbolic-neural allocation.

Yongchao Huang

Latent Dynamics Modeling Joint-Embedding Predictive Architecture Predictive Representation Learning Neurosymbolic Learning

Aug 3, 2026cs.LG

WorldDynCache: Risk-Controlled Latent Dynamics Approximation for Diffusion World Model

Diffusion world models generate high-quality futures, but re- peated transformer evaluations make inference prohibitively slow. Existing caches reuse intermediate features, selectively update tokens, or reuse and extrapolate denoising outputs ac- cording to local drift or short native-space histories. These criteria can miss both approximation-induced latent transition defects that accumulate across skipped steps and phase- or condition-dependent changes in the direction of latent evo- lution. We propose WorldDynCache, a risk-controlled latent dynamics approximation framework with two core compo- nents. First, a lightweight latent-transition risk estimator tracks the accumulated future impact of approximation defects and calibrates its predictions against counterfactual defects ob- served at exact anchors. Second, a condition- and phase- aware lifted latent surrogate approximates latent evolution without extra transformer evaluations. On HunyuanVoyager- 13B and Aether-5B, WorldDynCache achieves 4.92 times and 2.15 times speedups, respectively, while attaining the best gen- eration quality among the compared caching methods across WorldScore, PSNR, SSIM, and LPIPS.

Leyang Chen, Junyi Wu, Shaoqiu Zhang +1

Shanghai Jiao Tong University

World Model Learning Latent Dynamics Modeling Diffusion Model Caching Diffusion Model Inference Acceleration

Aug 3, 2026stat.ML

The Label Defines the Timescale: Trait-State Limits of Temporal-Aggregate Learning

Machine-learning benchmarks often pair a label that aggregates a long temporal horizon with input observed through one or a few short windows. Their apparent performance ceiling may therefore be an acquisition-protocol ceiling rather than a model-capacity ceiling. We study labels of the form

Θ_{g,T}=T^{-1}\int_0^T g\{Z(t)\}\,\mathrm{d}t

when the latent Gaussian process contains both a stable individual trait and a correlated within-individual state. An exact protocol-conditioned Bayes-risk identity provides a common tool. First, we decompose label variance into an

O(1)

trait component and an

O(T^{-1})

state component, explaining why a snapshot can retain cross-sectional predictability while poorly tracking within-person change. Second, we derive task-dependent effective temporal spans: mean labels depend on the ordinary correlation time, whereas occupation-time labels depend on an entire spectrum of higher-order correlation times. Third, state-driven occupation-label variance is maximal when the stable trait lies at the threshold; window efficiency decays much more slowly away from that boundary. Under an equal segment budget, exact risks and Monte Carlo experiments show that repeated segments at one time rapidly saturate, whereas temporally dispersed observations continue to increase state explainability. The trait ceiling uses quantities available from ordinary test-retest data; only the state ceiling requires short-lag temporal calibration. The results distinguish architectural limits from protocol limits and show that the label, rather than duration or segment count alone, defines the relevant timescale.

Xizhe Zhang

Latent Dynamics Modeling State Tracking Statistical Learning Theory

Jul 31, 2026cs.LG

Latent Lie-Poisson Neural Networks (LLPNNs): Discovering the motion of Lie-Poisson systems through observable data and latent dynamics

Structure-preserving neural networks are essential for the long-term prediction of Hamiltonian systems from data. Many important Hamiltonian systems in mechanics and control admit symmetry reduction to Lie--Poisson systems, including rigid bodies, underwater vehicles, fluids, plasmas, and optimal control problems. A fundamental challenge in learning such systems is that their dynamics evolve in momentum variables that are typically unobservable, while available data consist only of observable quantities such as configurations and velocities. In optimal control applications, the situation is further complicated because the latent variables contain unobservable co-states and the Hamiltonian may be degenerate, preventing the existence of a corresponding Lagrangian and rendering the encoder-decoder approaches inapplicable. We introduce Latent Lie--Poisson Neural Networks (LLPNNs), a structure-preserving framework for learning Lie--Poisson dynamics directly from observable data. The proposed approach exploits three geometric ingredients: (i) learning either a Hamiltonian decoder or a pseudo-Lagrangian encoder on the active variables, (ii) constructing latent trajectories through a universal Noether invariant arising from Lie--Poisson symmetry reduction, and (iii) reconstructing observable and latent dynamics through Lie--Poisson flows combined with Magnus-based Lie-group updates. The resulting method preserves the geometric structure and is applicable to both regular and degenerate Hamiltonian systems. We demonstrate the method on three examples: a generalized rigid body on SO(3), Kirchhoff's underwater vehicle on SE(3), and an optimal-control problem for interacting vehicles on

SE(2)^N

. Numerical experiments show excellent long-term predictive accuracy, strong robustness to noise, and competitive performance using only modest datasets and lightweight neural-network architectures.

Vakhtang Putkaradze

Department of Mathematics, The University of Alabama, Gordon Palmer Hall, Tuscaloosa, AL, 35401, USA

Latent Dynamics Modeling Hamiltonian Neural Networks Hamiltonian Dynamics

Jul 30, 2026cs.LG

ODEWorld: A Continuous Predictive Architecture via Physical-Time Flow

In the physical world we inhabit, space and time are fundamentally continuous. However, existing machine learning paradigms for world modeling are largely confined to discrete-time prediction, thereby exhibiting significant inefficiency in capturing the dynamics of physical world. We introduce Physical-Time Flow (PT-Flow), a novel approach that learns a continuous latent velocity field operating in physical time. Crucially, the underlying dynamics of sequential data are parameterized by an ordinary differential equation (ODE) embedded in a well-structured representation space. Under this paradigm, the prediction of future can be recast as temporal integration via an ODE solver in the compressed latent space. Building upon PT-Flow, we construct ODEWorld, a continuous-time latent world model that is both efficient and versatile. By extracting time-variant features and enforcing ODE properties on both the dynamical representation space and the latent velocity field, ODEWorld effectively addresses the long-standing representation collapse issue in latent world model literature. This also enables high-quality image reconstruction even after long-horizon prediction. Moreover, its continuous nature allows for arbitrary temporal resolution and even backward prediction, which is impossible for most discrete-time models. Lastly, ODEWorld can provide rich planning-oriented information to facilitate downstream policy learning. Comprehensive experiments demonstrate that ODEWorld successfully reconciles planning-conducive dynamics abstraction with visual realism, excelling in both video generation and robotic control. Project page: https://odeworld.github.io/.

Dongxiu Liu, Haoyi Niu, Peng Cheng +5

Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China · 2Berkeley Artificial Intelligence Research (BAIR), University of California, Berkeley, CA, USA

Robotic Control Latent Dynamics Modeling World Models Video Prediction Latent World Models

Jul 29, 2026cs.RO

DLAM: Distributional Latent Actions with Temporal Constraints

Vision-language-action (VLA) models remain constrained by scarce action-labeled robot data, whereas action-free videos offer abundant observations of physical change. Latent action models can extract such priors, but reconstruction-trained codes may predict future observations without the structure required for joint generation with robot actions. Existing structured methods add temporal constraints but retain deterministic transition points, so residual errors in locally inferred transitions may propagate and compound under recursive composition. We introduce DLAM, a distributional latent-action model that represents each transition as a diagonal Gaussian. Reconstruction conditioned on the reference frame grounds the mean in observed visual change, while normalized composition and reversal over equal-gap triplets constrain both the mean and dimension-wise variance. Variance composition uses a lightweight shared-correlation coefficient to account for dependence between adjacent transitions that share an intermediate frame, whereas reversal negates the mean and preserves the variance. For downstream policy learning, we freeze the encoder and train a flow-matching policy to jointly generate mean transition sequences and robot actions. On held-out transitions, DLAM learns more temporally consistent latent dynamics than existing latent-action baselines and achieves stronger direct and cumulative reconstruction on held-out videos. Under the same controlled

π_0

transfer protocol, it also improves policy performance on MetaWorld MT50, LIBERO, and real-world manipulation tasks. Controlled ablations show that normalized mean constraints account for most of the reconstruction gain, while learned variance and correlation-aware composition provide complementary improvements in downstream control.

Zuojin Tang, Feifan Luo, Haoyun Liu +10

Zhejiang University · Nanjing University · Shanghai Jiaotong University +4

Latent Action Learning Latent Dynamics Modeling Visuomotor Policy Learning Vision-Language-Action Models

Jul 27, 2026physics.flu-dyn

The balance between compactness and forecast accuracy of data-driven latent-space reduced-order models in controlled wake flows

Model-based active flow control requires predictive models that are accurate, stable, and fast enough for real-time optimisation. In controlled wake flows, this is often achieved through Reduced-Order Models (ROMs) that first compress high-dimensional velocity snapshots into a latent space and then learn a time- stepping predictor for the dynamics in the latent space. Here, we study how the choice of the spatial encoder affects the predictability of the resulting latent coordinates for wake flows under control inputs. Using two actuated 2D wake configurations, a simplified truck wake and the fluidic pinball, we compare Proper Orthogonal Decomposition (POD) against nonlinear Convolutional Autoencoders (CAEs) and two types of variational autoencoders for compression, and evaluate several temporal predictors based on Long Short-Term Memory networks. CAEs achieve higher compression efficiency and sharper short-term reconstructions, but they produce latent dynamics that are more irregular and with broadband spectral content. As a consequence, long-horizon forecasts degrade faster and show a higher probability of catastrophic divergence than POD-based models. POD yields smoother latent trajectories that are easier to learn and extrapolate, leading to more reliable predictions beyond the short- term regime. These results reveal a clear trade-off between compactness and forecast accuracy, and suggest that the stability of the latent dynamics prediction can outweigh maximal compression. This is particularly relevant for control strategies rooted in forecasts of the dynamics, such as model predictive control and reinforcement learning. The findings provide practical guidance for designing actuation-aware, hardware-feasible predictive ROMs for real-time flow control.

Alberto Solera-Rico, Patricia García-Caspueñas, Carlos Sanmiguel Vila +1

Sub-directorate general of aeronautical systems, Spanish National Institute for Aerospace Technology (INTA), ctra. M-301, km. 10.5, 28330 San Mart´ın de la Vega, Madrid, Spain. · Departamento de Ingenier´ıa Aeroespacial, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Legan´es, Madrid, Spain. · Department of Mechanical Engineering, University of Washington, 1410 NE Campus Parkway, Seattle, WA 98195, USA.

Variational Autoencoders Latent Dynamics Modeling Autoencoders Proper Orthogonal Decomposition Convolutional Autoencoder Feedback Control+2

Jul 27, 2026cs.SD

Modeling Stylistic Co-evolution in Symbolic Music Heritage Collections

Digitized musical heritage collections offer new opportunities to examine how stylistic traditions change over historical time, but computational analyses often reduce musical works to static classifications or similarity scores. This article proposes a representation-to-dynamics framework for studying cross-cultural harmonic change in Western art music. Starting from symbolic chord sequences, we derive contextual chord embeddings, project work-level representations into a shared harmonic space, and reconstruct country-level trajectories through temporally causal Kalman filtering. These trajectories are then modeled with DeGroot and Friedkin--Johnsen dynamics, yielding interpretable influence-like networks and estimates of stylistic anchoring. We apply the framework to a curated corpus of 480 dated works from 1875 to 1940 across Russia, France, Germany, Austria, and a heterogeneous ''Others'' group. Models fitted on 1875--1925 are evaluated through recursive forecasts for 1930--1940, testing whether the estimated dependency structure remains informative across a potentially changing historical and stylistic regime. The estimated trajectories and influence patterns are broadly consistent with established music-historical accounts of late Romantic and early modernist exchange, including the close relationship between German and Austrian traditions and historically plausible cross-currents between Russian and French traditions. PCA-variance-weighted estimation provides modest improvements while preserving a single interpretable influence network. Rather than treating the estimated matrices as direct causal evidence, the framework offers a reproducible quantitative layer for cultural heritage research, complementing archival and musicological interpretation.

Yulong He, Ivan Smirnov, Yanming Li

St. Petersburg State University, St. Petersburg, Russia · ITMO University, St. Petersburg, Russia · St. Petersburg State Institute of Culture, St. Petersburg, Russia

Latent Dynamics Modeling Cultural Evolution Music Information Retrieval Cultural Heritage

Jul 25, 2026cs.LG

Neural operator discovery from heterogeneous trajectories

Neural operators provide data-driven mappings for modeling dynamical systems. Extending them to families of systems typically requires explicit conditioning variables such as physical parameters, geometries, or boundary conditions. In many real-world settings, these quantities are unobserved. Here, we formulate neural operator discovery (NOD) as the problem of learning both shared solution operators and system-specific variation directly from heterogeneous trajectories without access to labeled governing factors. We introduce a factorized latent-conditioning formulation that jointly learns a neural operator and a low-dimensional latent representation through factorized prediction, trajectory-decoupled sampling, and dimension selection. Across diverse systems, the learned latent representation captures the intrinsic dimensionality of system variation and organizes system instances in a smooth and approximately invertible latent structure aligned with the underlying governing factors. This organization enables generalization to previously unseen system instances, including zero-shot extrapolation across regimes and stable long-horizon prediction. These results establish an interpretable paradigm for operator learning in the absence of explicit factor supervision.

Zituo Chen, Qiaofeng Li, Jiaxin Hu +1

Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, 02139, MA, USA. · State Key Laboratory of Fluid Power & Mechatronic Systems, Zhejiang University, 866 Yuhangtang Road, Hangzhou, 310058, Zhejiang Province, China.

Latent Dynamics Modeling Nonlinear System Identification Operator Learning Neural Operators

Jul 25, 2026cs.CV

Inverse Bayesian Inference for Extracting Lesion Dynamics from Longitudinal Spectral CT

Longitudinal medical imaging captures temporal evolution of lesions, yet extracting the underlying dynamical parameters governing this evolution remains challenging. We propose an inverse Bayesian framework for inferring lesion dynamics from longitudinal spectral CT. We decompose spectral feature (

x

) evolution into three components: \begin{equation*} \frac{dx_i}{dt} = A_i x_i + B \cdot n + C \cdot Δx_{\text{sat}} \end{equation*} where

A_i

captures intrinsic dynamics (lesion-autonomous evolution),

B

captures local environment tumour burden (organ tumour burden through satellite count coupling), and

C

captures environment/satellite state change (i.e., whether surrounding lesions move similarly or not). We demonstrate the framework on photon-counting NSCLC CT data from metastases, recovering distinct dynamical regimes: lung lesions exhibit significant satellite count coupling (

B=-0.34

,

p<0.05

) suggesting competitive dynamics, while liver lesions show synergistic satellite behaviour coupling (

C\approx+1.0

,

p<0.05

). Synthetic validation confirms parameter recovery, and cross-coupling analysis validates that our method detects non-zero coupling when present. This work establishes inverse dynamical inference as a principled methodology for extracting interpretable parameters from longitudinal imaging, moving beyond static feature extraction toward mechanistic characterisation of lesion behaviour. The code and data are available at: https://github.com/lukasf98/inverse-bayesian-inference

Lukas Förner, Melina Wördehoff, Julian Steffens +6

Dept. of diagnostic and interventional Radiology and Neuroradiology, University Hospital Augsburg, Germany · Digital Medicine, University Hospital Augsburg, Germany · Chair for Computer-Aided Medical Procedures and Augmented Reality, Technical University of Munich, Germany +5

Latent Dynamics Modeling Bayesian Inverse Problems Longitudinal Medical Image Analysis Oncology

Jul 24, 2026cs.LG

On the Identifiability of Controlled World Models

World model serves as a promising tool to infer environment dynamics under high-dimensional observations and candidate actions. Recently, LeCun's JEPA provides a compelling framework for learning such models in representation space. Its action-conditioned extension plays a central role in visual control and latent-space planning, but leaves a fundamental question: can it recover the controlled dynamics from nonlinear observations? This paper presents a joint identifiability condition for controlled world models with Gaussian latent states, which consists of two coupled components: (1) representation identifiability and (2) transition identifiability. The former depends on the spectral separation property while the latter is related to non-degenerate variation of conditional action. We prove that when this condition holds, minimizing the LeJEPA-style predictive objective can recover both latent states and controlled dynamics in the sense of orthogonal transformation. We further prove that the upper bound of transition prediction error is inversely proportional to the spectral separation margin. We also characterize an attainable amplification of counterfactual prediction error that scales inversely with the weakest conditional action-excitation margin. The theoretical predictions are empirically supported across four nonlinear observation settings.

Xiangteng Zhang, Yang Guan, Bo Zhang +3

School of Vehicle and Mobility, Tsinghua University · 2Didi Voyager Labs, Didi Autonomous Driving · School of Computing and Data Science, The University of Hong Kong +2

Parameter Identifiability Latent Dynamics Modeling Action-Conditioned World Models State Representation Learning

Jul 24, 2026stat.ML

Variational Low-rank Tensor Decomposition for Multisubject Spatiotemporal Data Analysis

Modeling shared and subject-specific structure in multisubject spatiotemporal data remains challenging, particularly in neuroimaging, where both spatial and temporal patterns exhibit rich variability across subjects. Existing matrix and tensor decompositions provide interpretable factorizations, but rely on fixed multilinear structures or coupling schemes that may limit their flexibility in capturing complex variability. In this work, we introduce a spatiotemporal variational tensor decomposition (ST-VTD) framework that combines a tensor factorization generative model with structured priors to jointly represent spatial maps and temporal dynamics. Spatial factors are regularized to promote a low-rank structure inspired by the LL1 decomposition, while temporal factors are modeled using a learned Long short-term memory (LSTM)-based prior, enabling flexible and adaptive dynamics. Posterior inference is performed using an amortized variational formulation by unrolling iterations of an optimization algorithm, leading to an interpretable and parameter-efficient architecture. The proposed inference framework employs a warm-start strategy based on group independent component analysis, which we found to improve optimization performance. Experiments on a realistic synthetic functional MRI (fMRI) dataset demonstrate that the proposed approach significantly improves latent factor recovery compared with representative classical and probabilistic decomposition benchmarks.

Laura M. Montaldo, Ricardo A. Borsoi, Sebastian Miron +1

CRAN, Université de Lorraine, CNRS, Vandoeuvre-l`es-Nancy, France. · Department of CSEE, University of Maryland Baltimore County, Baltimore, MD 21250, USA.

Latent Dynamics Modeling Low-Rank Matrix Decomposition Tensor Decomposition Variational Inference

Jul 22, 2026cs.LG

Koopman Dreamer: Spectrally Constrained Latent Dynamics for Stable World-Model Imagination

Latent world models improve sample efficiency in continuous control by optimizing policies over imagined latent trajectories, but common neural transitions offer limited direct control over modal persistence and error accumulation in long rollouts. We propose Koopman Dreamer, a Dreamer-style world model with a spectrally constrained deterministic latent dynamics core. Its Koopman-inspired backbone uses two-dimensional rotation--scaling blocks with bounded radii to represent damping, rotation, and near-periodic modes. Linear and low-rank bilinear action terms capture global and state-dependent control effects, while stochastic-state modulation supplies local correction information. To reduce the mismatch between posterior-conditioned training and prior-only imagination, the model combines posterior-conditioned EMA teacher targets with one-step consistency, multi-step rollout, and open-loop observation-prediction objectives. We further derive a multi-step rollout-error bound that separates amplification by the spectral backbone and bilinear interaction from the additive effects of stochastic-state mismatch and modeling residuals, clarifying the trade-off between error attenuation and long-term information retention. Experimental results on proprioceptive continuous-control tasks from the DeepMind Control Suite and UAV-LiDAR autonomous navigation demonstrate that Koopman Dreamer improves the stability of long-horizon latent rollouts and achieves stronger closed-loop control performance on tasks that rely on high-quality multi-step imagination.

Jiaqi Li, Xinglong Zhang, Haibin Xie +3

College of Intelligence Science and Technology, National University of Defense Technology, Changsha, China

Koopman Operator Learning Latent Dynamics Modeling World Models Latent World Models Model-Based RL

Jul 21, 2026cs.LG

Multi-Horizon Consistency as Geometry: When Latent Dynamics Contract, and When They Do Not

Multi-horizon latent consistency is a common training knob in video predictors and world models, but practitioners rarely know what it does to transition geometry. We treat lambda, the weight on multi-step latent agreement, as a diagnostic control and measure an empirical expansion proxy L20,q95 together with horizon-20 prediction error E20. On Moving-MNIST (n=6 seeds at the critical pair), raising lambda from 0 to 0.8 cuts L20 from 4.96 +/- 2.01 to 1.01 +/- 0.06 (paired t p=0.005, Wilcoxon p=0.031) and halves E20 (0.365 to 0.177, paired t p=1.1e-13). Four of six seeds cross L<1 at lambda=0.8. The same loss does not produce population L<1 on action-conditioned Pendulum-v1 or CartPole-v1, nor on KTH Actions video, even when E20 improves. An associational mediation analysis on MMNIST gives r-hat=0.94 (95% CI [0.88, 1.00], n=27, B=2000); lambda was not randomized. Defensive checks (architectural baselines, exogenous stress, WorldTest, MPC, scaling) mostly support a narrow claim: soft consistency can push passive video toward a near-contractive band, and that band is domain-limited. A stochastic-forcing law L20 ~ 1.23 + 1.82 eta at lambda=0.8 (bootstrap slope CI [1.73, 1.92], R^2=0.96) unifies control domains on the same curve via calibrated eta_eff. Complete joint slices at lambda in {0.4, 1.2} (30/30 cells, 5 eta x 3 seeds) show comparable linear L20(eta) slopes (~1.69 and ~2.00); we do not fit a continuous (lambda, eta) surface. We do not report DreamerV3 or TD-MPC2 returns.

Kavya Bhand, Aadi Joshi

Department of Computer Engineering Vishwakarma Institute of Technology, Pune, India

Latent Dynamics Modeling Latent World Models Consistency Regularization