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.

Autonomous systems increasingly rely on Large Language Models (LLMs) yet the safety infrastructure surrounding these models introduces latency and compute overhead. This limits utility in resource-constrained, time-critical deployments. Existing external guardrail models remain blind to the model's internal workings, creating a fundamental assurance gap. We ask: does the model already know when the content is harmful? We extract activations from LLaMA-3.1-8B and train lightweight MLP classifier probes (12.6M parameters) to detect harmful prompts. Evaluated on WildJailbreak, Beavertails, and AEGIS 2.0, our probes achieve F1 scores of 99%, 83%, and 84%, respectively competitive with 1000x larger guard models while cutting latency and compute costs.

Can a logged dataset visit every hidden state frequently and still be exponentially uninformative about a target policy's value? We show that it can when the logger depends on history. For every horizon $H \ge 3$, we construct two POMDPs with at most two latent states per stage, three actions, and a common logger with three memory states. Action coverage, belief coverage, and two behavior-marginal outcome-revealing conditions all have constants independent of $H$. Nevertheless, evaluating a known deterministic target policy to accuracy $1/8$ requires $Θ((3/2)^H \log(1/δ))$ logged episodes at confidence $1-δ$, for $0 < δ\le 1/4$, even when both candidate models are known. The mechanism is simple: a reset erases the unknown transition that determines the target value. We characterize the resulting statistical experiment exactly and obtain a matching optimal estimator. A directed two-lane gridworld realizes the construction, and trajectory simulations agree with its finite-sample prediction. The result establishes intractability for the history-dependent-logging, model-based case posed by Zhang and Jiang (2025, arXiv:2503.01134), under their behavior-marginal definition of revealing.

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.

Pretrained world models, learned simulators that encode an observation into a latent state and predict how it evolves under actions, are beginning to be reused as off-the-shelf dynamics backbones for control, like pretrained encoders and language models are reused today. We show that this reuse opens a supply-chain backdoor: an adversary who controls only a released checkpoint can hijack the downstream controller, even though the victim trains and evaluates entirely on clean data and never sees the trigger. The attack encodes no explicit trigger-to-action rule. Instead, the poisoned model routes trigger-bearing observations into a chosen latent region and reshapes the local dynamics there, so that the victim's own optimization (Dreamer-style actor training in imagination, or MPC/CEM planning over predicted futures) re-discovers the attacker's target action on its own. Across several control tasks and trigger families, the trigger steers the controller's action toward the attacker's target, controlling every action dimension and hijacking 100% of triggered steps on the strongest settings. The checkpoint still passes the clean-data diagnostics a victim would run before deployment, with clean-task success retaining at least $\sim$75%. The effect is temporally gated: it appears only while the trigger is present and disappears when the trigger is removed. Trigger-blind repair is budget-dependent: moderate clean fine-tuning can preserve clean utility while leaving the triggered failure intact, whereas sufficiently aggressive adaptation can remove it only after substantially degrading clean control. The world-model backbone itself is therefore an emerging and underexamined attack surface for control. The full code and artifacts are available in our repository.

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 $\href{https://github.com/DingjieFu/ACT-LAM}{url}$.

Image-metadata prediction requires fusing heterogeneous evidence whose reliability can vary across samples and latent factors. Existing representation-level fusion methods typically choose an aggregation architecture, such as concatenation, gating, conditional modulation, or attention, without explicitly defining what the fused representation should mean under modality uncertainty. We propose RiVaT-Fuse, a reliability-calibrated variational tensor fusion framework that defines fusion as sample-wise latent-state estimation. Rather than producing a fused vector by direct aggregation, RiVaT-Fuse estimates a consensus latent state through a variational objective that balances image evidence, metadata evidence, structured cross-modal interaction, and stability. The resulting framework replaces scalar modality confidence with matrix-valued trust geometry, decomposes interaction into additive, multiplicative, and relational components, and couples the latent state with conditional robustness and structured multi-task prediction. We provide well-posedness and stability interpretations of the latent solve and instantiate the framework with efficient low-rank-plus-diagonal trust operators. On an image-level image-metadata prediction benchmark, RiVaT-Fuse achieves the strongest overall predictive rank among direct representation-level baselines while improving probability and label stability under perturbation.

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.

Large language model agents produce fluent action sequences across a wide range of tasks, yet they fail in characteristic ways once the environment becomes partially observable. Ambiguous feedback pushes them into premature commitments. A single informative observation can collapse their uncertainty onto the wrong hypothesis. Policies drift as the history grows. We trace these symptoms to a common structural cause. An LLM agent, as commonly deployed, is a history-conditioned policy with no explicit belief over hidden state. We propose an architectural fix. The Belief-State Engine (BSE) is an inference module placed outside the LLM. It maintains a Bayesian posterior over the latent states of a given POMDP (Partially Observable Markov Decision Process) model, and at each decision step it exposes only that posterior to the LLM. The raw action-observation log is not shown. We set out a minimal four-axiom specification of what a belief-consistent internal state must satisfy, and prove that the LLM paired with the BSE is a sound Markov policy on the belief MDP induced by the underlying POMDP. It therefore inherits the Bellman optimality guarantees of classical POMDP theory, provided the LLM is never exposed to the raw history. We evaluate the architecture on the Tiger POMDP and a red-team attack-graph task, against six baselines: a reactive LLM, Chain-of-Thought, ReAct, a natural-language belief tracker, QMDP, and POMCP. Across both domains, the BSE-augmented agent improves task return, belief calibration, and decision consistency. Ten targeted ablations isolate the contribution of each architectural choice confirms that the effect is not specific to any one model. Code, environment specifications, prompt templates, and seed logs accompany this paper.

Formulaic alpha discovery is a pool-dependent symbolic search problem in which informative feedback is observed primarily when a complete expression is evaluated. This delayed feedback creates two coupled difficulties: the retained alpha pool does not preserve the full history of realized evaluation feedback, and the value of an intermediate construction action is uncertain because its consequence depends on the formula eventually completed. We introduce AlphaRJM, which addresses these difficulties through Reward-Jump Memory, an event-driven latent state that remains fixed during token construction and updates only at terminal evaluation events using the realized pool reward and evaluation outcome, and an action-conditioned SDE return critic that represents future discounted discovery returns with stochastic particles. The particles guide action selection through their mean and uncertainty and are learned using a distributional Bellman objective combining energy-distance matching, mean calibration, and jump regularization. Empirically, AlphaRJM delivers strong and stable gains across multiple equity universes, forecasting horizons, and random seeds, while ablations confirm the complementary roles of persistent evaluation history, stochastic return modeling, and distributional supervision.

Chain-of-thought (CoT) reasoning improves the reasoning ability of large language models by introducing intermediate computation, but explicit rationales increase decoding length, latency, and context cost. Implicit CoT offers a more efficient alternative by moving intermediate reasoning into continuous latent states. However, latent reasoning can be unstable: successive latent states may become overly similar and collapse toward a shared dominant direction, reducing the diversity of the reasoning trajectory. In this work, we identify $\textit{latent rank collapse}$ and propose $\textbf{WIDER}$, a lightweight spectral regularizer for implicit CoT. During training, WIDER estimates the shared direction of each latent trajectory and penalizes projections onto this direction, encouraging latent states to span a broader representational subspace. The method is plug-and-play and leaves the backbone model, latent schedule, and inference-time decoding procedure unchanged. We further formulate this collapse as a geometric bottleneck in implicit reasoning, casting its mitigation as a training-time regularization problem rather than an inference-time decoding change. Extensive experiments show that WIDER improves matched implicit CoT baselines, while mechanistic analyses reveal higher effective rank, lower dominant-direction energy, and reduced redundancy among latent steps. These results highlight latent subspace utilization as an important factor for efficient continuous reasoning, providing a geometric perspective for analyzing and improving implicit CoT. Code is available at https://github.com/whitesweater/WIDER.

LLMs latent-state reasoning methods replace discrete intermediate tokens with continuous states, such as weighted mixtures of token embeddings, to retain multiple possible reasoning directions rather than committing to one. Yet pretrained language models often fail to preserve these mixtures. We study why through a combination of theoretical analysis and controlled empirical investigations on a variety of models. We identify three independent, distinct sources of failure. First, transformer architectures already distort mixture geometry, and training substantially amplifies this effect. Moreover, the failure can occur even if the model transports mixtures perfectly linearly: the softmax readout and autoregressive feedback form a dynamical system that either amplifies small differences until one component of the mixture dominates or contracts different mixtures until they become indistinguishable. We verify this theoretical prediction empirically: the observed transition between contraction and amplification occurs near the theoretical threshold derived by our analysis, and pretrained-model rollouts lie predominantly on the amplifying side. Finally, we generalize to mixtures of many components and show that exact preservation generally requires context-dependent correction, whose required dimensionality can grow with the number of components.

LLMs are increasingly deployed as orchestrators that coordinate specialized subagents to solve complex tasks through natural language. However, in many important domains like game playing and robotics, the strongest available agents are not language models. Integrating non-language agents with LLMs would require \emph{verbalization}: compressing their rich continuous representations into sparse textual summaries at each interaction step. To study whether verbalization constitutes a bottleneck, we introduce \textsc{LLAMIA-Bench}, a suite of six diverse collaborative chess tasks spanning three facets: behavioral imitation, state assessment, and natural-language explanation. Each task instantiates a well-established chess problem that neither the LLM nor the chess engine can solve alone. To solve LLM collaboration with non-language agents, we introduce \emph{latent state internalization}, which projects the subagent's continuous representations directly into the LLM's token stream as learned state tokens, with dynamic re-encoding as actions advance the environment state. Comparing internalization to verbalized integration, our experiments reveal a consistent \emph{verbalization debt}: the performance gap widens throughout training and persists as the LLM scales from 4B to 14B parameters. A single 14B model, \textsc{LLAMIA}, trained with latent state internalization, matches or exceeds task specialists and frontier models including GPT-5.1 with tool access across all benchmark tasks, and generalizes out-of-distribution where task-specific finetunes collapse

World-Action Models (WAMs) build robot control on video-generation backbones, which jointly predict dense future visual trajectories and robot actions. We argue that video generation is an unnecessary intermediate objective for world-action modeling. For robotic manipulation, the goal of a world model is not to reproduce how the world looks at every intermediate moment, but to predict the state that the world will reach after an action is executed. The intermediate frames only describe the visual transition between physical states, which consumes substantial model capacity and computation, but do not directly specify the physical outcome that the robot action is intended to produce. In this paper, we propose DELE-w0.5, which infers robot actions from predicted future states without relying on video generation. Concretely, DELE-w0.5 infers the action sequence from its corresponding compact future latent state. The future latent state captures the action-relevant physical outcome of robot interaction and serves as an explicit bridge between world modeling and action generation. The core design principle of DELE-w0.5 is to model how the physical world changes under robot actions, rather than how its visual appearance evolves frame by frame. This formulation removes the high-dimensional visual redundancy introduced by dense video representations, and it therefore enables cheaper training and low-latency inference. Across 640 real-robot trials on four long-horizon manipulation tasks, our DELE-w0.5 achieves the best performance among all compared policies, attaining 62.5% overall full-task success and 81.3% macro ordered-stage progress. It outperforms the strongest baseline by 32.5 percentage points in full-task success and 20.1 percentage points in macro progress.

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.

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.

Latent world models plan by predicting future states from an action, but when a scene contains motion the agent does not control, they quietly go action-blind: predictions for different actions become indistinguishable even as the training loss keeps improving. Existing remedies suppress this distraction with reconstruction, task reward, or auxiliary objectives, each adding machinery or assumptions. We show that a minimal alternative suffices, borrowed from the dueling decomposition of value into a state baseline and an action advantage: in latent dynamics, subtracting a prediction's mean effect over actions cancels whatever the actions share--the action-independent variation where distractors live--leaving a clean, controllable channel, with no reward, no reconstruction, and no distractor-specific auxiliary loss. Because this is only a subtraction at readout time, it applies unchanged to any action-conditioned world model, including frozen pretrained ones. Across a gridworld, synthetic generators with known factors, distracting continuous control, and natural-pixel Atari, the isolated channel recovers the agent's own effect where entangled predictors fail, with nuisance leak indistinguishable from zero; applied post hoc it surfaces an action channel in off-the-shelf models that their raw readouts miss, and it converts into goal-reaching control in the gridworld. We prove the cancellation is exact in finite samples for both discrete and sampled action sets, and we state its measured boundary--distractors whose motion tracks the action--together with the remaining limitations in the appendix.

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.

Multimodal large language models excel at passive perception but struggle with complex visual cognitive tasks requiring multi-step temporal reasoning. This degradation largely stems from the inherent ambiguity of language-based reasoning, which often fails to accurately articulate continuous visual transformations. To address this, we propose ChronoVision, a multimodal framework designed to align visual logic with latent imagery. During supervised fine-tuning, a Reconstructive Visual Head predicts the latent representation of the final transformed state, while an ROI Attention Locating module focuses the model on key visual evidence via semantic span queries. In post-training, we apply reinforcement learning with an implicit process grounding mechanism, guided by a composite reward function that evaluates outcome correctness, latent process alignment, and unsupervised visual focus. Furthermore, we introduce Vbvr-VQA, a novel dataset that evaluates temporal tracking by reformulating video reasoning into a strict image-ordering task. Experiments demonstrate that ChronoVision achieves state-of-the-art performance on Vbvr-VQA with 74.8% in-domain and 71.6% out-of-domain accuracy, alongside a strong 55.0% accuracy on IntPhys2, a highly challenging cross-domain benchmark.

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

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.

We introduce the Unified Neural Variational Measurement of Proficiency (UNVaMP) architecture, a knowledge tracing method that integrates observed student-item interactions with internal memory to produce evolving latent representations of student knowledge. These representations support accurate predictions of future responses while enabling explicit control over the smoothness of estimated learning trajectories. UNVaMP can be configured as either a purely neural model or a hybrid model that predicts responses through an interpretable measurement function over the latent space. We show that a pure neural configuration (UNVaMP-MLP) achieves the strongest predictive performance among compared models on three out of four datasets. Meanwhile, a hybrid configuration (UNVaMP-MIRT, using a 1PL MIRT measurement function) lags only slightly behind UNVaMP-MLP, indicating that the predictive cost of interpretability is modest. Beyond predictive accuracy, UNVaMP provides the following: a principled mechanism for controlling volatility when estimating student latent variables, quantification of uncertainty over student knowledge state estimates, and flexible input specification that supports heterogeneous student-item interaction features. In addition, the hybrid UNVaMP-MIRT configuration generates interpretable moment-in-time student knowledge state estimates. Using an experimental dataset, we show that auxiliary inputs induce structured changes in the predictive behavior of UNVaMP-MIRT, consistent with sensitivity to underlying structure beyond response correctness. Furthermore, through a simulation study, we show that UNVaMP yields well-behaved knowledge state estimates under controlled measurement conditions. In total, these results indicate that UNVaMP is both useful for real-world education systems and capable of recovering underlying structure from student-item interactions.

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.

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.

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.

A temporally drifting data stream may pass through discrete regimes rather than changing continuously. We ask whether such regimes are recoverable from the weights of models trained on the stream, using a hidden Markov model (HMM) fit to the chronologically ordered trajectory of those weights. We study this question in two domains known to drift over time: multimodal misinformation detection, using the Fakeddit dataset; and sentiment analysis, using the Yelp dataset. We train classifiers on consecutive temporal windows and fit an HMM to the trajectory of their aligned weights, recovering latent states that partition each timeline into coherent phases. On both datasets, classifiers generalize better to data from windows sharing the state of their training window than to windows across state boundaries. This within-state transfer advantage survives a control for temporal proximity and modestly exceeds the advantage recovered by a naive partition into contiguous states of equal size. Although the states are estimated solely from model weights, they correlate more strongly with shifts in the data's class distribution than with the weight-space geometry used to estimate them. After class divergence and lag are residualized out, the within-state advantage exceeds its permutation null on both tasks, indicating that the states recover structure relevant to transfer beyond the data distribution. Every effect replicates on both tasks but is attenuated on Yelp, whose label distribution is more temporally stable.

Mechanistic interpretability has largely focused on language models and deterministic toy tasks. Much less is known about how sequence models internally represent latent stochastic dynamics under noisy, partially observed observations. We study this question in a controlled multivariate stochastic volatility setting, where models observe only returns while the ground-truth latent volatility state is known to the researcher. This setting provides a useful benchmark for mechanistic interpretability under partial observability: the latent state is hidden from the model but directly available for evaluation. Across architectures, losses, and output heads, we find evidence for a two-stage computation. Hidden representations encode substantial information about the next latent volatility state, and the output head maps this representation to squared return forecasts. Furthermore, in Transformers, latent-state decodability emerges at identifiable architectural stages whose location depends on the volatility period. In long-cycle regimes, this computation simplifies into an explicit latent-state filter consisting of a learned linear projection followed by $\ell^2$ normalization. Output-head replacement further shows that part of the degradation under noisy MSE training arises from readout misalignment rather than representation failure. These results suggest that stochastic volatility models provide a useful benchmark for mechanistic interpretability under noisy latent dynamics and partial observability.

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.

Vision-and-Language Navigation in continuous environments (VLN-CE) requires an agent to ground language in egocentric observations and plan in unseen scenes. Although recent multimodal large models and world-model-based methods have improved navigation, they often preserve excessive task-irrelevant detail, weakening generalization and increasing computational burden. We propose BrainNav, a navigation framework grounded in the Principle of Minimal Sufficiency. BrainNav consists of three components: a Logical Anchor Model that implements instruction-aware selective perception to suppress environmental noise, a Minimalist Constraint Alignment module that serves as a compact cross-modal bottleneck, efficiently synchronizing discrete linguistic intent with continuous latent dynamics while filtering out redundant information, and a Compression World Model that predicts action-conditioned states within a condensed, low-rank latent space. These modules align semantic intent with spatial perception, enhancing the agent's robustness and efficiency in complex tasks. Experiments show that BrainNav improves over prior SOTA by 2.0 % / 1.0 in SR/SPL on R2R-CE val-unseen and 0.94 % / 0.78 on RxR-CE val-unseen. These results indicate that minimally sufficient world representations provide an effective foundation for robust VLN.

In multi-agent reinforcement learning (MARL), inter-agent communication is effective for improving performance under partial observability. Representation learning-based approaches enable decentralized agents to learn messages grounded in their own observations, but they rely only on current observations and cannot convey information accumulated over time. We propose Dreamer-CPC, a decentralized model-based MARL method that integrates message learning based on Collective Predictive Coding (CPC) into the world model of DreamerV3. Each agent independently maintains a world model and a message module, and infers and exchanges messages from the latent states of the world model that reflect the history of past observations and actions. We evaluated Dreamer-CPC in two environments: Observer, a non-cooperative information-sharing task, and CatchApple, a newly introduced task in which task-relevant observations are temporarily missing. In both environments, Dreamer-CPC outperformed IPPO-CPC, an existing CPC-based method that generates messages from current observations, as well as no-communication baselines. In particular, in CatchApple, Dreamer-CPC achieved 4 to 5 times the episode return of IPPO-CPC, demonstrating effective coordination where other methods fail due to missing observations. These results suggest that communication grounded in the latent dynamics of world models can support decentralized decision-making when current observations alone are insufficient.

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.

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.

We present a goal-agnostic control framework for partial differential equations (PDEs) built around an end-to-end joint-embedding predictive architecture (JEPA). A lightweight 2D vision-transformer (ViT) and action-conditioned latent dynamics are trained offline without a reward or downstream goal, before being frozen and reused by a model-predictive path integral (MPPI) controller. We minimize a control objective in the latent space, initially expressed via the $L^2$ distance and additionally illustrate the benefit of recasting the control objective in terms of an explicit physical observable when available. By instead minimizing the tracking error for a learned linear kinetic-energy (KE) probe on the frozen latent-state rollouts, we demonstrate the ability to reproduce the control of held-out trajectories with $R^2=0.989$, while requiring no change to the underlying world model. For a controlled 2D Navier--Stokes benchmark, using a KE-probe within MPPI planning improves the mean native reward from $-12.08\pm0.86$ for latent-$L^2$ tracking to $-10.90\pm0.91$ (95% CI), all while lowering last-quarter velocity-field RMSE from $0.0765$ to $0.0692$. Across three intentionally withheld, dissimilar, aperiodic targets, KE planning lowers late field RMSE by $53\%$ relative to latent-$L^2$ planning ($0.0220$ versus $0.0469$), winning across 30 paired comparisons. The same frozen model also supports stabilization around a steady-state configuration via direct regulation of KE, achieving $2.7\%$ mean relative error. While the latent probe proves brittle to measurement noise and missing pixels, our findings support the claim that latent dynamics can remain flexible and goal-agnostic, particularly when calibrated observables (granted they guarantee unique continuation) are a suitable objective for state control.

Extended reasoning has become standard for frontier Large Language Models (LLMs), yet the trajectories these models produce remain largely uncontrollable. Existing methods for shaping how a model reasons are prompt based approaches and operate at the input level, offering no fine-grained control over the reasoning process itself. Related work analyzes and discovers latent transition dynamics in the reasoning traces from Large Language Models. Building on this, we statistically characterize these states, and show that failure trajectories get stuck in self-loops, exhausting the token budget without progress toward the final answer. To intervene on these failures, We propose SOPHIA: Steering Of reasoning Processes via Hidden-state Intervention and Activations. We treat each reasoning trace as a sequence of latent states rather than an unstructured texts, and investigate whether inference time interventions can provide fine-grained control over the self-looping reasoning process. We classify every prefix to a latent state, record step level transitions, and use them to construct a bank of steering vectors indexed by state pairs. At inference time, a controller infers the current state and, given a target state, retrieves the corresponding vector and can also detect self-loops online from the transition structure to prevent the model from sinking into a reasoning black hole. Through extensive experiments, our method reliably intervenes on self-loop failures, with steering vectors that generalize to different state pairs. End task accuracy and token efficiency indicate that fine-grained controllability results in better reasoning quality.

Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured. We propose a hybrid neural--physics framework in which the known components of the ODE are kept explicit and the missing components are represented by a neural network. The proposed method consists of two stages where we alternate between state and parameter estimation and iterate until a predetermined criterion is met. Specifically, in the first step, we treat the model parameters as being known and we infer the latent states from the available measurements using a Rauch--Tung--Striebel (RTS) smoother. In the second stage, we treat the smoothed trajectories as being known and use them to estimate the neural networks' parameters through backpropagation. We evaluate the method on benchmark systems spanning linear, nonlinear, and stiff dynamics under partial state observation. Across these settings, the proposed method learns missing ODE components from incomplete measurements while exploiting and retaining interpretable mechanistic structure and improving latent-state reconstruction and long-horizon prediction.

Accurately representing atmospheric aerosol populations is essential for simulating aerosol-cloud interactions, radiative forcing, and ice nucleation, yet existing reduced schemes impose structural assumptions that limit their ability to capture composition diversity and mixing state. Machine-learning approaches offer more flexible representations, but standard autoencoders do not preserve the mathematical structure of aerosol populations and therefore cannot support physically meaningful process operators. We introduce AeroMELD (Aerosol Measure Embedding for Latent Dynamics), a mathematically grounded framework for constructing low-dimensional latent variables that retain this structure. We show that any permutation-invariant linear encoder must take a scale-shape decomposition, with total number concentration represented explicitly and latent shape given by a barycentric combination of per-particle embeddings. This aggregated latent state retains the diagnostic expressiveness of a Deep Sets model by moving the nonlinear post-aggregation stage into the learned diagnostic map while preserving latent linearity. Using particle-resolved data as ground truth, we encode weighted particle populations directly rather than binned aerosol states; size-resolved mass and number distributions serve only as diagnostic targets and visual summaries. The latent space accurately reconstructs these distributions, CCN spectra, optical coefficients, and immersion-freezing behavior while preserving the linear population structure needed for hybrid ML-physics models. Although the experiments focus on diagnostic reconstruction, the embedding is designed so that emissions and mixing can be represented exactly and nonlinear microphysical processes learned in a controlled latent space. This work establishes a foundation for learning aerosol-process evolution directly in latent space.

Autonomous driving requires long-horizon closedloop decision making in dynamic traffic environments. Latent world models offer an effective framework for this problem by enabling imagination-based decision making in compact latent spaces. However, multi-source observations contain controlirrelevant redundancy, whereas reliable driving decisions rely on risk-relevant relations, future dynamics, and continuous action adjustments. This mismatch makes observation reconstruction and absolute action modeling suboptimal for learning decisionrelevant latent dynamics. We propose LIDAR-AD, a decoderfree Latent-Interaction Dreamer with Action-Residual Chains for autonomous driving. LIDAR-AD replaces observation reconstruction with redundancy-reduced latent alignment, encouraging compact representations of risk-relevant relations in multi-source driving inputs. It further models vehicle control as residual action updates and uses residual-action sequence contrastive learning to align multi-step residual-driven rollouts with future latent states. A deterministic analysis shows that the latent-tanh residual parameterization preserves interior action reachability while representing smooth long-horizon control as compact local updates. Together, these designs improve risk-aware state abstraction, continuous-control modeling, and long-horizon dynamics prediction. Extensive experiments across diverse simulated driving scenarios demonstrate that LIDAR-AD consistently outperforms world-model baselines, achieving the highest reward and the best success rate among learning-based methods. Evaluations on nuPlan-derived log-reconstructed scenarios further demonstrate the transferability of LIDAR-AD under real-world traffic layouts.

Does a reinforcement-learning agent that earns reward learn its task's hidden state? We study this question with hidden finite automata that the agent partially controls. Because each automaton is known, we can normalize reward by the best achievable return and probe the network for the true state at every step. Together the two measurements separate failures that reward alone conflates. An agent can encode too little of a state its network could hold, or encode the state and still control poorly. Weak on-policy RL matches random play while the state probe stays at chance. State learning depends on the optimizer, the training budget, and the task's structure. Permutation automata provide a warning before training: no input symbol maps two distinct states to the same successor. On a stratified held-out set, 86 of 103 permutation automata fail the state probe, and the classification is stable across probe read-outs and recovery thresholds. Most of these failures come with weak reward. High reward without the state occurs but is rare. Non-permutation automata can also fail. Oracle-normalized reward alone therefore does not establish that the task's state was learned.

Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements. This challenge is sharper for forced systems, whose responses depend on both intrinsic dynamics and time-dependent inputs. Here we introduce FLARE, a forced latent autoencoder for response equations that learns compact response coordinates, identifies sparse input-dependent latent dynamics and decodes equation rollouts to full responses. By estimating latent dimension from data and separating state estimation from external forcing, FLARE enables forecasts to be initialized from past responses and driven by prescribed future inputs. Across known dynamical systems, application-scale forced responses and visual observations, FLARE recovers compact forced dynamics and predicts long-horizon high-dimensional responses under inputs not used for training. By turning learned coordinates into a dynamical interface, FLARE extends equation discovery to systems whose effective states are hidden within complex observations, providing a route for interpretable modelling and prediction of high-dimensional responses in forced dynamical systems.

JEPA world models commonly predict the next latent state with one regressor. Under stochastic transitions, squared and cosine regression return the conditional mean and its normalized direction, respectively: a single compromise that may match no valid successor. MoP-JEPA instead uses $K$ hard-assigned heads and a context-only router to produce a finite candidate set in one pass. On held-out OGBench transitions, graph search with single-output predictors succeeds on $0.02$--$0.09$ of queries, whereas MoP-JEPA reaches $0.85$. To distinguish useful successors from indiscriminate coverage, we also measure verified-route success (\emph{realroute}), which checks after graph construction whether the proposal contains a path of real transitions. MoP-JEPA leads this same-protocol metric on all three mazes; an MDN attains high raw coverage but predicts many nonexistent edges.

We characterize observability in representation learning through Platonic Projection Structures (PPS), an operator-theoretic framework for analyzing representation accessibility under partial observation. Rather than treating observable outputs as direct reflections of latent representations, PPS models observation through a self-adjoint positive semidefinite operator acting on a latent representation space. A system is represented as a triple $(H, Π, O)$, where $H$ is a latent representation space, $Π\succeq 0$ is an observation operator, and $O(v)=\langle v,Πv\rangle$ defines an induced scalar observable. Observability is characterized by the quotient geometry $H/\ker(Π)$, representing equivalence classes of latent states indistinguishable under observation. We show that quantum measurement and representation inference under linear observation models share this operator-theoretic structure while differing in the algebraic properties of their observation operators; the correspondence is structural rather than physical. Representation transfer and knowledge distillation can likewise be interpreted as approximate preservation of observable geometry through $ΦΠ_T \approx Π_S Φ$. PPS also reveals a structural limitation of output-based interpretability: latent components in $\ker(Π)$ are inaccessible from induced observables, imposing intrinsic constraints on attribution and explanation methods. Controlled empirical validations demonstrate kernel-invariant observability, projection-induced attribution gaps, and rank-controlled observable geometry in latent representation spaces. PPS thus provides an explicit characterization of observability through operator-induced quotient geometry and a unified perspective on representation accessibility, interpretability, and projection-mediated inference.

We present FM-ChangeNet, a pathwise-supervised framework for change detection that reformulates bi-temporal reasoning as continuous transport in feature space rather than static endpoint comparison. Given encoded pre and post-temporal representations, we construct intermediate latent states and learn a time-conditioned velocity field $\hat{v}_θ(z_t,t)$ along the transformation trajectory. This pathwise formulation constrains the predictor over a continuum of intermediate states, providing a denser and less ambiguous supervision signal than conventional endpoint-only segmentation and enabling the model to capture temporal evolution explicitly. The learned velocity field is not only a transport mechanism but also an interpretable representation of change: its magnitude serves as a spatially localized change cue that helps distinguish true structural variation from nuisance effects such as illumination shifts and spatial misalignment. We develop a hierarchical multi-scale architecture with cross-temporal alignment, time-conditioned coarse-to-fine flow decoding, and a unified objective that couples flow supervision, trajectory consistency, spatial regularization, and segmentation loss. Experiments on remote sensing benchmarks show that the proposed framework produces more structured and robust change representations while achieving state-of-the-art performance.

Learning and planning in imagination using world models provides an effective paradigm for training agents for decision-making. However, existing approaches often rely on high-dimensional latent spaces or generic visual embeddings that retain many factors irrelevant to control, limiting efficiency and generalization across tasks. To this end, we study how agents can learn world models with representations that are task-specific, minimal, and sufficient for decision-making. We achieve this via a closed-loop synergy between the agent and the world model, in which structured world-model learning distills task-sufficient representations from informative interaction data. On the agent side, agents actively probe the environment to collect informative trajectories that expose task-relevant latent factors, guided by an adaptive curriculum. On the world-model side, we learn structured representations over observations to distill compact, task-sufficient latent states from the collected interaction data. This synergy enables the empirical recovery of task-sufficient latent representations that capture all control-relevant factors. Leveraging these representations, the resulting policies achieve improved sample efficiency and generalization, including generalization across skills, object-skill compositions, and previously unseen tasks on standard continuous-control and robotic-manipulation benchmarks.

World models -- compressed latent representations of an environment that support action-conditioned prediction and planning -- are typically presented as a product of modern self-supervised learning. This paper argues that the functional anatomy of a world model was independently developed, deployed, and formally analyzed decades earlier in the model-order-reduction (MOR) and control literature, under different names and for a different purpose: the real-time operation of physical systems. We trace the anatomy across three communities. Low-dimensional models of turbulence built on proper orthogonal decomposition (POD) supplied latent dynamics learned from data of a chaotic environment; eigenface methods in early computer vision supplied the encoder-decoder half, including a primitive runtime validity check; and measurement-based POD frameworks for facility thermal control assembled the complete loop -- POD coefficients as latent state, parametric dependence on actuator setpoints as action conditioning, modal reconstruction as decoding, and, critically, a priori analytical error bounds as a verification layer that certified when the model's predictions could be trusted in closed loop. We then examine what each tradition possesses that the other lacks: MOR contributes verification, physical grounding, and extreme data efficiency; learned world models contribute nonlinear representation, transferability, and horizon. We argue that the outstanding obstacle to deploying world models in systems that cannot fail -- power, thermal, process control -- is not predictive fidelity but verifiability, and we outline a research agenda for physics-grounded, verifiable world models that unifies the two lineages.

Diffusion Language Models (DLMs) have recently emerged as a promising alternative to autoregressive models. Unlike standard diffusion-based approaches, DLMs are not explicitly conditioned on a timestep, raising a natural question: do these models internally represent denoising progress, and how is such information used downstream? In this work, we show that DLMs do in fact encode a latent representation related to the diffusion timestep within their residual streams. We find that this signal can be reliably extracted using probes across layers, indicating that denoising progress is decodable from internal activations. We further demonstrate that steering the model along a low-dimensional subspace associated with the inferred timestep allows us to systematically modulate its notion of denoising progress, leading to predictable changes in model confidence and entropy. Finally, we analyse the geometry of the identified representation, showing that it exhibits structured and interpretable properties in activation space, and shedding light on how such a signal is processed by these models.

Time-series models are often evaluated by what they can forecast or classify, but those scores do not show whether their representations preserve the process state a user may want to inspect: event timing, phase, amplitude, frequency, or regime variables. We introduce Aionoscope, a generator-based diagnostic tool for debugging latent-state accessibility in frozen time-series representations. Aionoscope separates process generation from observation rendering, producing seeded synthetic streams with exact categorical and dense labels across mixture complexity and nuisance variation. We instantiate Aionoscope as Primitive Process Mixtures and evaluate 37 model-plus-adapter systems with a common pooled linear-probe protocol. The main result is a mismatch between coarse and fine-grained accessibility. Most systems make component presence easy to recover, but expose dense process state much less reliably: the highest observed dense-probe row reaches 0.689 mean masked $R^2$, while a dense-feature oracle reaches 0.999. This is the failure mode Aionoscope is designed to surface: a representation can look informative at the level of "what kind of signal is present" while hiding the timing, phase, amplitude, frequency, or regime variables needed for debugging.

Pre-training on large-scale videos to improve reinforcement learning efficiency is promising yet remains challenging. Existing methods typically treat the agent as an indivisible entity, modeling motion patterns globally. Such global modeling is tightly coupled with the morphology, hindering transfer across domains. In contrast, despite the vast disparity in global motions, the local components exhibit similar motion patterns across different agents. Building on this insight, we propose a novel Deconstruct-Recompose Paradigm (DRP) for learning transferable local motion representations. Specifically, in the Deconstruct phase, we identify multiple local points and track their frame-wise motions, defining each as an Atomic Action. We introduce a Dual-Attention Encoder (DAE) to learn local motion representations from these Atomic Actions, capturing their spatiotemporal relationships. In the Recompose phase, we compose local motion representations with a learnable Motion Aggregation Token [MAT] via latent dynamics model learning. Additionally, an adapter bridges local motion and downstream action-specific dynamics to accelerate policy learning. Extensive experiments demonstrate that our method effectively transfers to diverse robotic control and manipulation tasks, significantly improving sample efficiency and performance.

Always-on agents are systems whose future behavior depends on durable state accumulated across earlier interactions. We treat them as persistent-state systems: the operative system includes retrievable memories, but also task ledgers, permissions, credentials, commitments, provenance and audit records, shared state, trigger conditions, and externally committed effects linked to those records. The survey reads the literature through six diagnostic axes for each state item, authority, scope, mutability, provenance, recoverability, and actionability, and through a lifecycle in which state is written, validated, organized, retrieved, acted upon, updated, forgotten, audited, and sometimes rolled back. Across a 435-work coded corpus, treated as a scoped map rather than an exhaustive census, the literature concentrates more heavily on accumulating and retrieving state than on governing, recovering, or relinquishing it. We therefore introduce the Always-On Evaluation Protocol (AOEP-v0), a pilot evaluation contract that makes these governance requirements concrete by scoring state mutation and recovery obligations rather than answer quality alone. The resulting agenda connects always-on agents to databases, distributed systems, formal methods, capability security, and machine unlearning.

Large language models achieve high reasoning performance via explicit chain-of-thought and reinforcement learning, but require long output sequences and extended inference time. Latent reasoning reduces this cost by shifting computation into a latent space; however, continuous latent methods are hard to train, suffering from unstable and uninterpretable reasoning trajectories. We argue these issues stem from a misalignment between continuous-space reasoning and discrete symbolic supervision, as continuous states lack explicit anchors for step-by-step alignment. To resolve this, we propose \textbf{Discrete Latent Reasoning~(DLR)}, the first method that converts continuous latent states into explicit discrete tokens. Inspired by render-based compression, we render textual chains of thought into images, extract visual features, and construct a discrete latent vocabulary via clustering-based fine-tuning. Expanding the vocabulary and output head enables standard autoregressive modeling over both natural language and latent tokens, supporting pretraining alignment, SFT, and RL. Experiments on five reasoning benchmarks and two model series~(Qwen3-VL and LLaMA-3) confirm that \textbf{DLR} outperforms prior latent reasoning baselines with up to \textbf{20$\times$ compression}. Furthermore, the learned latent trajectories retain an interpretable semantic structure. Overall, discrete latent tokens provide a controllable and interpretable basis for efficient latent reasoning.

We propose a path-space formulation of prediction in AI world models. Rather than sequences of one-step conditional distributions, we argue that a world model implicitly defines a probability measure over future trajectories. In the local regime where latent dynamics admit an effective Markovian description, this path measure takes the Onsager-Machlup form. Within this framework, prediction (most probable trajectory), planning (constrained optimization), and uncertainty (fluctuations) emerge as operations on a single action functional. We decompose the latent dynamics into reversible and irreversible components and introduce operational measures of entropy production from model rollouts. In controlled small-scale attention-based models, we find that attention asymmetry is acquired during training in proportion to the irreversibility of the data. Symmetrizing the learned attention suppresses entropy production and selectively degrades long-horizon prediction of irreversible dynamics while preserving relaxational prediction. These results suggest that irreversibility may serve as a computational resource for predictive world models. More generally, the fundamental predictive object is a distribution over future paths rather than states.

Causal representation learning for time series has developed strong identifiability results in discrete-time latent causal models, but identifiability in continuous-time latent stochastic differential equation (SDE) models remains largely open. We address this gap using environment-induced shifts in diffusion covariance. We study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism, with shared drift but environment-specific diffusion covariance. We show that two diagonal diffusion regimes with pairwise distinct coordinate-wise variance ratios identify the latent coordinates up to permutation and scaling, without any sparsity assumption on the drift. We first prove this result for linear Ornstein--Uhlenbeck systems and then extend it to general additive-noise latent SDEs. Under mild smoothness, the instantaneous drift-Jacobian causal graph is identifiable up to the same permutation. We propose a two-stage estimator for latent disentanglement and optional graph recovery; experiments on synthetic systems confirm the predicted identifiability boundary, and an application to Hardanger Bridge monitoring data illustrates the approach on real sensor trajectories.

World models in partially observed environments rely on latent representations that summarize interaction history, but in many modern LLM-based architectures predictive performance fails to reflect representation quality due to history bypass, rendering the latent state unidentifiable. Strict latent state mediation, requiring predictions to depend only on the latent state and action, is a classical principle that resolves this, but enforcing it in text-based settings is an open challenge: textual latent states are discrete and non-differentiable, precluding variational training, and expressive LLM decoders readily ignore the bottleneck. We show how to make strict mediation work in the text domain. We formalize why it is necessary, showing that strict mediation makes representation quality empirically testable while history-leaky architectures break this connection. We then introduce textual latent states, which are discrete, interpretable, and variable-length, and factorized GRPO (fGRPO), a tree-structured reinforcement learning method that enforces strict mediation during training. Experiments on TextWorld and ScienceWorld show preserved one-step prediction accuracy alongside up to 57% gains in representation quality and 98% improvements in rollout performance, increasing with task complexity and horizon.

Embodied Visual Tracking (EVT) requires an agent to continuously follow a specified target while actively moving through dynamic environments. However, prevailing EVT paradigms predominantly rely on language-based target indication. While language is expressive and convenient, cluttered scenes often contain multiple objects that satisfy the same semantic description, leading to ambiguous target grounding. We therefore propose a paradigm shift, reframing target indication in EVT from text-only specification to unified spatial-semantic prompting. Based on this paradigm, we introduce Unified Spatial-Semantic Prompts for Embodied Visual Tracking with Latent Dynamics Learning, USS, an end-to-end embodied tracking framework that supports text, point, bounding box, and mask prompts within a unified architecture. USS encodes heterogeneous prompts with modality-specific encoders, fuses prompt tokens with visual features through hybrid attention, and decodes compact prompt-conditioned representations into egocentric waypoints. To further improve temporal robustness, USS incorporates a latent world model that predicts future representations through self-supervised alignment. Real-robot experiments demonstrate that explicit spatial target cues yield higher success rates than text-only prompts, particularly in scenarios involving similar distractors and longer-horizon tracking where maintaining instance-level target identity is critical. In the simulation benchmark, USS also achieves state-of-the-art performance among non-MLLM-based methods and competitive results against recent MLLM-based approaches with faster inference speed. Our findings reveal that spatial-semantic prompting provides a more precise and flexible target indication interface for embodied visual tracking. Project site: https://arescheah.github.io/uss-project-page/.

Learning Koopman operators with autoencoders enables linear prediction in a latent space, but long-horizon rollouts often drift off the learned manifold, leading to phase and amplitude errors on systems with switching, continuous spectra, or strong transients. We introduce two complementary components that make Koopman predictors more robust. First, we add an attention-free latent memory (AFT) block that aggregates a short window of past latents to produce a corrected latent before each Koopman update. Unlike multi-head attention, AFT operates in linear time and adds only $\approx$30k parameters ($3d^2 + T^2$, fewer than matched multi-head attention), yet captures the local temporal context needed to suppress error divergence. Second, we propose dynamic re-encoding: lightweight, online change-point triggers (EWMA, CUSUM, and sequential two-sample tests) that detect latent drift and project predictions back onto the autoencoder manifold. Across three benchmark systems -- Duffing oscillator, Repressilator, IRMA -- our model consistently reduces error accumulation compared to a Koopman autoencoder and matched-capacity multi-head attention. We also compare against GRU and Transformer autoencoders, evaluated both from initial conditions and with a 50-step context, and find that Koopman+AFT (with optional re-encoding) attains markedly lower long-horizon error while maintaining lower inference latency. We report improvements over horizons up to 1000 steps, together with ablations over trigger policies. The result is a fast, compact predictor that stays on the learned manifold over long horizons.

Recently, world models have emerged as a promising paradigm for building intelligent agents by learning predictive models that estimate future environment states conditioned on observations and actions. In particular, JEPA-style latent world models provide an efficient alternative to pixel space prediction by learning action-conditioned dynamics in compact representation spaces. However, existing latent world models typically rely on one-step prediction and must be recursively rolled out for long-horizon planning, which leads to compounding errors and a mismatch between training objectives and downstream planning tasks. To address this limitation, we propose Variable-length Latent World Models (VLWMs), a framework that learns to predict future latent states conditioned on action sequences of variable lengths. Instead of training only on one-step transitions, VLWMs directly model temporally extended dynamics, allowing the same predictor to evaluate action plans over different horizons. We further introduce a curriculum training strategy that progressively expands the action horizon, stabilizing optimization from short-range dynamics to long-range prediction. At test time, we design planning methods tailored to VLWMs to better exploit their variable-length predictive capabilities. Experiments on long-horizon control tasks show that VLWMs significantly improve latent space world models, achieving 13% average improvement over the state-of-the-art LeWM across different datasets, with especially large gains on tasks requiring extended planning. These results suggest that VLWM provides a simple yet effective paradigm for improving long-horizon prediction and planning in latent world models.

In many domains, practitioners seek models that produce accurate forecasts while faithfully capturing latent system dynamics. Existing approaches typically sacrifice one of these goals: deep state space models often assume Gaussian latent transitions, limiting fit and forecasting, while diffusion models are highly expressive but lack principled inference for the underlying dynamics. To combine the strengths of both, we introduce the Diffusion-Driven State Space Model (DDSSM), which replaces the conventional Gaussian transition distribution with a diffusion model. Our DDSSM resolves the open problem of how to jointly train an autoencoder and a diffusion model on sequential data, thereby extending the literature on latent diffusion models for time series. Moreover, we find that the DDSSM empirically outperforms a state-of-the-art deep SSM at fitting and forecasting a simulated time series with multimodal transitions.

Decision-making under partial or adversarial observability requires accurate inference of the environment's latent state and its associated uncertainty. This work analyses adversarial attacks on linear probabilistic state-space models, commonly integrated within reinforcement learning architectures, where the attacker alters observations under likelihood constraints that ensure the perturbations remains consistent. We analyze how such adversarial yet realistic observation shifts influence the latent state and influence policy decisions. This perspective provides a principled pathway toward building more robust reinforcement learning systems, with direct relevance to safety-critical domains such as robotics, where reliable operation under sensor noise, partial failures, and adversarial conditions is essential.

Direct Advantage Estimation (DAE) has been shown to improve the sample efficiency of deep reinforcement learning algorithms. However, its reliance on full environment observability limits its applicability in realistic settings, and its requirement to model transition probabilities incurs substantial computational overhead for high-dimensional observations. In the present work, we address both limitations. First, we extend the theoretical framework of DAE to partially observable domains with minimal modifications. Second, we reduce its computational complexity by introducing discrete latent dynamics models that efficiently approximate transition probabilities. We evaluate our approach on the Arcade Learning Environment and find that DAE scales effectively with function approximator capacity while retaining high sample efficiency.

Perception for action suggests that representations of the world should be shaped not by visual fidelity alone, but by their relevance for actions. At the same time, latent JEPA-style world models advocate learning compact predictive states from high-dimensional observations to facilitate the prediction of future states, but end-to-end training of these models is nontrivial because representations may collapse if our only goal is to construct a latent state that is easy to predict. We introduce a sensorimotor world model (SMWM): a latent world model trained end-to-end with inverse dynamics regularization. This single regularizer addresses both issues: it prevents representation collapse and induces action-aligned representations. By forcing latent states to preserve information about the action underlying a transition, it biases the model toward the controllable degrees of freedom of the environment while discarding uncontrollable distractors. This yields stable latent world models trained from offline, reward-free trajectories, without frozen encoders, exponential moving averages, or complex latent regularizers. Empirically, SMWM learns compact, interpretable latent spaces and enables competitive planning performance across simple 2D and 3D control tasks.

Model-based Reinforcement Learning (MBRL) has achieved remarkable success in continuous control by leveraging latent world models. However, prevailing approaches typically rely on monolithic latent dynamics, entangling environment dynamics into a coupled process. This coupling severely limits reusability: altering the agent necessitates retraining the entire world from scratch, even if the environment remains constant. To address this, we introduce BRICKS-WM (Building Reusability via Interface Composition Kinetics for Structured World Models), a framework for the modular assembly of structured world models. Driven by the insight that the physical world is composed of independent entities, we posit that global dynamics can be modeled as a composition of distinct dynamical modules interacting via latent interfaces. As a minimal instantiation, we factorize the latent state space into an actuated Agent module and an external Background module, bridged by a learned latent interface. Unlike prior object-centric methods that prioritize visual segmentation, BRICKS-WM enforces a functional separation in transition dynamics, ensuring that background dynamics remains agnostic to the agent's dynamics. Empirically, BRICKS-WM achieves control performance comparable to strong monolithic baselines when trained from scratch, and enables the reuse of frozen background dynamics across agents.