世界模型

We study how to predict the downstream closed-loop performance of a learned latent world model from validation-time diagnostics alone. Choosing the right checkpoint from a world-model training run is difficult: validation loss and multi-step prediction RMSE keep improving long after closed-loop performance has collapsed. We present a suite of structural validation-time diagnostics drawn from optimal-control theory and apply them to Gymnasium's LunarLander v3, which features shaped rewards. We train an RSSM [5, 4] world model on it and treat per checkpoint CEM-MPC return as the oracle for closed-loop quality. By evaluating 40 metrics against this oracle, we find that the strongest single predictor is the Reward Observability Fraction (ROF), which measures the reward predictor's dependence on the observable subspace. We combine ROF with three structural regularizers into a single-number offline checkpoint selection score, the Composite Reward Observability Fraction (CROF). The CROF-selected world model trains a model-based A2C policy that beats a fairly evaluated model-free A2C baseline by ~24.5 return points while using ~65x fewer real-environment interactions, and the same world model also drives a strong zero-shot CEM-MPC policy. Code and data: https://github.com/nsmoly/LunarLander_RSSM.

Radio Environment Maps (REMs) have the potential to serve as an important enabler for intelligent modeling and control in emerging AI-native 6G networks. Despite significant progress, most REM construction methods remain passive, relying on interpolation or static uncertainty models and lacking an explicit mechanism to reason about how future measurements will affect reconstruction quality under a limited measurement budget. In this paper, we formulate REM construction as a sequential decision-making problem and propose a world-model-inspired framework for active Received Signal Strength Indicator (RSSI) map reconstruction. By learning an internal representation of the radio environment and employing a dreaming mechanism to simulate the impact of candidate measurements, the proposed approach actively selects measurement locations under a limited budget. Experimental results on real indoor RSSI data demonstrate that the proposed method significantly outperforms Gaussian Process-based interpolation in the few-shot regime, achieving up to a fivefold reduction in Root Mean Square Error (RMSE) with the same number of measurements. These results highlight the potential of world models as a powerful paradigm for sample-efficient radio environment mapping and intelligent model-based sensing in 6G and beyond networks.

World models have recently re-emerged as a central paradigm for embodied intelligence, robotics, autonomous driving, and model-based reinforcement learning. However, current world model research is often dominated by three partially separated routes: 2D video-generative models that emphasize visual future synthesis, 3D scene-centric models that emphasize spatial reconstruction, and JEPA-like latent models that emphasize abstract predictive representations. While each route has made important progress, they still struggle to provide physically reliable, action-controllable, and long-horizon stable predictions for embodied decision making. In this paper, we argue that the bottleneck of world models is no longer only whether they can generate realistic futures, but whether those futures are physically meaningful and useful for action. We propose \emph{Hamiltonian World Models} as a physically grounded perspective on world modeling. The key idea is to encode observations into a structured latent phase space, evolve the latent state through Hamiltonian-inspired dynamics with control, dissipation, and residual terms, decode the predicted trajectory into future observations, and use the resulting rollouts for planning. We discuss how Hamiltonian structure may improve interpretability, data efficiency, and long-horizon stability, while also noting practical challenges in real-world robotic scenes involving friction, contact, non-conservative forces, and deformable objects.

Decision-time planning with action-conditioned world models has become a popular paradigm for embodied control. However, the standard planning cost judges a candidate solely by how close its predicted terminal state lies to the goal, leaving the realizability of the intermediate transitions unchecked -- a predicted trajectory can look convincing while the environment rollout drifts away from it. In this paper, we propose ACID, a decision-time planning framework that introduces cycle action consistency: the action inferred backward from a predicted transition by an inverse dynamics model should recover the one that was conditioned on. We fold this per-step residual into the planning cost via a scale-invariant adaptive weight. Across four action-conditioned world models and six tasks spanning rigid and deformable manipulation, articulated control, and visual navigation, ACID consistently improves planning and matches the baseline's accuracy with substantially less planning compute.

World models are increasingly used in embodied intelligence and generative simulation, yet their scope remains ambiguous across communities. This tutorial presents a design-space view of world models as action-conditioned predictive models that estimate the future evolution of task-relevant observations or states. We categorize existing methods into observation-space and state-space world models, comparing their trade-offs in visual fidelity, spatial structure, physical interpretability, and control usability. We further introduce world action models, which connect predicted futures with executable robot actions, and summarize four representative paradigms: imagine-then-execute, video-feature-conditioned action prediction, joint video-action modeling, and auxiliary video prediction for policy learning. The goal of this tutorial is to clarify the conceptual scope of world (action) models and provide a structured taxonomy for embodied prediction and control.

Despite rapid progress in interactive world models (IWMs), existing benchmarks evaluate action following only at trajectory level and ignore memory and interaction physics. We introduce WorldOdysseyBench, an open-world benchmark for long-horizon stability across four dimensions, each with tailored innovations: (i) Action: per-frame action metric bypassing cross-model semantic scale disparity and exposing failures hidden by trajectory; (ii) Vision: segment-based drift metric capturing non-monotonic mid-sequence collapse missed by start-vs-end comparisons; (iii) Physics: controllability-gated evaluation over mechanics, optics, and 3D consistency, scoring plausibility under faithful action execution; (iv) Memory: action-decoupled protocol evaluating scene memory via transition-localized 3D point-cloud reconstruction and subject memory via tracking-plus-VLM reasoning. The benchmark comprises 600+ test cases across Nature, Urban, and Indoor scenes in first/third-person views with WASD 10-60s continuous interaction. Evaluating 10+ open/closed-source models reveals none reliably satisfies all dimensions; even the best achieves only moderate scores. Advances on WorldOdysseyBench are steps toward IWMs that are stable, physically grounded, memory-faithful, and deployable in real-world applications.

We ask a representation-learning question about physical world models: when does a conservation law remain certifiable after a model learns a latent representation? A certified horizon bounds -- in advance, from measurable model defects -- how many steps a rollout provably stays on a physical invariant's level set. The key design choice is what is certified: not a learned latent Hamiltonian or a learned scalar witness (a model can conserve either while drifting in true energy), but the decoded physical invariant obtained by decoding the latent state and evaluating the known invariant. Around this object we derive shell-horizon certificates whose budget decomposes into representation, readout, and latent-dynamics defects, with a monotone alignment bridge through which a soft learned witness yields a certified horizon for the decoded invariant, and test them across state, learned-lift, and pixel observations on conservative systems. Conservation certificates can survive learned representation, but not all geometric priors survive equally. Hard canonical symplectic structure yields the longest horizons in known phase coordinates yet does not cross a learned chart, whereas a controlled-Lipschitz-aligned soft invariant survives in the nonlinear learned-representation settings we test -- two lift systems, with the gain growing with nonlinearity, and pixels. Pixel certification is recovered on a readout-stable sub-tube, and the Kepler problem exposes a geometric boundary. The central object is therefore not a latent Hamiltonian, but a decoded physical invariant whose robustness to representation learning can be measured, certified, and falsified.

Scale buys interpolation; structure buys certifiable transfer. A world model's average error does not say whether a particular rollout can be trusted, or for how long. For equivariant latent world models we give a predictability certificate: a computable region spanning configuration, horizon, and resolution. Under exact equivariance, rollout error is invariant over the monoid generated by k primitive symmetries and is certified from the k generators (Theorem A); universal orbit-flatness over equivariant targets characterizes equivariance at the function level (Lemma 2), so an unconstrained architecture cannot certify the property by construction. Approximate orbit-transfer defects propagate by the finite-time Lyapunov spectrum (Theorem B): expanding channels give a logarithmic horizon $T_j(ε)\sim\log(1/ε)/λ_j$, neutral channels accumulate recurrent defect linearly, and contracting channels accumulate a bounded nonzero floor. Exact conserved charge values are certified to all horizons only at zero defect; with one-step defect $η$, charge-value error grows at most as $Tη$. Empirically, on a 40-dimensional learned model a $\mathbb{Z}_N$-equivariant network recovers the full Lyapunov spectrum ($R^2=0.98$-$0.99$) where dense and recurrent baselines fail. A cone/adapted-metric certificate reads an a-priori horizon off the model's own Jacobian, tight on uniformly hyperbolic dynamics and self-abstaining elsewhere; the resulting horizon improves a budgeted re-observation decision. For public non-equivariant world models the tangent spectrum gives a training-free candidate horizon, paired with a held-out divergence cross-check that abstains or corrects when the learned loop over-promises.

Certified world models estimate how long their predictions remain valid. We turn this validity horizon into an operational sensing clock: a rule for when an agent should stop coasting and re-sense. Starting from an audited equivariant world model, we derive a deadline for no-sensing intervals and show that deployable deadlines in learned world models must be drift-aware: on-manifold Lyapunov rates alone overestimate coasting validity, while calibrated native rollout-drift envelopes carry the deployed guarantee. On a frozen 3D VN-JEPA model, the resulting clock controls held-out interval-simultaneous certificate violation across seeds and data shards. In a cue-conditioned theorem-bed (a synthetic bench where all schedulers share the exact model, isolating the scheduling rule), the clock remains valid on the deployment distribution and substantially reduces eventful-tail violations relative to exact-mixture expected-belief scheduling at matched sensing budget. We also report limits: in the short-horizon frozen VN-JEPA regime, empirical conformal horizons match the deployed clock on validity and budget, and a partial-reset exploration finds no clean budget-matched advantage for the spectral term. Thus the contribution is a certified sensing-clock primitive and drift-aware deployment method, not a claim that spectral clocks empirically dominate all non-spectral schedulers.

World models for language agents come in two useful forms. An agent-based world model calls an LLM API and reasons flexibly in language, but its errors appear as hallucinated state changes that are hard to score with ordinary regression losses. A parameterized world model is a trained transition predictor; its errors are easier to measure with quantities such as NodeMSE, delta accuracy, and validity accuracy, but it is usually weaker as a standalone planner. We compare these two families on four graph-structured planning benchmarks and introduce operational hallucination metrics for the agent-based case. The comparison motivates Grounded Iterative Language Planning(GILP), which trains only a small parameterized backbone and combines it with API-based agent reasoning. The backbone supplies valid actions, predicted state deltas, risk, and value; the LLM drafts an action and imagined delta; and a consistency gate asks for revision when the two disagree. On real GPT-4o-mini calls, GILP reduces hallucinated-state rate from 0.176 to 0.035. In calibrated simulator ablations, it raises success from 0.668 to 0.838 while adding only ~22% extra LLM calls.

Attention enables a world model to condition on its entire history, providing long-term memory that facilitates long-range predictions. While the local Onsager--Machlup theory in our companion paper assumes a temporally local predictive action, we investigate the conditions under which this locality holds. We derive the predictive path measure for latent dynamics that become non-Markovian due to attention-induced memory, demonstrating that this measure is the projection of a hidden linear Markov augmentation. Eliminating the auxiliary field results in a nonlocal Onsager--Machlup action, where memory manifests as a nonlocal quadratic form rather than a force. These kernels are completely monotone and exactly match a hidden Markov embedding with a finite relaxation spectrum; otherwise, the dynamics remain fundamentally nonlocal. By expanding the action in terms of the scale-separation parameter $ε=τ_{\text{mem}}/τ_{\text{dyn}}$, we show that the leading order recovers the local action of the companion paper, establishing locality as the short-memory limit of a nonlocal theory. We verify the reversible sector of this expansion term by term against an exactly solvable vector linear model.

Reinforcement learning (RL) can overcome the demonstration-coverage limitation of imitation learning (IL) by allowing robots to improve through trial-and-error interaction beyond the states observed in demonstrations. However, deploying RL on real robots remains constrained by high interaction costs, since each physical rollout is costly and reflects only one realized action-outcome path. To address this challenge, we propose WorldSample, a physically grounded data augmentation framework for real-robot RL that closes a real-synthetic loop between physical rollouts, world-model generation, and policy improvement. Grounded on real rollouts, WorldSample generates high-fidelity synthetic transitions through a post-trained world model, which greatly lowers the visual hallucination. Specifically, rather than simply using these transitions as real-world experience, WorldSample introduces Policy-Paced Learning (PPL) to regulate the training process through sample selection and scheduling, balancing useful augmentation against value overestimation and mitigating the hallucination-induced noise. Experiments on robot manipulation tasks involving contact-rich and precise tasks show that WorldSample improves policy success rate by 28% while reducing training steps by 59% compared with baselines. Furthermore, WorldSample improves world model visual fidelity by 19.4dB in PSNR and 0.47 in SSIM over demonstration-only post-training, validating the effectiveness of the real-synthetic loop for both policy and world model performance.

Learning how an environment behaves from interaction is central to building agents that adapt to unfamiliar tasks. World models learned with deep networks are flexible but data-hungry and transfer poorly beyond their training distribution. Program-synthesized world models, written as source code by LLMs and refined through counterexample-guided inductive synthesis (CEGIS), are instead data-efficient and reusable, yet they have been demonstrated mainly on structured-state worlds with a given object vocabulary, and a single program search does not scale to pixel-rendered environments whose object structure must be hypothesized flexibly. We introduce OPINE-World, an LLM agent that learns an object-centric programmatic world model online from interaction. OPINE-World couples two cooperating agents in a loop of hypothesis and test, one acting in the environment and one synthesizing the model in code with replay verification and model-based planning, and it steers exploration with a Bayesian measure of object-type adequacy we call ontology error. We evaluate OPINE-World on ARC-AGI-3, a benchmark for skill-acquisition efficiency in which the object vocabulary, the goal, and the action semantics are withheld. OPINE-World solves 20 of 25 games without per-game training and reaches an action-efficiency score of 78.4 against the human baseline.

The key challenge in articulated 3D object generation from a single image is accurately predicting the underlying kinematic structure. Existing methods either infer kinematic parameters directly from a static image that lacks dynamic part-level kinematic relationships, or estimate parameters from visual dynamics generated from a single image, which is prone to accumulated errors of two steps. Moreover, the limited scale and diversity of existing annotated datasets further hinder generalization to complex, real-world objects. To overcome these limitations, we propose to learn the joint distribution of visual dynamics and kinematic parameters. Recognizing that articulated objects can be formulated as dynamic systems, we propose a unified Part World Model called PWM-ArtGen. To leverage unannotated data, this model couples action diffusion and image diffusion with independent diffusion timesteps, which enables visual branch co-training. We further curate a photorealistic dataset of 19.7k part-level image pairs without kinematic annotations, to support co-training. Experiments demonstrate that PWM-ArtGen substantially outperforms existing baselines in the resting state and exhibits strong zero-shot generalization to out-of-distribution objects.

As agent planning moves from short tool chains toward persistent workflows with thousands or tens of thousands of steps, failures will occur inside large planning graphs rather than in isolated predictions. Replanning the entire graph after every mistake is neither computationally realistic nor desirable: full-graph replay consumes large context budgets, exposes the LLM to many irrelevant symptoms, and can degrade long-context retrieval. This paper studies the missing component in such systems: a world-model corrector that repairs the failed planning graph in place. We compare two families of correctors. The first is the common engineering approach: scan nodes and edges, choose a suspicious local region, and ask an LLM to repair it. We implement strong engineering LLM correctors and find that they can help, especially when given very large contexts. The second family is our approach, WM-SAR (World-Model Subgraph Amplification Repair): instead of scanning for visible symptoms, it works backward from subgraph amplification, identifies the nodes and edges that keep re-amplifying error, and sends only that causal subgraph to the LLM. Across graph simulations and LLM repair experiments, WM-SAR substantially outperforms engineering correctors under realistic token budgets, achieves near-whole-graph stabilization with a compact region, and gives the LLM a cleaner repair target.

As the scale and complexity of cloud-based AI systems continue to escalate, ensuring service reliability through rapid fault detection and adaptive recovery has become a critical challenge. While existing approaches integrate Large Language Models (LLMs) for semantic understanding and Deep Reinforcement Learning (DRL) for policy optimization, they often rely on sequential, loosely coupled architectures that underutilize the generative and reasoning capabilities of LLMs. In this paper, we propose a paradigm shift with PASE, a Planning-Aware Semantic self-healing engine, a novel fault self-healing framework that reconceptualizes recovery as a neuro-symbolic program synthesis task. PASE employs an LLM as a core Plan Synthesis Engine to generate structured recovery plans from a library of semantic primitives. A Neural-Symbolic World Model verifies plan feasibility through simulation, while a Meta-Prompt Optimizer, trained via DRL, learns to generate optimal prompts that guide the LLM's planning process. This tight reason-plan-verify-adapt loop enables dynamic, context-aware recovery strategy generation beyond predefined action spaces. Experiments on a real-world cloud fault injection dataset demonstrate that PASE significantly outperforms state-of-the-art methods, reducing average system recovery time by over 40% and improving fault detection accuracy in unknown fault scenarios. Our framework advances autonomous system management by unifying LLM-based reasoning with model-assisted verification and meta-learned guidance.

We present WorldDirector, a highly controllable video world model framework designed for persistent dynamic object memory and unrestricted viewpoint exploration. Unlike existing world models that entangle physical dynamics with pixel rendering and rely on continuous visual observation to sustain motion, our framework explicitly decouples semantic motion orchestration from visual generation. By leveraging an LLM to coordinate 3D trajectories with camera movements and subsequently employing these orchestrated trajectories as control signals for video generation, our approach ensures strict physical logic and appearance stability, successfully preserving the exact visual identities of dynamic entities even when they re-enter the scene after prolonged periods out of view. Experimental results demonstrate that our method supports the synthesis of complex and extended events with unprecedented controllability and persistent dynamic object memory. Project Page: https://worlddirector.github.io/

End-to-end autonomous driving increasingly leverages self-supervised video pretraining to learn transferable planning representations. However, pretraining video world models for scene understanding has so far brought only limited improvements. This limitation is compounded by the inherent ambiguity of driving: each scene typically provides only a single human trajectory, making it difficult to learn multimodal behaviors. In this work, we propose Drive-JEPA, a framework that integrates Video Joint-Embedding Predictive Architecture (V-JEPA) with multimodal trajectory distillation for end-to-end driving. First, we adapt V-JEPA for end-to-end driving, pretraining a ViT encoder on large-scale driving videos to produce predictive representations aligned with trajectory planning. Second, we introduce a proposal-centric planner that distills diverse simulator-generated trajectories alongside human trajectories, with a momentum-aware selection mechanism to promote stable and safe behavior. When evaluated on NAVSIM, the V-JEPA representation combined with a simple transformer-based decoder outperforms prior methods by 3 PDMS in the perception-free setting. The complete Drive-JEPA framework achieves 93.3 PDMS on v1 and 87.8 EPDMS on v2, setting a new state-of-the-art.

Video generation models aspire to simulate dynamic environments, and several benchmarks now evaluate memory consistency across frames. However, most assess consistency only while the target remains in view, and the few that force objects out of view evaluate static scenes where nothing changes during occlusion. To bridge this gap, we introduce MemoBench, a diagnostic benchmark built around the disappear-and-reappear paradigm in dynamically changing environments: a target object undergoes a physical process, disappears from view, and must be correctly recovered in its updated state upon reappearance. We curate 360 ground-truth clips spanning synthetic and real-world scenes, and design an evaluation suite combining automated metrics with VQA-based assessment across four diagnostic pillars. Evaluation of eight state-of-the-art models reveals key insights and open challenges regarding memory consistency under the disappear-and-reappear paradigm.

Recent advances in agentic AI are producing increasingly complex autonomous systems that integrate large language models, world models, optimization engines, specialized neural architectures, autonomous platforms, and human operators. While much current research focuses on improving reasoning capabilities, safety-critical real-time deployment also requires bounded and verifiable coordination among heterogeneous components operating concurrently under uncertainty. Software-mediated coordination presents fundamental limitations in domains where bounded latency, deterministic coordination, and enforceable safety guarantees are essential. Hence, we propose a hardware-enforced semantic coordination architecture in which selected coordination semantics are implemented directly at the hardware level via field-programmable gate arrays (FPGAs). The approach builds on the Topic-Based Communication Space Petri Net (TB-CSPN) framework, which separates semantic reasoning from interaction management. In this approach, selected TB-CSPN coordination mechanisms are mapped onto FPGA primitives, creating a hardware-native semantic coordination layer. Focus is not on acceleration, but on enforcing temporal synchronization, semantic gating, authorization constraints, and bounded coordination behavior directly in hardware. Semantic reasoning remains adaptive and software-driven, while embedded coordination semantics become deterministic.

How can Large Language Models (LLMs) solve problems they currently cannot? Repeated sampling scales test-time compute but GPU cost grows linearly with attempts, while reinforcement learning (RL) with verifiable rewards improves single-attempt accuracy at the expense of sample diversity. Both strategies ultimately fail when the base policy has near-zero probability of producing a correct solution: no amount of sampling or gradient signal can overcome a search space that is simply too large. We take a different approach: rather than sampling harder, we make the task easier by decomposing problems into smaller, independently solvable sub-functions whose implementations can be recombined. Since off-the-shelf models are not trained for this modular generation, we introduce DecompRL, an RL algorithm that explicitly learns to decompose and implement hierarchical code structures. Recombining $k$ implementations of $n$ modules yields up to $k^{n}$ candidate solutions, shifting the bottleneck from GPU inference to cheap CPU evaluation and cutting GPU token cost by $\sim$50$\times$. On LiveCodeBench and CodeContests (Qwen~2.5~7B, Code World Model~32B), DecompRL outperforms standard and diversity-optimized RL baselines beyond $10^5$ tokens per problem, solving problems that standard generation cannot reach.

General-purpose vision-language-action models benefit from large vision-language priors, but effective manipulation also requires anticipating action-relevant scene changes. Existing world-action models often rely on large generative world models or dense future rollouts, which are expensive and spend capacity on visual details weakly coupled to control. We present Bridge-WA, a lightweight world-action framework that distills a frozen future-change teacher into three compact priors: future tokens for intended outcomes, change maps for intervention support, and motion-flow maps for local transition direction. A WorldBridge conditions the action transformer on these priors through multi-source attention memories and spatial-temporal biases, while the teacher model is removed at inference. Across VLABench, RoboTwin2.0, LIBERO-Plus and real-robot evaluations, Bridge-WA improves task success, progress, and robustness, with particularly clear gains under out-of-distribution visual shifts. By focusing action generation on where and how the scene will change, Bridge-WA suppresses nuisance appearance factors such as background, lighting, and distractors, leading to better generalization without deployment-time dense future-image generation. Code and visualizations are available at: https://hcplab-sysu.github.io/BRIDGE-WA .

Large Language Models (LLMs) in multi-agent systems (MAS) have shown promise for complex tasks, yet current training methods lack principled ways to connect system-level evaluation with agent- and message-level learning. We propose a theoretical framework that unifies cooperative game-theoretic attribution with process reward modeling to transform system evaluation to agent credit to response-level signals. Unlike prior approaches that rely only on attribution (Shapley) or step-level labels (PRM), our method produces local, signed, and credit-conserving signals. In success cases, Shapley-based credit assignment fairly allocates outcomes across agents and is refined into per-message rewards that promote cooperation while discouraging redundancy or sabotage; in failure cases, first-error localization yields repair-aware preferences that penalize harmful steps while rewarding corrective attempts. The resulting signals are bounded, cooperative, and directly compatible with reinforcement- or preference-based post-training, providing a unified and auditable pathway from global evaluation to local supervision in LLM multi-agent training. Our contribution is conceptual: we present a theoretical foundation and training signals, leaving empirical validation for future work.

Video-based embodied world models provide an appealing substrate for robotic manipulation by predicting future states, yet current approaches remain limited by a fundamental entanglement: accurately modeling dynamics typically requires low-level temporal reasoning, while producing high-resolution frames demands expansive visual synthesis according to high-level semantics. This entanglement results in slow inference speed for iterative planning or too coarse predictions to retain contact-rich details. To solve this dilemma, we present Disentangled Video Generation World Model (DVG-WM), an efficient framework that explicitly decomposes world modeling into dynamics learning and visual synthesis. Conditioned on an initial observation and a language instruction, our model first generates a plausible sequence of intermediate visual states to preview the physical interaction and refines them to obtain high-fidelity videos. Furthermore, an efficient cascading mechanism is proposed, where DVG-WM uses flow matching to directly map the dynamics to video latents, and introduces a latent degradation mechanism to regenerate contact-rich details. Experiments on LIBERO and real-world platforms demonstrate improved video quality with up to 3.97 times acceleration, validating that disentangled video generation can be an efficient embodied world model for robotic manipulation.

Manipulating fast and dynamically moving targets in unstructured 3D environments remains challenging for embodied AI. Existing visual-language-action models and world models struggle with accurate 3D geometry and physically meaningful forecasting. We propose PhysMani, a framework that couples a physics-principled 3D Gaussian world model with a future-aware action policy model. The world model learns a divergence-free Gaussian velocity field via online optimization for fast and physically grounded future dynamics prediction. The policy model integrates the predicted 3D scene future dynamics through a learnable token based cross-attention module. We introduce PhysMani-Bench, a dynamic manipulation benchmark with 16 tasks, and demonstrate a superior success rate over strong baselines in both simulation and real-world robot experiments.

A latent world model built from an equivariant encoder and predictor inherits a provable symmetry of its training loss: when the dynamics carries a group $G$ acting on latents by an orthogonal representation $ρ(g)$, the one-step prediction relMSE is exactly invariant across the whole group, so fitting a restricted slice of orientations mathematically determines it on the entire orbit. The symmetry survives a real Muon/AdamW+EMA+VICReg run -- composed residual $\sim 10^{-6}$ after training, under any optimiser (intrinsic Vector-Neuron/e3nn parametrisation) -- and one-step error is flat across the group (5-seed medians: equivariant $\times 1.00$ vs a higher-capacity non-equivariant baseline $\times 12.7$ in 2D, $\times 17.2$ in 3D), while that baseline fits the slice but breaks out-of-distribution. The flatness is not a synthetic artefact: on real-robot DROID end-effector trajectories the equivariant model stays flat across the orbit ($\times 1.000$, rotation residual $1.5\times 10^{-16}$) while a $4.5\times$-larger baseline degrades $\times 11$. One caution is load-bearing: flatness is necessary, not sufficient -- the theorem transports the in-distribution error level unchanged but does not lower it (3D relMSE $\approx 0.43$): across-group error is constant, not low. The same isometry lifts to a closed-loop corollary: under a matching equivariant planner the control error is invariant across the group -- float-floor-exact in 2D/SO(2), statistically flat in 3D/SE(3). Stress-tested against Sutton's Bitter Lesson (augmentation, scale, soft-equivariance), each closes at most the across-group task metric, never the float-floor exactness. This is the generalisation-side foundation of a certified-world-models programme (arXiv:2606.13092, 2606.24945, 2606.24946): flatness transports competence, and the trust bounds built on it are downstream products.

Multivariate time-series models for prognostics are often evaluated by point prediction accuracy, yet their internal states rarely expose a coherent degradation process. We study liquid neural networks as latent dynamics models for aircraft engine health monitoring on the C-MAPSS benchmark. The proposed model encodes a history window into a latent state, evolves that state with a liquid transition model, and decodes future sensor observations. To separate health evolution from operating-condition variation, the latent state is factorized into degradation and condition components. Remaining useful life, monotonic risk, and latent-consistency losses supervise the degradation component, while condition prediction and decorrelation losses discourage operating-condition leakage. Across FD001--FD004, the full disentangled model improves overall sensor forecasting RMSE from 0.2438 for a GRU baseline to 0.2266, with the largest gains on the multi-condition subsets FD002 and FD004. The learned degradation state also forms a clearer temporal degradation axis, reaching an average state-speed Spearman correlation of 0.5960. Direct remaining-useful-life regression remains stronger for the GRU baseline, indicating that the proposed representation is currently more effective as an interpretable world model for degradation dynamics than as a calibrated lifetime regressor. These results suggest that liquid latent dynamics can bridge predictive maintenance forecasting and inspectable health-state modeling.

Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable. The problem becomes even more severe when the model must also predict beyond the training time range. Existing methods usually cannot handle parameter generalization and temporal extrapolation at the same time. Standard parameterized models treat time as just another input and therefore fail to capture intrinsic dynamics, while recent continuous-time latent methods often rely on expensive test-time auto-decoding for each instance, which is inefficient and can disrupt continuity across the parameterized solution space. To address this, we propose Disentangled Latent Dynamics Manifold Fusion (DLDMF), a physics-informed framework that explicitly separates space, time, and parameters. Instead of unstable auto-decoding, DLDMF maps PDE parameters directly to a continuous latent embedding through a feed-forward network. This embedding initializes and conditions a latent state whose evolution is governed by a parameter-conditioned Neural ODE. We further introduce a dynamic manifold fusion mechanism that uses a shared decoder to combine spatial coordinates, parameter embeddings, and time-evolving latent states to reconstruct the corresponding spatiotemporal solution. By modeling prediction as latent dynamic evolution rather than static coordinate fitting, DLDMF reduces interference between parameter variation and temporal evolution while preserving a smooth and coherent solution manifold. As a result, it performs well on unseen parameter settings and in long-term temporal extrapolation. Experiments on several benchmark problems show that DLDMF consistently outperforms state-of-the-art baselines in accuracy, parameter generalization, and extrapolation robustness.

Semi-supervised imitation learning (SSIL) consists in learning a policy from a small dataset of action-labeled trajectories and a much larger dataset of action-free trajectories. Some SSIL methods learn an inverse dynamics model (IDM) to predict the action from the current state and the next state. An IDM can act as a policy when paired with a video model (VM-IDM) or as a label generator to perform behavior cloning on action-free data (IDM labeling). In this work, we first show that VM-IDM and IDM labeling learn the same policy in a limit case, which we call the IDM-based policy. We then argue that the previously observed advantage of IDM-based policies over behavior cloning is due to the superior sample efficiency of IDM learning, which we attribute to two causes: (i) the ground-truth IDM tends to be contained in a lower complexity hypothesis class relative to the expert policy, and (ii) the ground-truth IDM is often less stochastic than the expert policy. We argue these claims based on insights from statistical learning theory and novel experiments, including a study of IDM-based policies using recent architectures for unified video-action prediction (UVA). Motivated by these insights, we finally propose an improved version of the existing LAPO algorithm for latent action policy learning. We experiment on the Procgen, Push-T and LIBERO benchmarks.