Publication Radar.

AI agents increasingly act as analysts whose decision can often be cast as hypothesis tests. Classical tests control the Type I error rate, the probability of rejecting a true null hypothesis, for fixed procedures. However, AI analysts introduce internal randomness and can evolve continuously over time. As AI analysts evolve, the risk of approving versions with Type I error rates above the target can accumulate, and adaptive use of evaluation feedback can lead to overfitting. We introduce continual validation, which evaluates each proposed AI analyst version before deployment using simulated data under the null hypothesis, with scenarios that can be randomized and expanded over time. We prove that, regardless of how updates are chosen or how many are proposed, the lifetime probability of ever deploying a version whose Type I error rate exceeds the allowed level remains bounded. This guarantees that every subsequent decision controls the Type I error rate at the target level across these scenarios. At the same time, updates with sufficiently low Type I error rates pass validation with high probability, allowing the analyst to continuously improve its performance without sacrificing rigor. In two examples involving evolving AI analysts for bioequivalence studies and product A/B tests, Type I error rates reached 0.098 and 0.183 without continual validation, compared with at most 0.045 and 0.044 with it, while retaining 82% and 96% of the power from optimally selected valid updates.

Deep neural networks often struggle to provide reliable confidence estimates, making post-hoc calibration essential for reliable decision-making. Existing post-hoc methods largely rely on score-based transformations, which improve marginal calibration but often fail to capture spatially varying miscalibration in local regions of the learned feature space. To address this gap, we propose Local Adaptive Probability Estimation (LAPE), a post-hoc residual calibration framework. Specifically, LAPE treats the global calibrator output as a stable anchor and refines the individual prediction by leveraging non-parametric local evidence from neighboring calibration samples. As a plug-and-play refinement module, LAPE effectively utilizes the information about feature-space geometry and can reuse the calibration data that are used to construct the global calibrator. Furthermore, we extend LAPE to the setting with multi-view inputs through Cascade Feature Augmentation Fusion (CFAF). Extensive experiments demonstrate that the proposed methods can improve the calibration quality of various existing baselines and remain efficient and robust across different settings.

Social world models predict how interactions develop after an action, helping agents negotiate, cooperate and mediate. In these situations, one action can lead to several plausible futures, hence predicting only one future can overlook consequential alternatives, while exploring them through repeated simulations increases inference cost. We propose DSWM, a Distributional Social World Model that predicts alternative responses, their probabilities and immediate and final outcome values in one output per candidate action. We train a 4B model on repeated simulations using supervised fine-tuning and GRPO. At inference time, the actor uses these possible consequences to choose an action. Across three seen and two unseen environments, with interaction backbones absent from training collection, DSWM achieves the best average performance on 13 of 15 metrics. Ablations show that retaining multiple futures and their predicted probabilities improves outcomes in all five environments.

Recent advances in text-to-video generation have substantially improved visual fidelity, yet existing models still struggle to understand the physical evolution implicit in user prompts, making it difficult to generate videos with continuous physical state evolution. Here, we propose PhyEvolve, a multi-agent framework that enhances natural-language prompts through structured state-evolution planning. PhyEvolve consists of three agents: a Director, a Physical Evolver, and a Composer. Given a user prompt and an optional first frame, the Director grounds the scene and disentangles physical events from observation changes. The Physical Evolver uses scene evidence to identify physical mechanisms then constructs causally linked state transitions that unfold throughout the video, whether visible or not. The Composer utilizes these transitions to enhance the original prompts. Without retraining or model modification, PhyEvolve works directly with existing generators through prompt replacement. Extensive experiments on four major benchmarks show that PhyEvolve achieves state-of-the-art performance, outperforming the cutting-edge prior agentic baseline by 7.9 percentage points on average. These results demonstrate that explicit causal state-evolution planning improves physical consistency and state continuity in generated videos through natural-language prompt enhancement.

Video provides a natural source of supervision: what happens next serves as a learning signal for visual world modeling. Yet masked video pretraining focuses on recovering missing content from surrounding context rather than predicting the future from the past. Autoregressive methods instead predict forward one token at a time, but have yet to match joint-embedding methods in representation quality. This gap motivates us to revisit the granularity and space of future prediction. In this work, we introduce VANE, a self-supervised visual pretraining framework built on next-frame prediction in embedding space. A causal encoder summarizes past observations for a state predictor that infers the representation of the entire next frame, making temporal evolution the primary learning signal. This prediction is carried out in a fixed embedding space provided by a frozen semantic tokenizer, emphasizing scene content and structure. To retain fine-grained spatial detail alongside semantic content, a lightweight auxiliary generative decoder reconstructs future-frame patches conditioned on the predicted representations. To unify visual modeling across images and videos, we construct a local-to-global crop sequence for still images, allowing the same encoder to predict newly revealed regions from earlier crops under the same objective. Experiments show that VANE improves with model and data scaling, achieving SOTA on most anticipation, recognition, and dense perception benchmarks among unified encoders. Especially on EPIC-KITCHENS-100 action anticipation, it surpasses V-JEPA 2.1 by 7.1 points in mean-class recall@5. These results demonstrate that next-frame prediction in embedding space is effective and scalable for visual world modeling.

Recent work established that the infinite-width and infinite-depth limits of residual networks commute at initialization when residual branches are scaled by $1/\sqrt{depth}$. In particular, the network output converges to the same limit whether width and depth tend to infinity sequentially or jointly. We extend this commutativity result to training in linear residual networks. Under the same $1/\sqrt{depth}$ residual-branch scaling (Depth-$μ$P) and the $μ$P width parameterization, we prove that, for any fixed number of gradient-descent steps with gradient clipping, the network output converges in $L^2$ along every joint width--depth growth path as both width and depth tend to infinity. Consequently, the infinite-width and infinite-depth limits commute throughout any finite training horizon. Without gradient clipping, the corresponding $L^2$ convergence does not hold in general, but we establish the weaker convergence in probability.

Before acting on an object, a robot needs to anticipate how its hand motion will change the physical world and what the resulting scene will look like. Existing approaches typically entangle action-conditioned dynamics, camera motion, and visual synthesis within a video generation model, or represent dynamics as point trajectories without explicit object structure. We introduce DeXplicit, a dexterous manipulation world model that instead predicts how the world evolves explicitly in metric 3D before rendering its visual consequences. Given an initial scene and a future hand trajectory, a lightweight 3D dynamics network predicts object-centric motion and deformation, providing structured and geometrically grounded future world states. These predictions then serve as a strong scaffold for video generation: appearance is transported through the predicted 3D motion and projected into future views, allowing the renderer to focus on completing uncertain and newly visible content rather than implicitly learning world dynamics from pixels. This explicit-3D-first decomposition also enables efficient causal generation, requiring only two denoising steps per block while conditioning on generated history. Across HOT3D, OakInk2, and PhysTwin, DeXplicit reduces moved-point error by 27-40% relative to PointWorld and improves object fidelity IoU+ by 47% on HOT3D under a shared renderer. Our design with two-step causal generation achieves a 57x speedup from our 14B bi-directional configuration in video synthesis.

World models have recently emerged as a promising direction toward developing generalist agents capable of understanding, predicting, and interacting with diverse environments. However, despite growing interest, the concept of a world model remains loosely defined, encompassing approaches ranging from predictive dynamics models and learned simulators to models that jointly generate future observations and actions. This introductory paper aims to clarify the concept of world models and provide a unified perspective on their role in developing generalist agents. Starting from the partially observable Markov decision process (POMDP) framework, we connect world modeling to classical control, dynamical systems, signal processing, and reinforcement learning. We introduce different approaches to world modeling, emphasizing the knowledge they capture, their learning objectives, and how they support decision-making. We further explore the relationship between world modeling and policy learning, highlighting how these capabilities can be unified through conditional prediction without requiring separate models. Rather than offering an exhaustive survey of existing methods, this paper focuses on fundamental concepts, modeling principles, and connections, with the goal of providing an accessible and unified introduction to world models for generalist agents.

Loco-manipulation extends the workspace of conventional manipulation by combining mobility with physical interaction, while aerial loco-manipulation further expands this capability into three-dimensional space, enabling robots to reach environments inaccessible to ground-based systems. Moving to an aerial platform, however, gives rise to a demanding control problem, since the vehicle must track trajectories accurately in three dimensions while the motion of the arm and its interaction with the environment continuously shift the center of mass, alter the inertia, and impose force and moment disturbances on the body. Conventional controllers address these effects through explicit models and estimation, whereas learning-based controllers infer dynamics from experience, yet control rewards provide no direct target for the response information retained from history, and fixed task sampling can leave persistent tracking difficulties insufficiently explored. We present ALMA, an aerial loco-manipulation framework for adaptive flight control under external arm commands. ALMA employs a contextual flight policy that adapts from recent measurements and actions, using action-conditioned prediction of future measurement representations to train its context to retain response information relevant to flight control. To expand the experience available for this adaptation, an evolutionary process uses a large language model (LLM) to analyze observed control difficulties and propose new structures of arm motion for subsequent training. In simulation, ALMA reduces position root-mean-square error (RMSE) by up to 24.7% relative to the strongest baseline, while the same policy transfers zero-shot to the aerial manipulator and reduces hover position RMSE by 79.6% during periodic arm motion relative to the real-world baseline.

World models are increasingly used to reduce environment interaction when post-training vision-language-action (VLA) policies with reinforcement learning. Yet they are typically trained to predict pixels one step ahead, even though their role here is not merely to render visually faithful videos but to produce learning signals from imagined rollouts that improve the policy. We show that this mismatch is substantial: lower pixel MSE can produce worse policy gradients, and a world model trained for policy utility can yield better downstream policies despite 17% higher pixel MSE on the next frame. We propose the Downstream-Return Imagination Learning Loop (DRILL), a bilevel framework that updates the world model to maximize the policy's return after an inner GRPO update on imagined rollouts. DRILL has two instantiations. DRILL-VWI is a closed-form surrogate, requiring no additional simulator rollouts, that reweights prediction errors by policy visitation, the group-relative GRPO advantage, and model confidence. DRILL-IMG is a full meta-gradient method that differentiates through the inner update using truncated Hessian-vector products. We show that DRILL-VWI recovers the local one-step component of the DRILL-IMG meta-gradient under score-compatibility and small-residual assumptions. Across five manipulation simulators and two VLA backbones, DRILL-IMG raises mean success rate by 13.1 points over WMPO and 7.9 points over RLVR-World, and complements RLVR pretraining rather than competing with it. More broadly, we believe video world models for VLA reinforcement learning can be productively trained by the policy gradients they produce, not only by pixel-level prediction.

Graphs play a crucial role in many applications, ranging from drug discovery to social network modeling and astronomy. Generative models for graphs have substantially advanced in recent years, but we identify relatively simple scenarios where state-of-the-art models struggle to converge within a standard compute budget, or exhibit prohibitively slow generation times. We propose a generative architecture that achieves quality competitive with state-of-the-art models and is orders of magnitude faster at generation. Our approach is inspired by the Aldous-Hoover theorem, a classic representation theorem that characterizes any probability distribution of graphs that is invariant to permutations of node indices or exchangeable. This theorem establishes that three ingredients suffice: a graph-level latent variable, a set of exchangeable node-specific latent variables, and a so-called graphon function that maps graph- and node-level variables to the probability of an edge between any node pair. Given a training set of graphs, our exchangeable Variational Graph AutoEncoder (xVGAE) learns an approximation to their underlying graphons, as well as graph- and node-level latent variables. We show that our xVGAE encodes latent representations that correlate with graph- and node-level properties, and can (quickly, in one shot) generate new graphs that closely match key training set statistics.

Deep Gaussian processes (DGPs) are appealing Bayesian regression models, but their standard discrete-depth parameterization often becomes harder to optimize as depth grows. We argue that depth is better treated as a latent continuous evolution than as a long discrete stack. We therefore propose a continuous-depth formulation in which the latent representation follows a stochastic differential equation with a depth-indexed drift family equipped with a GP-based prior. This reframes the core design choice as the prior placed on that family, rather than adopting a purely neural continuous-depth parameterization as in neural ODE or neural SDE models. We study two instantiations of this idea: CDGP, a direct GP prior over the state--depth drift, and FlowDGP, a flow-evolved prior that captures richer depth dependence at lower training cost. To motivate the redesign, we analyze how the single-sample DGP objective can become increasingly sensitive under repeated layer composition, while residual DGP is a useful first repair that still remains a finite discrete construction. We also give pathwise sensitivity analysis for the continuous-depth formulation. Experiments on synthetic, benchmark, and large-scale regression tasks show that residual DGP improves over plain DGP, while CDGP and FlowDGP provide a stronger overall story across the regimes we study.

Random projections (RP) offer an effective method for reducing computational and storage overhead while preserving the geometric structure of data. However, existing studies have primarily focused on the optimal generalization performance of specific kernel-regularized algorithms with RP in the well-specified setting and under restrictive conditions. In this paper, we provide a comprehensive and improved analysis of the generalization performance of RP-based spectral algorithms under general conditions \change{without sacrificing statistical efficiency}. By leveraging the embedding property of the reproducing kernel Hilbert space (RKHS) and a refined analysis of the operator similarity, we establish optimal learning rates in Sobolev norms that match the minimax lower bounds up to logarithmic factors. For two common implementations of RP, randomized sketches and Nyström sub-sampling (uniform or leverage-based), we show that the projection dimension required for optimality is proportional to the average or maximal effective dimension, yielding a significant reduction in computational cost while maintaining the statistical efficiency. Our results do not rely on the uniform boundedness assumption on the regression function and are valid across a wide range of source conditions, i.e., $s> α_0-1/β$, where $s,β$, and $α_0$ denote the smoothness index, capacity index, and the embedding index, respectively. In the benign case when $α_0=1/β$, the optimality holds for all $s\in (0,2τ]$ with $τ$ and $γ$ denoting the qualification index and norm index. Experimental results demonstrate both the theoretical validity and the practical effectiveness of the proposed method.

Robust manipulation of soft objects, such as garments, is a critical skill for service and household robots to adopt, but remains challenging due to its high-dimensional state space, and material-dependent deformations. Humans address this challenge by using mental world models that "imagine" the shape and material properties from partial observations, which enables them to predict how actions affect future states. As such, embedding such world models in robots allows for better generalization in manipulating a wide variety of garments in the real world. However, learned world models typically require large amounts of real world data that is strenuous to collect, and a mechanism to infer latent properties that govern dynamics. We present a Soft-Object World Model that performs generative full-state estimation and action-conditioned dynamics prediction using a transformer backbone trained on large-scale simulated soft object interactions, with measures to mitigate the sim-to-real gap. By learning to infer latent shape and material cues through in-context learning over a variable-length partial point-cloud history, the model generalizes across robot embodiments, material parameters, garment types and shapes, and manipulation coordination modes without weight updates. The world model is then integrated with a Goal-Conditioned action planner for motion synthesis. We validate the approach in simulation and real world for bimanual garment folding, reporting improvements in reconstruction fidelity, prediction accuracy, and task success.

Robot demonstrations record what the robot saw and what it did. They do not specify how the 3D world changed in between. Scene-level 3D flow describes it by tracking 3D scene points, providing the world representation with 4D geometry. Prior work has used flow to improve robot policies. Flow served as an intermediate prediction that a separate model converts into actions, as a prior injected at inference time, or as an extra output learned together with the action. In all of these designs, flow stays outside the policy, as a separate module or as an extra prediction head. We introduce UniFlowWAM, a Unified World-Action Model that makes 3D scene flow a third modality on par with vision and action. Its world representation therefore covers both visual semantics, through future visual features, and 4D geometry, through 3D flow, and flow receives its own supervision. UniFlowWAM is a diffusion transformer with one expert per modality, and the three experts exchange information through joint attention. We train UniFlowWAM under a ten-objective role grid, where each objective assigns every modality exactly one of three roles, namely target, condition, or absent. The same model thus serves as a policy, as forward and inverse dynamics, and as a predictor of future visual features or 3D flow. We evaluate UniFlowWAM on RoboCasa-GR1, LIBERO, and LIBERO-Plus in simulation, and on four real-world bimanual manipulation tasks. On RoboCasa-GR1, UniFlowWAM raises the success rate of its base model without flow from 52.1% to 56.4%. It preserves in-distribution success on LIBERO at 98.1% and reaches 87.7% zero-shot on LIBERO-Plus. On the real robot, it achieves 87.0% average success, compared with 68.5% for the strongest baseline.

Decision support has become sophisticated at exploring uncertainty, but much less so at representing the architecture of the decision itself. As a result, the decision space is often narrowed before uncertainty is analyzed, leaving interactions among choices and the effects of alternatives they imply largely invisible. This paper introduces multichoice modeling, a framework for making large decision configuration spaces explicit and computationally explorable under uncertainty. Drawing on the logic of rugged landscapes, we conceptualize such problems as contingent performance landscapes, where interdependent choices generate configuration-specific outcomes whose value changes across uncertain futures. The computational framework combines multidimensional decision and uncertainty spaces in a single simulation. Further, variance-based sensitivity analysis is used for identifying influential choices, and conditional distribution analysis for comparing configuration-specific performance profiles. We demonstrate the framework through three case studies: a manufacturing process upgrade, M&A strategy, and mortgage design. By contrasting conventional uncertainty-only analysis with multichoice modeling, the cases show how opening the decision configuration space can reveal unexpected complementarities, near-best configurations with different risk profiles, and strategies that were not apparent as alternatives at the outset.

World Models (WMs) can support Multimodal Agents (MAs) through simulated experience, while Agent trajectories can inform World Model refinement. Evaluating this interaction requires separate evidence about action selection and state evolution. We introduce Dual Exam, which tests Agents under fixed environment response mechanisms and World Models under fixed action interventions across physical, digital, social, and scientific domains. The Agent track compares 10 configurations on 1,088 items in 15 reporting categories. The World Model track contains 400 cases across eight scenarios; 15 configurations have full coverage and one covers six scenarios. GPT 6 Astra leads the case-weighted Agent Index at 31.3, and GPT-Image-2 leads the full-coverage WM Overall at 21.7. These scores use different tasks and metrics and are not directly comparable. A 150-case pilot of one coupled pairing records zero task successes and motivates component-level diagnosis. Results reveal uneven task performance and failures to preserve task-relevant state. Their value for predicting coupled success or sustained reciprocal learning remains to be established.

Modern transformers often solve complex tasks by generating and refining intermediate reasoning steps. To develop a theoretical understanding of chain-of-thought (CoT) reasoning, a notable recent study by Huang et al. (2025) viewed transformers as algorithm executors, and showed that when transformers' CoT steps are supervised by a gradient-descent teacher, they can learn to implement gradient descent for in-context weight prediction in linear regression. In this paper, we study the same in-context weight prediction task but ask whether CoT reasoning can go beyond merely imitating the teacher algorithm. We show that, after initial supervision from a gradient-descent teacher, further trajectory-level supervision using the true regression weights leads the model to implement the Heavy-Ball method, thereby achieving acceleration over the original teacher. Notably, this accelerated algorithm emerges without supervision from any Heavy-Ball teacher. Our results provide a concrete theoretical example in which transformer reasoning can discover new algorithms through training, rather than merely imitate the algorithm used for supervision.

In real-world applications, being able to explain why a prediction is made is often as important - if not more so - than achieving high accuracy. However, existing methods for sequential event prediction typically prioritize accuracy at the expense of interpretability. Neuro-symbolic approaches offer a promising direction to improve interpretability by learning symbolic rules, but extending them to next-event prediction is challenging due to the presence of temporal dependencies. We introduce RULES, a neuro-symbolic model that learns sequential rules directly from data, and combine it with a residual network to form RUNES (Rule Network for Event Sequences). RULES accurately recovers ground truth rules from synthetic data and discovers compact, interpretable rule sets on real data. RUNES combines these rules additively with a residual network, achieving competitive accuracy while providing transparent access to active rules and how residuals adjust predictions.

Computer-model calibration is usually undertaken in service of prediction, yet neither Bayesian Kennedy-O'Hagan (KOH) calibration nor amortized simulation-based inference is built to control the predictive error of the calibrated simulator. When parameters are weakly identified or the data-model discrepancy is misspecified, the simulator-output bands induced by a nominal posterior level can be far from nominal. We propose a two-layer framework that targets predictive miscoverage directly. First, a conditional flow-matching model learns an amortized posterior for the calibration parameters, trained on simulator outputs perturbed with Gaussian-process discrepancies of varying structure. Second, conformal risk control arranges posterior draws for the target observation into nested candidate sets and selects the smallest one whose fixed-rank pointwise bands attain a prescribed time-averaged miscoverage on a synthetic calibration sample. Under exchangeability of calibration and target observations, the bands control expected miscoverage in finite samples. In a synthetic benchmark, the proposed bands are roughly 20% the width of KOH-MCMC bands with miscoverage near the 10% target. In calibrating an age-structured SEIR model to the 2010 Malawi measles outbreak, they are again sharper and near-nominal, and the weeks they fail to cover coincide with the asymmetric epidemic decline, exposing structural inadequacy of the mechanistic model.

Joint-embedding predictive architectures (JEPAs) learn world models in latent space, enabling efficient planning but leaving their states opaque. We introduce Inside-JEPA, which places relational channels for ordered entity pairs inside the JEPA latent state and shows that an inverse-dynamics loss can ground these channels without relation labels when its head reads them, either alone or as part of the full state. On Something-Something V2, latent prediction alone performs no better than a random relation head, while inverse-dynamics supervision that recovers actions from channel changes improves relational AUROC by .065-.103 across ten settings with annotated boxes, by .081 on RH20T robot episodes with held-out tasks, and by .050-.061 across five relations using off-the-shelf detection and tracking. An inverse head on entity latents decodes actions more accurately but barely improves relational grounding; shuffled labels, two label-free objectives, and action labels on only 5% of the pairs also fail to ground the channels. Given an action, predicted relational changes approach the quality of observed future relations (AUROC .599 vs .621). For one-step relational goals, a supervised readout of the 16 channels ranks the correct action among the top five of 65 in 43% of cases, compared with 24% for prediction-only latents and 17% for a frequency prior.

Risk prediction models are frequently evaluated with AUC, which means that during evaluation we are blind to performance heterogeneity, which could lead to bad decision-making in clinics. In this work, we aim to change that by identifying patient cohorts for whom the risk prediction model might not be an accurate predictor. To separate these cohorts, we use a version of the weighted AUC, which we call Localized AUC or LAUC. Using this metric, we build a method that we coin LOCATOR. This method is able to identify cohorts of patients for whom the risk prediction model is inaccurate. We test this method both in real-world data and in simulations. We also build a statistical background for the use of Localized AUC for our purposes.

Real robot data, rich across tasks and morphologies, is often treated as the bottleneck for training robot learning models, including embodied foundation models that aim for zero-shot physical transfer. In this paper, we investigate the degree to which such models can acquire necessary structure using data from systems without embodiment. To this end, we test if inexpensive, procedurally generated synthetic data can yield useful priors before a model observes any real-world behavior. We study this through robot action prediction, a natural pretraining objective and a direct test of whether structure learned from arbitrary synthetic tasks transfers to embodied settings. We introduce three data generation pipelines that model mathematical abstractions of robotic control, and use them as pretraining priors for a Transformer. We demonstrate that a model trained purely on this non-robotic data attains non-trivial zero-shot prediction performance on unseen physical robot tasks via an in-context learning mechanism, and that our specialized control priors notably improve upon generic causal priors. We also compare against a compute-matched baseline trained on real robot data, and find that it outperforms our model but only on the datasets it was trained on. These findings suggest that procedurally generated, mathematical abstractions can yield useful robotic priors, offering a potential complement to expensive embodied data collection.

Deep learning (DL) methods have substantially improved predictive performance across a wide range of downstream prediction tasks, enabling new discoveries in multiple domains. However, principled DL methods for non-Euclidean random objects remain relatively scarce, despite the growing importance of modern biomedical outcomes taking the form of probability distributions, random graphs, functions, and other random objects in metric spaces. Motivated by a new generation of digital and clinical biomarkers, we propose a deep learning framework for regression with random objects in metric spaces. Our approach operates directly on the metric structure of the response space, avoiding restrictive manifold or Euclidean embedding assumptions imposed by many existing methods. At the same time, it retains modern statistical guarantees under the stated statistical assumptions. We establish statistical consistency and convergence rates for the proposed estimator, and characterize conditions under which it can mitigate the curse of dimensionality for hierarchically compositional regression functions. Extensive simulation studies demonstrate competitive predictive performance, with gains over several competing approaches in multiple Euclidean and non-Euclidean configurations. Finally, we demonstrate the practical utility of the proposed framework in two digital health case studies with distribution-valued outcomes in Wasserstein spaces, using high-resolution accelerometry and continuous glucose monitoring data. Embedding-based deep-learning methods may be less suitable when no informative low-dimensional representation exists or when the learned embedding does not adequately preserve the intrinsic geometry of the response space.

We introduce the conditional expected local radius (CELR) and develop a new conformal prediction method for non-Euclidean responses in general metric spaces. CELR measures local conditional probability concentration, allowing prediction sets to accommodate heterogeneity and multimodality without requiring densities or a vector space structure. Its conditional distribution yields a nonconformity score that is comparable across covariate values and avoids costly transport comparisons between distance profiles. We further adapt a metric distributional random forest that handles multivariate covariates and nonlinear interactions, while a single forest fit supplies all score components, reducing computation by eliminating repeated local fitting. We establish uniform consistency of the estimators and asymptotic conditional validity under suitable regularity conditions, together with finite-sample marginal coverage under exchangeability. Numerical studies demonstrate effective uncertainty quantification across different metric spaces and substantial computational savings over the conditional profile score method.

World action models increasingly rely on pretrained video models assumed to capture physical dynamics for prediction, planning, and action generation. Existing evaluations assess plausibility, probe representations, or measure predictive surprise, but rarely identify which history-conditioned physical expectations conflict with observations. We introduce PhysTrace, a training-free framework aligning MLLM-generated, history-conditioned expectations with observed video windows to temporally localize physical violations and provide interpretable descriptions without task-specific probes or classifiers. We also introduce IntPhys2-Timing, adding violation intervals to IntPhys2. PhysTrace achieves a Hit Rate of up to 70.7% across physical principles on IntPhys2-Timing and outperforms the compared methods in overall possible-impossible discrimination accuracy on IntPhys2. Applied to reconstructed videos along the trajectories of pretrained diffusion/flow-based video models, PhysTrace reveals attribute- and noise-dependent patterns in physical violation localization, enabling interpretable physical consistency analysis across timesteps.

The Unadjusted Langevin Algorithm (ULA) is widely used for high-dimensional Bayesian inference. Classical analyses in Wasserstein-2 distance predict an asymptotic bias and a mixing time that grow with dimension, but this metric is stronger than necessary for many statistical tasks. We instead analyze the bias in subspace robust Wasserstein distance, which controls the mean and arbitrary low-dimensional marginals and is therefore well suited to observables typically estimated in practice. For ridge-separable potentials formed with i.i.d. data, we prove high-probability bounds showing a bell-shaped mixing profile as the number of data points $N$ varies relative to the dimension $d$. In the overparameterized regime, the effective dimension is the rank $N$ of the data-dependent perturbation, leading to complexity depending on $N$ rather than $d$. In the large-sample regime, Gaussian-perturbation estimates yield dimension-free complexity once $N$ is sufficiently large. In contrast, near the proportional regime $\asymp d$, we prove that dimension-free guarantees are impossible in general.

Robot world models simulate how environments evolve in response to robot actions. Latent action models enable learning dynamics from videos by encoding visual transitions as proxy actions. However, reconstruction-driven latent actions mix robot motion with object responses and other scene changes, complicating their correspondence with robot controls. We propose SkeLAM, a skeleton-guided latent action model for controllable robot world modeling. SkeLAM decomposes latent actions into a kinematic component grounded by robot skeleton supervision and a residual component retaining complementary visual dynamics. Cross-modal swap reconstruction encourages RGB-derived and skeleton-derived kinematic representations to be interchangeable during video reconstruction. The world model incorporates both components through separate conditioning pathways, while branch dropout reduces its dependence on future-derived residual information. A lightweight adapter maps robot actions to the kinematic space, and subsequent world-model fine-tuning adapts generation to these predicted conditions. At inference, the model generates future observations from the current observation and robot actions. On DROID, SkeLAM reduces end-effector ADE by 19.5% and LPIPS by 11.1% compared with DreamDojo. Motion probing supports kinematic specialization, while qualitative results demonstrate zero-shot human-to-robot motion transfer in generated rollouts. Policy evaluation shows agreement between predicted success rates and those measured in real robot executions.

Vision-language models (VLMs) can perform a broad range of tasks across diverse settings, yet their performance in agentic contexts remains poorly understood. Although online evaluations in simulators and real-world environments are essential for measuring interactive agent performance, they are costly and challenging to scale. Complementary offline VQA benchmarks can enable faster and more reliable comparisons across agentic domains, yet existing benchmarks remain limited and fragmented. To address this gap, we introduce AgentVQA, an offline benchmark for evaluating VLMs on realistic agentic scenarios across five agent domains: Web Agents, Robotics, Egocentric Videos, Games, and Spatial Planning. We build AgentVQA by manually selecting 1000 challenging, real-world agent examples from 23 source datasets and adapting them for reliable offline evaluation. The resulting benchmark preserves realistic scenarios from interactive environments across diverse domains, and its model rankings track those from corresponding online evaluations. Across the 22 evaluated models, the best achieves only 58.5% accuracy. Our cross-domain analysis shows that errors are driven primarily by failures to ground and maintain accurate representations of the current and evolving visual state, including localizing relevant UI elements, interpreting motion, tracking state changes over time, and inferring 3D spatial relationships, rather than by task misinterpretation or downstream logical reasoning.

Complex objects such as engineering designs and proteins are often difficult to optimise because their design spaces exhibit high-dimensional structure and objective evaluations are expensive. Generative models provide continuous latent representations, but their latent spaces can have thousands to tens of thousands of dimensions, creating a regime where the latent dimension $D$ greatly exceeds the evaluation budget. We introduce SABLE, a Bayesian optimisation method for high-dimensional latent spaces with an isotropic distribution and limited budget. SABLE uses a Bayesian affine surrogate for prediction and acquisition, treating higher-order structure as surrogate discrepancy. After $N$ observations, the slope update has dimension at most $N-1$, yielding a decomposition of each query into an in-span component optimised by expected improvement (EI) in at most $N$ dimensions and an off-span component governed by a scalar norm. We show that the off-span norm implicitly selected by affine EI can lead to underexploration, and SABLE instead prescribes it using a finite-horizon schedule, without restricting search to a learned subspace. A recompression scheme reduces information to $\mathcal O(M)$ pseudo-observations, bounding refitting cost by $\mathcal O(M^2D+M^3)$ while keeping parameter inference, prediction, and acquisition decisions to tens of milliseconds. Across synthetic benchmarks and latent-space optimisation tasks, SABLE achieves high sample efficiency and reduces decision time by several orders of magnitude at large budgets.

Nonparametric estimation of joint probability distributions is a core problem in statistics, which is notoriously challenging with high-dimensional data. Such challenges also arise with conditional distribution estimation and have led to flexible algorithms that aim to tackle the ''curse of dimensionality'' by exploiting predictive structures of lower dimension than the ambient space. In this paper, we study the use of such conditional distribution estimators to estimate joint distributions by factorizing the latter in an ''autoregressive'' way. We show that for loss functions satisfying a subadditivity property, bounds on the convergence rate of an autoregressive estimator can be derived from bounds on the convergence rate of the conditional distribution estimators. These bounds relate the difficulty of estimating the joint distribution to that of estimating the most challenging factor in the autoregressive factorization. When the conditional estimators adapt to sparsity in their conditioning sets, we characterize this difficulty through variable elimination in an undirected dependence graph. This allows bounding the rates of convergence by quantities related to the sparsity of the graph, and provides an additional motivation for the autoregressive approach. We then evaluate the practical performance of an autoregressive estimator based on parallel gradient boosting, a flexible nonparametric method for estimating conditional distributions. The estimator demonstrates competitive estimation performance on various simulated and real datasets, even without optimizing the factorization order. Together, these results support nonparametric autoregressive estimation as a practical approach to flexible joint distribution estimation.

\emph{Continuous-space} attacks find prompts that trigger malicious behaviors, such as overthinking, in black-box LLMs by sampling or optimizing over a low-dimensional Gaussian latent space and decoding it to text through a \emph{random mapping} and nearest-token lookup. Because the random mapping is not learned from language, its prompts can be highly unnatural, and as such easily detectable through input guardrails, and the risk estimates they yield are not grounded in natural prompts. In this paper, we demonstrate that the same continuous latent-space framework can be coupled directly to a learned generative distribution over language, a continuous diffusion language model (dLLM), which removes the artificial random mapping while preserving the standard-Gaussian latent formulation and the downstream sampling or optimization procedure. We evaluate this approach under two settings: sampling-based estimation using \emph{RareTrap} and optimization-based search using \emph{ThinkTrap}. We find that character-level perplexity drops from $10^3$--$10^7$ to 3--5 in RareTrap and from 20--28 to 4.3--5.4 in ThinkTrap. We also find that model risk estimates can differ by an order of magnitude across the two mappings.

Online Policy Distillation (OPD) often outperforms offline methods such as Supervised Fine-Tuning (SFT) by training on trajectories sampled directly from the student. However, standard OPD trains the student to follow the teacher at every state of the trajectory, assuming that teacher guidance is always beneficial. We instead distinguish between what the teacher prefers and what actually helps the current student succeed. We introduce Advantage-Based On-Policy Distillation (AOPD), which weights teacher actions by their counterfactual advantage under the student. Teacher actions that improve the student's expected outcome are reinforced, while those that do not are downweighted. Directly computing these advantages requires trying alternative teacher actions at each step and running new rollouts from each. Instead, we show that the AOPD objective can be estimated using only standard student rollouts and their terminal rewards. Our estimator uses teacher importance weights on the student-sampled actions to provide unbiased advantage-weighted supervision, without any additional rollouts or reward evaluations. This allows AOPD to focus teacher supervision on actions that help the current student while preserving the rollout efficiency of standard OPD. Experiments on math, coding, and Medqa show gains over distillation and RL baselines in both external-teacher and self-distillation settings.

The attention mechanism underpins modern large language models, yet their dynamics remain only partially understood. Recent perspectives interpret attention blocks as interacting particle systems, whose mean-field limits correspond to gradient flows of energy functionals on spaces of probability densities on $\mathbb R^d$ equipped with Wasserstein-type metrics. We extend this viewpoint by deriving accelerated attention blocks from inertial, Nesterov-type damped Hamiltonian dynamics on these density spaces, developing the geometry and differential calculus needed to make the construction rigorous. In particular, we introduce a local-mobility geometry for the Otto-Wasserstein and softmax-Wasserstein settings, and a quotient Stein geometry that resolves the degeneracy of the linear-attention kernel to yield a well-defined metric and differential calculus. We provide rigorous foundations when softmax attention admits a gradient-flow formulation and when its inertial counterpart admits a damped Hamiltonian on explicitly characterized domains. For linear attention, we obtain a finite-dimensional solution theory with sharp conditions for global existence versus finite-time second-moment blow-up. We further prove a quantitative link between continuous moment blow-up and the discrete-layer depth at which token norms cross a prescribed threshold. Finally, motivated by the finite-token geometry, we propose geometric corrections to token and momentum updates. In decoder-only, nanoGPT-style experiments on TinyStories and OpenWebText, these corrections lower validation negative log-likelihood on next-token prediction relative to momentum-only controls.

Tasks such as quadrotor dynamic-gate racing require agents to anticipate external motion while maintaining precise high-frequency control. World-model-based reinforcement learning provides a natural solution by learning latent dynamics for future imagination, yet it often entangles environmental evolution and the robot's own dynamics in a single learned rollout, where model bias can affect policy optimization efficiency. We propose DiffDreamer, a differentiable reinforcement learning framework that tightly couples a learned world model with differentiable simulation for actor optimization. In one optimization step, the learned world model propagates latent states that capture external dynamics and history-dependent features, while the differentiable simulator propagates the robot's explicit physical state. We further decompose the actor objective into a critic-driven pathway for non-differentiable task rewards and a simulator-driven pathway for differentiable motion rewards. Experiments on aggressive tracking and dynamic-gate racing show that DiffDreamer improves training convergence over the model-free, model-based, and differentiable-RL baselines, and final performance over these baselines and classical planning and control methods. Additional experiments assess reward decomposition and the odometry-conditioned relative-state representation through ablations. We also provide proof-of-concept real-world flight experiments for validation.

We consider online monitoring of an AI system that produces a sequence of decisions. At each round, the system outputs a proposed decision together with a confidence score estimating the trustworthiness of the decision. The decision and confidence score need not be produced by the same model: for example, one agent may propose a decision, while a separate verifier agent evaluates it and outputs a correctness or safety score. Based on this information, we must decide whether to accept the AI decision automatically or consult an expert, such as a human auditor, who reviews the proposal and either accepts or corrects it. We formulate this task as an online constrained optimization problem in which the goal is to minimize the frequency of expert auditing while guaranteeing that the fraction of AI errors that go unaudited stays below a user-defined threshold. We derive a family of algorithms with provable error-control guarantees with no assumptions, including a method that is optimally efficient: it asymptotically attains the best achievable auditing rate for both adversarial and i.i.d. data streams. Experiments on screening harmful requests to large language models, qualitative text annotation, and data labeling show that our methods achieve valid error control in practice while substantially reducing the need for human auditing compared to baselines.

Constructing accurate and computationally tractable approximation spaces is a fundamental task in scientific computing. Partially trainable neural networks bridge fixed random features and fully adaptive representations. This paper quantifies a phase transition pattern in approximation bounds and observes analogous behavior in training errors: a rapid but smooth initial improvement followed by diminishing returns, with a sharper transition under greater initialization mismatch. Under polynomial spectral decay with exponent $α>1$ and leverage compatibility, we establish a squared $L_2$ approximation rate $\mathcal{O}((κ_P\log(m/δ)/m)^α)$ for two-layer networks of width $m$ and trainable proportion $P$, where $κ_P=(P/κ_1^*+(1-P)/κ_0^*)^{-1}$. The bound holds uniformly over the unit ball of a reproducing kernel Hilbert space (RKHS) with probability at least $1-δ$. The constants $κ_0^*$ and $κ_1^*$ quantify the fixed and trainable groups' sampling mismatches relative to the target RKHS. For spherical biased-ReLU features in dimension $d$, we verify these assumptions with $α=(d+2)/(d-1)$ and $κ_0^*=4\sqrt{2}τ(d+1)/d$ for initialization scale $τ\ge1$, and $κ_1^*=1$ under ridge leverage sampling. For $d=5$ and $τ=10$, a trainable proportion of approximately $4.1\%$ captures $90\%$ of the reduction in the approximation bound from $P=0$ to $P=1$. A structured three-layer example illustrates how a few trainable first-layer neurons exploit fixed downstream blocks through nonlinear composition. Numerical experiments across diverse settings, including networks with up to 15 layers, exhibit similar phase transitions in training errors.

Video foundation models have advanced rapidly in understanding and generating visual sequences, while video world models seek to capture the underlying dynamics of the world they depict. Despite their different objectives, both concern the relationship between video observations and an evolving world. This survey adopts world modeling as a unifying lens for examining these developments. Viewing an observed video as a partial, lossy, and temporally ordered projection of a latent temporal world, we organize the literature around four complementary operations: reading infers world properties from observed video; writing synthesizes video from specified or learned world conditions; sharing integrates understanding and generation through common modeling mechanisms; and interacting predicts and updates world states under actions and evolving observations. This perspective distinguishes temporal coherence in observed or generated sequences from consistency in the underlying world state. Across tasks, representations, models, datasets, and benchmarks, we trace a shift in emphasis from clip-level recognition and perceptual fidelity toward persistent state, controllable evolution, physical and causal validity, and evaluation grounded in interaction and downstream decisions, and we distill the open challenges that follow.

Robotic foundation models are typically evaluated through costly closed-loop rollouts, which motivates cheap offline proxies for model capability. The Platonic Representation Hypothesis (PRH) suggests that as representations improve, different modalities such as vision and language converge toward a shared statistical model of reality. We ask whether motion trajectories form another such modality: as embodied models become more capable, should their sensory representations converge toward the structure of physical motion? To examine this, we propose Sensorimotor Alignment ($S^2$), a training-free offline metric that measures how well a model's sensory representation aligns with the geometry of physical motion. We find that $S^2$ correlates positively with downstream robot task success across embodied model families, making it a low-cost offline proxy for prioritizing models before closed-loop evaluation. $S^2$ can also identify promising vision-language model (VLM) backbones even before costly fine-tuning into vision-language-action models (VLAs). Beyond this correlation, $S^2$ offers representation-level explanations for phenomena observed in VLAs and world action models (WAMs). With $S^2$, we extend PRH to embodied models and make sensorimotor alignment empirically measurable, offering insight into why an embodied model succeeds beyond its closed-loop success rate.

We study a jump-modified Wasserstein gradient flow of the squared maximum mean discrepancy generated by the energy kernels $K(z)=-|z|^q$, $0<q<2$, in every dimension $d\ge2$ as well as the one-dimensional range $1\le q<2$. Under subcritical density and finite-moment assumptions, we prove global well-posedness. The added jumps transfer mass toward smaller values of the first variation and dissipate the same MMD energy as the transport term. Under our hypotheses on the target and jump rates, every Borel probability measure with finite MMD energy and zero jump dissipation is equal to the target. Combining this rigidity with compactness and a second-moment identity yields convergence to the target from finite-second-moment data, without additional uniform-in-time density or moment assumptions. We also construct a global collision-free particle process whose energy is nonincreasing along each path. A quantitative mean-field estimate applies to general initial empirical approximations, including deterministic configurations; propagation of chaos for exchangeable data and long-time target approximation follow as consequences.

Amodal video segmentation asks for the complete mask of an object in every frame, including the parts hidden behind other objects. The best current methods generate these masks with fine-tuned video diffusion models, which need many denoising steps and an extra depth network, and give a different answer for every sample. Self-supervised video world models of the JEPA family are trained on a closely related task: predicting the representation of masked space-time regions from the visible ones. We therefore treat occlusion as masking. The tokens that the object's visible mask does not cover are dropped, the pre-trained V-JEPA 2.1 predictor fills them in, and a light head decodes the observed and predicted features into amodal masks. The resulting model, OccJEPA (Occlusion-as-masking JEPA), is deterministic and 33.5x faster than the diffusion-based state of the art, and more accurate on SAIL-VOS, on TAO-Amodal, including a held-out test split (+4.00 AP50) and visible masks tracked by SAM2, and on Kubric. Controlled experiments trace the gain to the predictor's pre-trained weights rather than to its capacity, for world models from 87M to 1.85B parameters. Code is available at https://github.com/zgp110/occjepa.

Reward guidance methods sample an exponential tilt of a base density using a diffusion model trained with only samples from the base distribution. Existing methods use what we call external guidance: additive terms in the drift or multiplicative terms on the transition probabilities. We propose internal guidance which leaves the output of the base denoiser unmodified and instead changes the point at which it is evaluated. For discrete distributions embedded in the hypercube $\{-1,1\}^{d}$, the denoiser of any linearly tilted density is exactly the base denoiser evaluated at a shifted and rescaled input. In practice the base denoiser is a neural network trained on noised samples of the base distribution. The required evaluation points for sampling the tilted density would be out-of-distribution for basic noising of the base distribution. We modify the training algorithm with random diagonal rescalings of the data, so that the denoiser network learns both in- and out-of-distribution evaluations of the denoiser relative to the base distribution. A single denoiser network samples binary reward tilts, class labels, and infilling with no fine-tuning and no external guidance term.

World models predict how embodied systems evolve under actions, but their accuracy can degrade when physical conditions move outside the training distribution. We study two components of causal modeling: which inputs a predictor may use, and how its mechanism computes their effects. In a synthetic benchmark with shortcut features, a frozen dependency mask derived from paired interventions reduces mean out-of-distribution (OOD) RMSE from 1.769 for a fully connected predictor to 0.697, close to the generator-oracle mask (0.694). For robot link-mass extrapolation in CausalWorld, with disjoint training and test mass ranges, we develop finger-local world models in which link masses enter inertia and dynamics-bias terms through explicit affine coefficients, actions act through either a learned torque network or the known PD controller, and learned residuals capture contact-related effects. Compared with a separately trained control whose mass inputs are fixed at training means, the known-PD model turns out-of-range masses into a consistent predictive gain: median time-averaged joint R2 over 150-step rollouts rises from 0.609 to 0.727, with improvement in all ten task-seed runs (exact two-sided sign test, p = 0.002). In a shared 100-step forecast, the learned-torque model is competitive with the strongest recurrent robotic world model (RWM) configuration (median joint R2 of 0.755 - 0.768 versus 0.752), whereas supplying out-of-range masses sharply degrades the MLP and recurrent predictors. These results indicate that how a physical parameter enters the dynamics mechanism determines whether its out-of-range value helps or harms prediction.

Individual patient data are the gold standard for secondary analysis of time-to-event evidence, but they are rarely released, and reconstruction from a published Kaplan-Meier figure could help. Existing methods all claim high fidelity, each judged by whichever agreements it happens to achieve, and each returns a single dataset although the map from figure to data is not bijective. We define fidelity explicitly: a dataset is admissible when it reproduces the risk table exactly, follows the digitized curve to within the image resolution, and respects the printed median, interval and event count. We propose StochIKM, a stochastic algorithm that digitizes the figure with a vision-capable language model and uses the high-fidelity definition as constraints, returning an admissible set of individual patient datasets. A solution is guaranteed to exist whenever the figure has been read correctly, so a failure indicts either the published figure or its digitization. In simulation and in 79 arms from published oncology trials, StochIKM reproduces the published risk tables and medians more closely than LLM-improved IPDfromKM, a high-impact alternative.

Frontier black-box Large Language Model (LLM) agents are proficient at long-horizon reasoning and precise action generation. However, when it comes to a specific agentic task, they have no internalized knowledge of how that particular environment unfolds. A world model offers a natural remedy, providing the agent with environment specific knowledge by foreseeing how the environment will respond to the action it is about to take. Prior world models for LLM agents mainly predict next observations at each step, which is costly and often uninformative because individual observations provide limited task-relevant guidance and not every step requires call for foresight. This raises a key question: what a world model should predict and when should it be invoked for agentic tasks? Our pilot study suggests that world model guidance is most useful when it anticipates pitfalls within a bounded multi-step future. Motivated by this, we introduce Pitfall Anticipation World Model (PAWM), which selectively intervenes when a potential pitfall arises and predicts the impending failure to steer the agent away from it. PAWM is trained in two stages: Supervised Fine-Tuning (SFT) on synthetic data labeled with agent pitfalls, followed by GRPO co-training with a black-box LLM to further optimize it in the target environment. PAWM improves Claude Sonnet 4.5 performance by 24.3% on ScienceWorld and 7.7% on WebArena-Lite, outperforming a range of baselines. These results demonstrate that PAWM provides an effective form of world model guidance for black-box LLM agents.

World action models (WAMs) are shown to substantially diverge under generalization performance based on their generative backbones. We investigate this gap through the representational geometry that WAMs inherit from their backbones and how policy training reorganizes it. Our central hypothesis is that a useful representational prior would structure geometry that separates nuisance information from the in-distribution manifold in advance of training as a policy. We quantify this with nuisance orthogonality; orthogonality of the feature under visual variation outside the empirical in-distribution manifold. Across various image and video backbones, we show that a higher orthogonality from the representational prior is associated with stronger robustness to visual variations after WAM training, enabling policy generalization measurable prospectively for world models. In addition, analyzing the resulting robust WAMs reveals nuisance suppression; relative suppression of feature displacement caused by such variations and robust action generation of the policy. Together, these findings provide a geometric perspective on how the representational prior of the world model shapes the generalization performance of WAMs.

Motivated by ten years of Learning-Based Control Invited Sessions at the IEEE Conference on Decision and Control (CDC), this tutorial paper reviews key advances at the intersection of machine learning and control. We focus on methods that combine the flexibility of machine learning techniques with the structure and theoretical foundations of control to design autonomous systems that are capable, reliable, and safe. We first introduce core notions for establishing stability and safety guarantees, then review approaches that learn dynamics models to improve control under uncertainty, and finally discuss data-driven methods that directly synthesize or learn policies, including reinforcement learning, imitation learning, and Bayesian optimization. We further discuss representative applications and open challenges. The goal is to provide an accessible entry point to the field and to support continued progress toward reliable learning-based control in real-world systems. To support learning and practical exploration, we share implementations and illustrative examples along with our discussion, together with additional resources on our website: https://learning-based-control.github.io/tutorial/.

Sharpness-Aware Minimization (SAM) has established itself as a widely used method for training deep neural networks. Despite its popularity, existing convergence guarantees for SAM-type methods require smoothness, a restrictive assumption. Generalized smoothness conditions have recently been proposed in the analysis of gradient methods but remain underexplored for SAM. To analyze the effect of SAM's perturbation under generalized smoothness, we use relative gradient distortion to quantify how the sharpness-aware direction departs from the original gradient. Under $(L_0,L_1)$-smoothness, we show that this distortion can become unbounded near stationarity for SAM and at large gradients for its unnormalized variant (USAM), with examples where SAM cycles and USAM diverges. We then establish a necessary condition for uniform distortion control among perturbations along the gradient whose nonnegative multipliers depend only on its norm. Motivated by this condition, we propose Curvature-Scaled SAM (CS-SAM), which scales both the perturbation and the descent step by suitable curvature upper bounds, and prove that it uniformly bounds the distortion. Under both $(L_0,L_1)$- and $(H_0,H_1)$-smoothness, we establish deterministic $\mathcal{O}(1/T)$ rates for the best squared gradient norm on nonconvex objectives, last-iterate $\mathcal{O}(1/T)$ rates for the function gap on convex objectives with a minimizer, and linear convergence under the Polyak-Lojasiewicz condition. With zero perturbation, our guarantees recover the rates for gradient descent with $(L_0,L_1)$- or $(H_0,H_1)$-based step-sizes. Minibatch experiments on computer vision tasks demonstrate competitive performance for both variants, with the $(H_0,H_1)$ variant achieving the highest mean best-test accuracy in all four settings against tuned SAM and USAM with constant and cosine annealing schedules.

Barycenter models, based on stochastic and deterministic optimal transport bridges between probability measures, have proven to be useful for supervised and unsupervised learning for (probability) measure-valued data. In this paper, we utilize the directional asymmetry and dual drift-diffusion control arising in the recently proposed Schrödinger-Bass Bridge (SBB) between two measures, and propose \textit{SBB-encoder}, \textit{SBB-decoder}, \textit{SBB-symmetric}, and \textit{SBB-Markovian} barycenter models. For each of these novel models, our first theoretical result establishes the existence of the SBB-barycenter under mild assumptions. Our second theoretical result characterizes the decoder SBB-barycenter of Gaussians where we show that for Gaussian input measures, the decoder formulation admits a Gaussian minimizer, reducing barycenter computation to a finite-dimensional optimization and yielding a compact algorithm. For general input measures, we derive a hybrid Wasserstein gradient particle descent scheme for all four formulations using the SBB dual representation. Finally, we utilize these algorithms for solving distributional-inverse/interpolation problems arising in the context of spatial images and single-cell RNA sequencing data, where we show that the SBB-decoder and Markovian barycenter allow us to interpolate between successive time points. Results show that our method outperforms existing barycenter models for measure interpolation and inference.

Thermal cameras enable robots to perceive human activities in darkness while revealing less personally identifiable appearance information and fewer details of the surrounding environment than RGB cameras. As vision-language models (VLMs), originally developed for RGB imagery, are increasingly integrated into embodied systems for scene understanding and high-level planning, thermal sensing offers a promising way to extend activity perception to low-light and privacy-sensitive settings. However, the failure modes of VLMs in thermal human activity understanding for human-robot interaction (HRI) remain underexplored. We fill this gap by evaluating seven locally deployable VLMs, including models developed for physical AI and robotics, on two person-centric thermal datasets. Our diagnostic tasks examine fine-grained action recognition, activity timeline reconstruction, and the ability to withhold unsupported answers. Paired RGB recordings serve as a performance reference, while controlled variations in frame sampling, thermal input presentation, and reasoning are used to assess whether the observed errors can be mitigated. Our results show that models can recognize broad activity categories but struggle with fine-grained actions such as coughing, sneezing, and yawning. They also produce inaccurate event timelines and hallucinate actions involving objects. Simple thermal input preprocessing and additional reasoning offer only limited, model-dependent gains. Abstention behavior also varies across models even under explicit instructions, limiting their reliability for practical robotic use.