Papers

State-of-the-art reinforcement learning agents are capable of outperforming human experts at games like chess, Go and StarCraft II. These agents do not simply take advantage of their digital hardware in being able to react and calculate faster than humans, but employ better strategies that lead to more victories. Interpreting these strategies would give human players valuable insight into how to improve their play. In this preliminary work, we propose a symbolic sub-policy model for playing chess. Inspired by chess tactics, our model attempts to incorporate domain knowledge to improve interpretability. We adapt patterns learned by an inductive logic programming system called PAL to derive our model. We contribute a divergence metric to evaluate our model against a random baseline, and find a set of tactics that is able to suggest moves of similar playing strength to a human beginner. Finally, we propose a computational evaluation scheme for the model by augmenting an off-the-shelf engine with it.

As part of learning to play complex games, human players develop develop abstractions for concepts and strategies of gameplay consistent with game rules to improve their performance. These concepts are applied to explain other players' actions, and to inform their own actions in-game. Understanding other players' strategies is a crucial part of such improvement, but requires time and effort. In this paper, we propose a strategy similar to human cognition for training RL agents to synthesize learned strategies and policies as executable procedures based on sequences of gameplay actions. We present methods to automatically learn such programs to play chess and to solve tasks in a grid-based environment. We show that the learned strategies produce effective actions, and can be learned from gameplay data.

Many real-world datasets exhibit unusually large values far more frequently than predicted by Gaussian models. Heavy-tailed distributions capture this behavior, yet evaluating learning performance under them remains challenging because rare, large feature entries retain non-vanishing effects even in high dimensions. Even in the canonical setting of empirical risk minimization for linear regression with entry-wise i.i.d. symmetric $\alpha$-stable data, a precise asymptotic characterization of prediction has been lacking. In this work, we introduce a functional order parameter that describes the random effective problem associated with each coefficient. Using the replica method, we fully characterize the generalization error in the proportional high-dimensional limit where the sample size and feature dimension diverge at a fixed ratio. Additionally, this analysis establishes a heavy-tail universality law, scaling laws relating typical errors to prediction reliability, and the Bayes-optimal prediction error. In addition to characterizing the effects of extreme entries on the learning process, our method applies broadly to other systems with persistent local heterogeneity.

Out-of-distribution (OOD) generalization remains challenging for graph neural networks (GNNs), as graph distributions can vary substantially across time and domains. Supervised and self-supervised graph representation learning are guided by distinct objectives and offer different perspectives on graph representations. In this work, we study whether self-supervised representations (SSL) can provide complementary signals to improve supervised OOD node classification. We develop two backbone-agnostic frameworks that exploit such information at different stages of learning and prediction. Co-Train jointly learns supervised and SSL representations and adaptively integrates them during training, while Dual-Space Retrieval performs non-parametric prediction in the two representation spaces and combines their predictions through confidence-aware fusion at inference time. The supervised and SSL encoders are separately parameterized and need not share the same GNN architecture. We evaluate multiple GNN backbones and two distinct SSL objectives, DGI and GRACE, on four graph benchmarks spanning temporal and cross-domain distribution shifts. Extensive experiments show that Co-Train consistently outperforms strong supervised OOD baselines, while Dual-Space Retrieval achieves competitive performance as a flexible non-parametric alternative. Results across different backbones and SSL objectives, together with representation analyses and ablations, demonstrate that SSL representations provide complementary information to supervised representations and can improve OOD node classification across diverse settings.

Automated research systems increasingly run LLM agents over long horizons, but more inference does not by itself produce more progress: agents replay growing histories, duplicate one another's work, or stop experimenting while token consumption continues. Yet most evaluations use short budgets or benchmarks that saturate early, leaving these failure modes untested. We trace these failures to two choices: where research state lives and who decides what to try next. We introduce Stateless Language Agents (SLAs), built on the principle of stateful search with stateless agents: no agent carries its conversation across invocations; instead, the harness owns the research state (candidate solutions and measured outcomes) and reconstructs a fresh and role-specific context for every invocation. What each agent sees becomes an explicit design choice rather than a history that grows with the run. We implement this principle in the SLA framework, where a stateless Advisor reads harness-summarized evidence across search directions and assigns concrete experiments to parallel Workers. We evaluate SLA against three recent frameworks on software engineering, kernel optimization, and algorithm design at budgets of up to one billion tokens. SLA achieves the best final result on every task and reaches the strongest kernel baseline's final performance with over 84% fewer tokens. Ablations from shared checkpoints show that focused contexts and explicit assignments each contribute to SLA's progress, with effects that can compound over full runs, while the Advisor consumes less than 0.6% of tokens. These results argue for SLAs, which keep durable research state out of agent conversations, and show that short evaluation horizons can misjudge research systems and their components.

Probability forecasts are calibrated when predicted probabilities match empirical outcome frequencies: among events assigned a probability $p$, we'd hope that the fraction of positive outcomes is close to $p$. We study the problem of sequential forecasting of binary outcomes. The classical $O(T^{2/3})$ bound on expected cumulative $\ell_1$-calibration error established by Foster and Vohra stood for over two decades until Dagan et al. reduced the exponent $2/3$ by an unspecified constant. We establish a new two-phase recursive labeling strategy for the sign-preservation-with-reuse game that yields the bound $O(n^{\alpha}t^\beta)$ for all choices of space and time. We then sharpen the reduction from upper bounds on sign preservation to calibration by modifying the equivalence of Dagan et al. to use only $O(\log T)$ instances of the sign-preservation-with-reuse game. This lets us establish an explicit bound of $O(T^{0.662942288})$, the first explicit exponent below $2/3$ for sequential calibration, by combining both improvements and choosing explicit feasible parameters.

Scientific law discovery requires selecting measurements and converting evidence into a governing equation. We evaluate an explore-then-commit protocol in which a large language model proposes hypotheses, a programmatic planner gathers measurements, and a fresh prompt synthesizes the final law from fixed observations. The protocol combines structured probes, automatic numerical diagnostics, restricted measurement batches, and optional interpreter access. Across 576 NewtonBench trials, we compare eight configurations on 12 physics modules using GPT-4.1-mini and a medium-difficulty GPT-4.1 replication. On medium tasks, interpreter-enabled planners use 8.6 versus 22.5 measurements per trial for GPT-4.1-mini and 8.9 versus 43.0 for GPT-4.1. Their mean magnitude-based root-mean-squared logarithmic error falls from 2.514 to 0.202 and from 0.626 to 0.149, respectively. An additional audit retains incomplete and invalid submissions in a coverage-sensitive analysis. Observed symbolic-accuracy gains are less consistent across modules, and random acquisition is competitive with disagreement scoring. Measurement savings occur in every module, but unequal batch constraints prevent attributing them solely to acquisition quality. These results support the complete protocol as a promising measurement-efficient configuration, while leaving its causal components and generalization beyond noiseless direct-equation tasks unresolved.

Active Feature Acquisition (AFA) is a classification problem in which an agent decides which costly features to acquire before predicting each sample's label. Unlike batch AFA, which trains a fixed policy and classifier offline on fully observed data, online AFA updates its predictor from revealed labels as samples arrive. Existing online methods either use deep reinforcement learning (RL) without performance guarantees or maximize cost-adjusted reward rather than enforce a global budget. We formulate online AFA as a combinatorial Bandits with Knapsacks (BwK) problem that couples acquisition and prediction. Unlike prior bandit-based AFA and classical BwK, our setting has combinatorial complexity, evolving rewards, a global budget, and structured side information. We obtain an improved regret upper bound over standard BwK bounds in this framework, leveraging a cardinality-aware confidence bound and the subset update structure. To avoid an exponentially large action space, we propose LP-Chain, a variant that searches a cost-aware chain of feature subsets with a size that grows linearly with the number of features. While the regret upper bound is specific to the combinatorial framework, LP-Chain empirically achieves comparable predictive performance. On synthetic data, LP-Chain outperforms HEDGE-based BwK and deep RL-based online AFA baselines and scales favorably to more features.

In mill yards, log loaders clear dense piles by a sequence of bundle grasps: hundreds of logs rest in contact, and each removal changes the pile available to the next grasp. A learned policy chooses where to place and orient the grapple from unsegmented point clouds and runs on a trailer-mounted hydraulic forestry crane. The policy classifies at which observed point to grasp and predicts depth and grapple orientation there. The same network outputs support behavior cloning (BC), reinforcement learning (RL), and deployment. BC learns from successful top-of-pile demonstrations; RL explores for improvements by fine-tuning the cloned policy (BC$\to$RL) or by training from scratch. In simulation, BC clears 98 of 100 piles of 200 logs, while BC$\to$RL improves load stability. Twelve field trials compare a geometric heuristic, RL from scratch, BC, and BC$\to$RL through complete grasp-transport-deposit cycles. BC and BC$\to$RL deposit 93.8% and 88.9% of pooled inventory, against 80.4% for the heuristic. BC$\to$RL deposits logs on 83.6% of its cycles, against 79.6% for the heuristic and 65.7% for BC, while its simulated stability gain does not carry over to the crane testbed. Trained entirely in simulation and run unchanged on the crane, the learned policies clear more than the hand-filtered heuristic while observing unfiltered clouds that still contain the storage rack's rails and poles.

Semi-supervised learning typically assumes that labeled and unlabeled data share an identical class distribution and label space. However, this setting is often violated: unlabeled data may be imbalanced and contain unknown class samples, causing mismatches in both class distribution and label space. Such dual mismatch leads to majority classes dominating the latent space and unknown class samples being overconfidently misclassified, degrading feature discriminability and pseudo-label quality. To address this, we propose a hub-spoke latent geometry, where known classes are uniformly distributed around a central hub and each class forms compact clusters around its prototype, while the hub provides an anchor for a low-evidence region specifically designed for high-uncertainty unknown class samples. Integrated with an evidence-based classifier, this geometry ultimately enhances feature discriminability and uncertainty separation by mitigating majority-class domination through structured feature organization and guiding high-uncertainty unknown class samples toward the hub. Extensive experiments show that our method outperforms state-of-the-art methods, with a maximum improvement of 3.25% across various settings.

Model-guided directed evolution seeks to identify high-fitness protein variants under limited oracle budgets. Protein language models (PLMs) provide rich representations for this task, but task-agnostic zero-shot scores can be misaligned with a target assay, while supervised search in high-dimensional embedding spaces can make surrogate modeling and uncertainty estimation sample-inefficient. We propose the Linear Fitness Subspace (LFS) hypothesis: within mutation-induced residue-level representation changes, a compact, assay-specific set of directions makes fitness variation linearly accessible from few labeled variants. This is a local, supervision-recoverable statement rather than a claim that protein fitness landscapes or global PLM geometry are universally linear. Building on this observation, we introduce Subspace-Guided Evolutionary Search (SGES), which estimates an LFS from a small initial sample and performs surrogate modeling, uncertainty estimation, and acquisition in the learned subspace. Across 10 core ProteinGym assays, 87 extended static-validation assays, and an 18-assay budgeted-search evaluation, SGES improves fitness prediction and search efficiency over zero-shot PLMs and recent ML-guided protein optimization baselines. Controlled comparisons with PCA, random projections, label-shuffled PLS, classical mutation features, and acquisition ablations further isolate the benefit of a fitness-aligned site-delta coordinate.

We develop a mesh-free neural JKO scheme for advection-reaction-diffusion equations with a gradient-flow structure in the Hellinger-Kantorovich (HK) geometry of unbalanced optimal transport. Each update is parametrized by a spatial map and a mass-changing factor, allowing spatial redistribution and local mass creation or loss to be treated jointly within a single variational step. Their cone action bounds the squared HK distance from above, yielding a sufficient condition for discrete energy dissipation through comparison with the identity pair. Minimizing the pair objective over all admissible pairs recovers the exact JKO minimum when the source and a minimizer have positive densities. We establish existence and mass bounds for JKO minimizers and, under additional assumptions, obtain positivity and regularity together with a discrete Euler-Lagrange equation and a metric-dissipation identity. The self-consistent chemical potential is then nonincreasing along an optimal map. There exist parametric pairs whose endpoint densities and objective values converge to those of an exact JKO minimizer, provided a regular-pair approximation hypothesis holds. Finally, we show that a primal-dual gap controls objective suboptimality and, for Boltzmann entropy, the $L^1$ density error, assuming exact-step regularity, positive-semidefinite interactions, and global dual feasibility. Numerical experiments examine pointwise agreement with the PDE, energy dissipation, and the roles of transport, reaction, and fully implicit interactions.

In this paper, we study robust decision-making in the latent space of world models (WMs). Robust optimization is a mathematical framework where, given explicitly specified dynamics and physically meaningful disturbances, a robot can select actions that remain effective even under worst-case disturbances. However, applying this principle to the learned latent space of WMs introduces a fundamental challenge: because WMs have fully learned state spaces and dynamics inferred from high-dimensional observations, it is unclear how to define latent-space disturbances that faithfully represent uncertainty in the underlying system. Our key idea is to model a latent-space disturbance as a perturbation to the learned latent dynamics that induces pessimistic but plausible transitions. Specifically, we construct a set of plausible latent dynamics by combining a dynamics-aware similarity metric that captures plausible transitions with out-of-distribution detection that excludes implausible latent states. We calibrate this uncertainty set over latent dynamics using conformal prediction, ensuring that WM imaginations induced by the latent disturbance remain plausible without becoming overly pessimistic. We then jointly optimize robust robot actions and the worst-case latent disturbances through game-theoretic optimization. We leverage this latent-space robust optimization to robustify policy steering, considering two paradigms: latent safety filtering and sample-and-verify steering of a generative control policy. Our controlled simulation experiments show that our latent disturbance enables robust decision-making directly in WM latent spaces, and hardware experiments with a Franka manipulator show that modeling latent disturbances enables robust policy steering, reducing failures by 70% in safety filtering and 54% in sampling-based policy steering. Project website: https://junwon.me/LatentDisturbance/.

A robot description does more than specify a physical mechanism: it also encodes arbitrary conventions, such as joint-axis direction, joint-angle zero, and the order and names of links and joints. Morphology-aware policies consume interfaces built from these descriptions, yet cross-embodiment evaluation typically changes the robot while keeping those conventions fixed. This leaves a simple question unanswered: does behavior survive when the robot stays fixed but its description changes? GaugeBench isolates this case by rewriting a fixed mechanism under physically equivalent conventions, verifying that its physics and policy interface are preserved, and then evaluating the same policy weights. The result is stark: three MetaMorph policies score 4030.6 on 80 familiar robots, but only 51.6 when those same robots are equivalently re-described, while 98 genuinely held-out robots score 1489.6. A new description can therefore be more damaging than a new robot. Tracing the failure reveals that axis reversal alone reproduces the collapse, joint-angle zero changes are nearly harmless, and reordering lies between them; moreover, changing joint-state and torque coordinates alone is sufficient to cause the failure, while changing description-derived features alone is not. The same phenomenon appears in ModuMorph and an unrelated PyBullet framework. Yet it is not irreversible: exact two-description transport restores the original controller, and training across equivalent axis conventions raises retained return under axis reversal from 3.6% to 80.6%. Together, these results separate mechanism robustness from representation robustness and show that cross-embodiment evaluation should test both.

Humanoid household manipulation requires the arms to act while the body balances, steps and changes posture. We present BiGym 2.0, an adaptation of BiGym for the Unitree G1 across 20 household tasks using a unified whole-body controller for demonstration and evaluation. The suite provides 60 native human virtual-reality demonstrations per task with synchronised multi-camera views and full-body execution records. We benchmark vision-language-action fine-tuning, imitation learning, demo-driven reinforcement learning, and cold-start coding agents given the interaction budget of online reinforcement learning. With the same onboard views, proprioception and whole-body controller for every method, vision-language-action fine-tuning has the highest nine-task mean, and agent-developed programs outperform every demo-driven reinforcement learning baseline on this mean and lead on bimanual reaching. Cross-workspace stacking remains open, $\pi_{0.5}$ stays low on pick-box, and multi-object transport is hard for imitation learning, demo-driven reinforcement learning and coding agents. All environments, human demonstrations, and evaluation traces are open-sourced at https://github.com/swirl-uk/BiGym2.

State tracking requires an update at every input, but the depth a Transformer applies to each token is fixed regardless of sequence length. We introduce the Recurrent Looped Transformer (RLT), which splits its layers between a parallel causal encoder and a recurrent decoder. At each token, the decoder merges the encoder output with the previous token's final decoder state, so the computation path grows with sequence length at a fixed per-token cost. On six algorithmic tasks, we compare five splits of eight layers with an eight-layer Transformer over three seeds. Trained on at most 40 bits, two RLT splits generalize parity to 256 bits with 100% accuracy in every seed, while the Transformer stays at chance. On swap-based $S_5$ permutation tracking at eight times the training length, RLT reaches 97% final-state accuracy versus under 1% for the Transformer, and accuracy increases with decoder depth. On modular arithmetic beyond the training lengths, RLT reaches up to 93% versus 33% for the Transformer. Ablations show that these gains depend on the feedback: removing it drops parity and swap-based $S_5$ to chance at every split. Updating the feedback once per four-token chunk lets known tokens in a chunk run in parallel and keeps 64-bit parity at 99%, while permutation tracking depends on per-token feedback: chunking lowers length-64 swap-based $S_5$ from 100% to 20%.

Modern recommendation is shifting from platform-centric personalization toward user-governed personalization, where a personal LLM agent can act on the user's behalf across services. We formalize this emerging paradigm as Personal-Agent Mediated Recommendation: a platform recommender ranks a candidate set using platform-local information, and a personal agent uses user-authorized cross-platform history to mediate the resulting ranking and produce the final top-K slate. Such mediation is nontrivial: the platform ranking can encode strong population evidence that the personal agent cannot observe, so effective mediation must therefore balance beneficial rescues against harmful overrides. To study this trade-off, we introduce MediateRec, a benchmark that includes scalable proxy cross-platform environments and a real cross-platform test under a controlled platform-agent information boundary. To train the agent to use cross-platform history effectively, we further propose Personal Attribution Mediation Optimization (PAMO), which counterfactually masks that history to estimate personal mediation support and reallocates rank-aware advantage mass under a platform-relative value floor. We theoretically prove that PAMO preserves cutoff-level advantage mass and is locally optimal among first-order reallocations that preserve this mass without lowering average platform-relative value. Experiments on MediateRec show that personal-agent mediation enables meaningful platform corrections, yet even strong proprietary LLMs introduce non-negligible harmful overrides. PAMO consistently improves over matched outcome-only RL across seen and unseen target platforms and on the real cross-platform test, while achieving a better rescue-harm balance.

We propose a scalable roto-reflection-group-equivariant vision transformer based on windowed group-convolutional self-attention and a hierarchical feature architecture. We demonstrate that our approach can be scaled to group-equivariant vision transformers (ViTs) with millions of parameters and large datasets with practically sized images, i.e., ImageNet. The code and pretrained weights for the proposed Hierarchical Windowed Roto-reflection Equivariant ViTs (REViT-v2) are available at https://github.com/kc-ml2/revit.

While AI weather models now rival operational forecasts, how they represent the atmosphere internally remains an open question: feature attribution reveals which input patterns matter, not what the model computes or how it combines information internally. We train sparse autoencoders (SAEs) on GraphCast to uncover its learned concepts, using atmospheric rivers as our phenomenon of focus. Both standard and Matryoshka SAEs show GraphCast computes atmospheric river intensity, measured by integrated vapor transport (IVT), as a stable internal variable, despite IVT being neither an input nor a target. In contrast to the unstructured concept retrieval of the standard SAE, the Matryoshka SAE orders concepts by importance and exposes their relations. Atmospheric river concepts persist across depth and direct interventions confirm causality. This method offers a way to find internal variables and determine which of them the model actually relies on, which is a prerequisite for asking whether those variables remain meaningful as the phenomenon changes under a warming climate.

Cassini synthetic aperture radar (SAR) images reveal the dunes, plains, and lake basins of Titan, providing an instance of representations learned from Earth imagery for planetary terrain classification. Cross-domain Evaluation of Earth-to-Titan Transfer Using SAR (CETUS) compares features from DINOv2, DOFA and CROMA with classical image measurements and features from an untrained vision transformer on the U.S. Geological Survey's Cassini SAR mosaic. The classifiers learn terrain labels from an expert geomorphological map and predict those labels in geographically separate Titan regions. Under logistic regression settings, pretrained encoders achieve higher mean macro F1 than the combined classical features. Encoder rankings change when feature scaling, optimization, and regularization change together. Further training on Titan improves DINOv2 performance, degrades DOFA performance, and leads to mixed results for CROMA under the tested settings. Architectural and input processing differences prevent these comparisons from isolating the effect of pretraining. Classifier fitting and performance on individual terrain classes matter when assessing representation transfer for planetary mapping. Since the map draws partly on the same radar observations, the scores measure agreement with expert interpretation.

In-context learning (ICL) adapts frozen large multimodal models (LMMs) to new tasks from a few demonstrations (demos), but re-encodes them at every query, where each demo image adds up to hundreds of visual tokens. Demo-free methods remove this cost with a compact task state. However, they add it at locations searched per task or at every decoder layer, where task parameters grow with depth. Moreover, inserted tokens or keys cannot change how the original prompt divides its attention within a layer. To address these issues, we propose Structured Task Adaptation via Embeddings (STAVE), which replaces demos with two task-specific vectors added to existing input embeddings. Specifically, a readout vector updates the answer-producing tokens and a context vector updates the other structural token groups. Both are trained with answer labels on prompts with and without demos. We justify these design choices theoretically using a first-order analysis of the loss and a margin bound. Extensive experiments on six LMMs and five large language models show that STAVE matches or outperforms state-of-the-art methods on multimodal tasks with far fewer task parameters and surpasses 15-shot ICL and prior task vectors on 18 text tasks, all at zero-shot inference cost.

Complementary Feature Domains (CFD) theory characterizes predictive value as a context-indexed contribution system induced jointly by representations and their realization family. We show that Shannon-information preservation does not imply preservation of this contribution system: an invertible representation transformation can leave target information unchanged while altering predictive contribution under a restricted decision family. We formalize the resulting transition through a CFD contribution defect that measures how contextual contributions change under controlled recoding. For bounded Lipschitz utility, we show that each coalition utility shift is bounded by the behavioral distance between the attainable action sets before and after recoding; consequently, every contextual contribution defect is bounded by the sum of the corresponding coalition incompatibilities. Exact behavioral closure yields invariance, while increasingly accurate compensation yields restoration. A controlled ECG experiment illustrates the mechanism: a nonlinear bijective recoding preserves the information in a frozen time-frequency representation but changes accuracy under a fixed affine learner; applying the exact inverse restores all tested coalition accuracies. The result separates information preservation from realization-dependent contribution and provides a quantitative transition law for multi-representation prediction.

Learning an ensemble of GFlowNets to sample from a discrete target distribution has become a common approach for achieving better state space exploration and convergence than that of a monolithic sampler. However, these methods often add a substantial runtime overhead to the base model, and their conceptual connection remains elusive. To address this, we first propose a general-purpose theoretical framework for describing a mixture of GFlowNets, which we specialize into continuously (CI) and discretely indexed (DI) collections. On the one hand, we show CI GFlowNets can be interpreted through the lens of a random features expansion, provably boosting the sampler's expressivity in graph-structured tasks and reducing learning instability via spectral shifting. On the other hand, we demonstrate DI GFlowNets encompass prior approaches for GFlowNet training and provide the foundation for the newly proposed Stratum-Conditioned (SC) GFlowNets. This method, which is inspired by the Doob's h-transform of Markov chains, decomposes the state space according to a prescribed modular function and restricts each component to sample from a distinct subset of it. Importantly, SC GFlowNets support centralized and component-wise embarrassingly parallel training, and we show both of them significantly speed up learning convergence and mode coverage without introducing any non-negligible extra computation.

Recent progress in tabular foundation models suggests that training on synthetic tasks can substantially improve in-context learning capabilities, with overall performance largely depending on how well models can infer task-specific predictive relationships from the available context during inference. In this paper, we introduce TAFFY, a tabular foundation model with an In-Context Diversity Prior and a Task-Conditioned Looped Transformer that strengthen this ability. Specifically, to construct each synthetic pretraining context, the In-Context Diversity Prior samples from multiple related environments derived via controlled interventions and distribution shifts on a shared causal process. This in-context diversity encourages the model to learn a more comprehensive and task-specific representation. Moreover, the Task-Conditioned Looped Transformer iteratively and selectively applies a shared group of Transformer blocks to refine contextual representations, with a task-conditioned gate modulating the final hidden-state update. This enables task-adaptive iterative refinement. Together, these components encourage the model to identify predictive relationships from contextual contrasts during pretraining and dynamically modulate context integration for each task. Across six classification and five regression benchmark datasets, TAFFY attains the lowest average rank.

Vision-Language-Action (VLA) models have become a major paradigm for Vision-and-Language Navigation (VLN). However, in safety-critical facilities, invisible risks such as radiation or temperature spikes cannot be detected by an RGB camera, and handling each risk is expensive, requiring a new encoder, new data, and model retraining. We propose Physics-Guided Visual Prompting (PG-VP), a plug-and-play multimodal perception module that instead reuses what a frozen VLA model already does well: avoiding visible obstacles. Given a proximal radiation or thermal source, PG-VP performs a physics-guided risk assessment to determine the avoidance direction and overlays a corresponding virtual obstacle that moves across consecutive frames (Dynamic Visual Prompting). The navigation policy then naturally detours around this invisible hazard. The identical virtual obstacle is used regardless of hazard type, so the visual prompting pattern remains fixed as sensors are added. When no hazard is detected, nothing is rendered, and the policy behaves exactly as it would without PG-VP. We evaluate PG-VP on OmniNav using the val-unseen splits of R2R-CE and RxR-CE, where it guides the policy toward intended low-risk actions in 84.9% and 83.2% of cases, at a cost of 6.8 and 7.9 percentage points in navigation success rate. We further test it with distinct scenarios on a real robot in the presence of actual thermal and radiation sources, all without any retraining. The real test shows that PG-VP effectively avoids these invisible hazards, improving worst-10% average trajectory safety by 63.45% and 32.59% against thermal and radiation sources, respectively.

Optimal-transport couplings have been shown to reduce training variance in unconditional flow models, but their role in conditional generation remains unclear. A natural approach constructs separate couplings for each condition, but this is impractical for large or continuous conditioning spaces found in modern image foundation models. We introduce Global Transport (GT), a global class-agnostic optimal-transport coupling, computed without class labels. GT can associate different conditions with different regions of the source noise, and consequently worsens performance without guidance. However, when combined with classifier-free guidance (CFG), GT consistently improves generation across domains, model scales, and sampling budgets. This reversal suggests that couplings for conditional flows should be evaluated both empirically and theoretically under the guided flow used at inference, rather than on unguided generation. We evaluate GT over both discrete class and continuous text conditioned image generation across model scales, and investigate how coupling choice alters guided trajectories. These results identify coupling design in the guided flow setting as a simple training time axis to improve performance without modifying existing architectures, samplers, or guidance mechanisms.

LoRA fine-tuning adapts small language models (SLMs) to heterogeneous instruction data within a low-rank update subspace, making it vulnerable to three structural problems: conflicting gradients that cancel, static data selection that cannot track evolving learning dynamics, and subspace saturation that causes later updates to overwrite useful directions. We argue that effective adaptation therefore requires controlling which data-induced gradients enter the LoRA subspace and when. We propose GRADE (GRadient-Aligned Data-centric rEcipe), a data-centric framework combining two mechanisms: a state-aware selector that continually admits samples aligned with the evolving multi-task gradient field, and a self-calibrating step-level gate that rejects updates likely to cause destructive overwrite near saturation. Across three current-generation backbones and a heterogeneous seven-dataset instruction pool, GRADE outperforms strong data-selection and PEFT-stabilization baselines in accuracy and robustness. It is the only method to improve consistently over standard LoRA on every architecture, while producing more coherent gradient trajectories and less destructive overwrite. These results show that successful SLM adaptation depends not only on which data are selected, but also on which gradients are allowed to enter and persist in the constrained update subspace.

Learning Gaussian mixture models (GMMs) using the Expectation-Maximization (EM) algorithm and its gradient-based variants is a fundamental problem in machine learning. It is known that randomly initialized (gradient) EM fails to learn multi-component GMMs in the exact-parameterized setting, where the number of components matches that of the ground-truth GMM. Recently, global convergence of gradient EM has been established in the over-parameterized setting, where more components are used, provided that the ground-truth components are well separated. In particular, the minimum separation between ground-truth components is required to scale as $\Omega(\sqrt{d})$, where $d$ is the dimension. In this paper, we show that this dimensional dependence is unavoidable in high-dimensional settings. Specifically, we consider a hybrid EM algorithm that uses standard EM updates for the mixing weights and gradient EM updates for the component means. For any $\epsilon > 0$, we prove that when the dimension is sufficiently large, in the worst case a separation of order $\Omega(d^{0.5-\epsilon})$ is insufficient to guarantee global convergence of population gradient EM in sub-exponential time under random initialization, even in the over-parameterized regime. Our result establishes an almost optimal worst-case lower bound on the ground-truth separation required for learning Gaussian mixtures via gradient EM in high dimensions.

Random access (RA) is one of the most foundational medium access control (MAC) layer scheduling schemes for handling unpredictable data traffic from multiple terminals. While multi-agent reinforcement learning (MARL) has been explored to optimize RA-based wireless networks, its reliance on experience-driven, distributed policy learning incurs significant training overhead for each optimization task, limiting its feasibility in real-world applications. In this work, we propose to leverage a foundation model (FM) to improve MARL efficiency across diverse RA network optimization tasks. Specifically, we design an FM-aided actor-critic algorithm within a consensus-based decentralized MARL architecture and provide its convergence analysis under local reward exchanges and nonlinear value function approximations to show that our algorithm achieves the same convergence order as the conventional MARL with critic model exchanges and linear approximations. Our numerical results show that our FM-based approach significantly enhances MARL speed for RA network optimization.

Robotic systems often exhibit unstable modes, along which small perturbations and disturbances can cause unbounded growth unless corrected through feedback. Controlling such systems from high-dimensional visual observations requires representations that preserve these modes. Joint-embedding predictive architectures (JEPAs) provide a natural framework for learning such representations and their dynamics from visual data. However, we demonstrate that next step prediction combined with anti-collapse regularization does not guarantee that controllable unstable modes are preserved: the training loss can be minimized while these modes are collapsed, making stabilization from the learned representation impossible. To address this, we augment world-model training with an action reconstruction objective (i.e., an inverse dynamics loss) that encourages control-aware representations, namely, visual representations that preserve crucial features for control. We prove that exact action reconstruction makes the encoder injective on the finite-horizon reachable subspace. Thus, the encoder cannot discard any state direction reachable by an action sequence within $H$ steps. Moreover, we show that, as $H$ grows, the dominant eigenspace of the finite-horizon controllability Gramian converges to the controllable unstable subspace. We establish our theoretical results for linear systems and demonstrate empirically that our findings extend to nonlinear visual control tasks (CartPole, Walker2D, and PointMaze), highlighting the benefits of control-aware representation learning.