Papers

AI agents can externalize what they learn from past tasks into reusable skills, such as procedures, checklists, code, or other executable artifacts, that can be retrieved and reused when solving new tasks. Self-evolving skill methods keep rewriting these skills after each round of practice on training tasks, and the skill is then used on new tasks of the same kind. We ask a question: does the improvement a skill shows on its training tasks carry over to new test tasks? We test five self-evolving methods and a one-shot skill on six benchmarks, with the same model, the same agent, and the same train/test split for every method. Of the 21 skills that improve on their training tasks, 5 keep all of that improvement on the test tasks, 13 keep part of it, and 3 keep none of it. No existing method is best everywhere. When we read the skills, the ones that carry over badly often fix details that should depend on the task, such as column names and output files, or turn a fix for one failure into a rule for every task. An LLM judge that reads the skill content can often see this: it ranks finished skills the same way the test results do in 86% of pairs. But it predicts the effect of a single edit poorly, so edits still have to be tested by running them. Based on these findings, we describe Generalizable Skill Optimization (GSO), which keeps only a guide for writing skills and writes a new skill for each task; it scores highest on all six benchmarks.

Current image-to-video models achieve visual realism and physical plausibility, but reasoning about mental states remains unexplored. Actions are driven by belief, desire, and perception, requiring inference beyond explicit instructions. We introduce MindWorldBench to evaluate mental-state-conditioned video generation. We formalize this as mental-state-to-behavior reasoning, where models generate actions from a world state and latent variables without explicit action prompts. MindWorldBench utilizes Zero-Action Prompting and a counterfactual design with 744 prompts to isolate the causal effects of mental states. An automated pipeline evaluates video quality, commonsense plausibility, and mental-state consistency. Evaluations of 11 models show that despite visual fidelity and physical reasoning, models fail to align behaviors with latent mental states. We identify a failure mode, termed Omniscient Bias, where models default to the objective world state rather than human's subjective belief. These results demonstrate a disconnect between visual generation and cognitive reasoning, suggesting a need for explicit mental-state modeling in video generation systems. Project website: https://richard2049-lee.github.io/MindWorldBench/

Multi-agent debate (MAD) can improve large language model (LLM) reasoning by allowing multiple agents to exchange and critique their answers to the same task. However, the interactions that enable agents to correct mistakes can also spread adversarial errors and steer the agents toward an incorrect answer. Although some efforts have been made to examine particular attack types on MAD, systematic evaluation of MAD under diverse attacks remains limited. A central question is whether debate mitigates adversarial influence or amplifies it. In this paper, we present MADBench, a benchmark for evaluating the security of MAD. We organize attacks into a layered taxonomy following the MAD workflow, incorporating both established attacks and new strategies tailored to debate. We evaluate six attack families over 356 source tasks and 3,958 test cases, examining their effects on the final answer and the propagation of adversarial influence. Our results show that, under attacks, MAD does not necessarily improve LLM reasoning. Compared with a single-agent baseline, MAD can mitigate attacks on answer accuracy in question-answering tasks while amplifying unauthorized reads or writes in both question-answering and workspace tasks. Moreover, even when three out of five agents collude, the attack changes the final answer from correct to wrong on only 28.30% of tasks answered correctly without attack, while only 3.26% of initially correct honest agents switch to wrong answers during debate.

Unreliable visual inputs can harm task performance and cause potential physical safety risks for vision-language-action (VLA) models. We analyze how $\pi 0.5$ and GR00T models act under input faults such as image blackouts and freezing. We find that blackout and freezing produce distinct physical failure modes even when task-success rates are similarly low: freezing causes more extreme joint behavior, whereas blackout after gripper closure can cause more object drops, most markedly without proprioception. Selective intervention studies reveal that proprioception (current robot state) partly compensates for the removed robot depictions and reduces non-target contact. However, it cannot sufficiently restore task success when wrist-view object information is removed, even when aided by the remaining scene view. We then evaluate two mitigation approaches: camera-blackout training and training-free replacement of faulty visual embeddings. Both improve task success in selected conditions, but can increase unintended contact or disturbance to surrounding objects. Real-robot trials further show that successful execution under camera faults can still involve unintended physical interactions. These findings motivate designing VLA policies that use the robot and object information still available under camera faults to limit hazardous motion.

We prove a sharp Gaussian approximation for the invariant law of constant-stepsize SGD with bounded additive noise generated by an exogenous uniformly ergodic Markov chain. For a smooth, strongly convex objective with a Lipschitz Hessian and nondegenerate long-run noise covariance, the centered iterate normalized by the square root of the stepsize is $O(\sqrt{\alpha})$-close in 1-Wasserstein distance to its limiting Gaussian. The proof combines blockwise Gaussian comparison with long-run contraction. A four-state example gives a matching lower bound although the one-time noise marginal is symmetric and every nonzero-lag autocovariance vanishes. In this example, an adjacent third-order mixed moment produces the leading correction.

Long-horizon agent interactions generate useful but noisy experience, and retraining models to absorb it is expensive. Context-evolving agents therefore need memory extraction methods that improve with more test-time compute without relying on gold labels. We propose RefCon, which combines sequential self-refinement with parallel self-contrast to extract higher-quality memories without gold labels. Evaluated on AppWorld and BFCL-V3 across multiple context-evolving agent frameworks, RefCon delivers strong and consistent gains, including relative improvements of 21.6% on ACE and 16.6% on ReMe over no-scaling baselines, while a diversity-focused variant (DivCon) achieves a 35.5% gain on ReasoningBank. RefCon consistently outperforms existing baselines without ground-truth labels, and generalizes across model scales and to software engineering tasks, where it surpasses even ground-truth baselines. We further analyze the accuracy-token trade-off and scaling behavior, showing RefCon maintains favorable efficiency and continues to improve as more trajectories are used, unlike diversity-only scaling which saturates earlier.

Can structured text replace vision for diagram reasoning? A wrong answer after textualization can arise because the representation omits information the question needs, or because the solver fails to use information that is present. We introduce a diagnostic protocol to distinguish these explanations. Using the same solver model and generation settings, we compare three input conditions: the original image, question-blind structure extracted by a vision-language model, or gold structure derived from the diagram source. Validity-triggered recovery tests truncation and schema failure, question-relevant fidelity measures preservation of answer-critical structure, and matched edge interventions test the effect of error location. On a reserved holdout of 240 public FlowGen diagrams, evaluated under a frozen protocol, gold structure reaches 87% accuracy while direct vision and learned text both remain below 30%. The aggregate comparison includes source-derived relation labels that may not be printed in the image and uses different learned and gold graph encodings, so it does not isolate extraction error alone. Retrying only invalid extractions makes nearly every public representation schema-valid yet leaves accuracy essentially unchanged. The public learned-text deficit relative to gold more than doubles with structural difficulty. Question-relevant topology predicts correctness better than whole-graph topology. In an exposed intervention study, a single answer-relevant edge edit reduces the primary solver's original-answer accuracy to near zero, while matched irrelevant edits largely preserve it. Supplied structure requires fewer solving tokens than vision, but learned acquisition removes this advantage at single use. These comparisons motivate evaluating acquired text by the answer-relevant evidence it preserves and by the solver's ability to use that representation.

We characterize bound entanglement in bipartite qutrit systems by combining the Positive Partial Transpose (PPT) criterion with a structural, non-completely positive map. Focusing on a comprehensive three-parameter bipartite qutrit family $\rho_{a,b,c}$, we present an exact analytical and geometric partitioning of the physical state space simplex. We derive the closed-form quadratic boundary governing the leaf-like PPT region $(a^2+ab+b^2-b \leq 0)$ over the domain $0 < a \leq \frac{1}{3}$, and identify the exact linear threshold $(a > c)$ that characterizes the PPT bound entangled sub-region. This family strictly generalizes the well-known Horodecki bound entangled states, which appear as a single slice of the three-dimensional leaf. Applying the structural map to this decomposition, we show that it certifies bound entanglement throughout the entire threshold region, accounting for $14.76\%$ of the total PPT leaf area.

Learning to complete tasks in unfamiliar environments with unknown rules remains a key challenge for LLM agents. Current LLM agents often record their discoveries in prose, which may not provide a compact, explicit account of how the environment works. Inspired by how scientists organize observations into testable, predictive theories, we introduce Schema, an agent harness that organizes learning and action through interactive program induction. The LLM agent decides what to investigate and how to act, expressing its evolving understanding of the environment as executable programs. The harness consists of a persistent program workspace and a small set of interfaces for checking these programs against the interaction history, planning within them, and executing plans under step-by-step verification. Schema raises ARC-AGI-3 RHAE from 58.7% to 99.2% with the same base model, solves 100% of the public DiG-bench games, and reaches the median performance of the top-50 human players on MazeBench. Extensive analysis shows the effectiveness of Schema in unknown mechanism discovery, and ablations confirm the contribution of each component.

Adaptive RAG uses signals such as confidence, relevance, support, and retrieval quality to decide when to search or correct evidence. In multi-step retrieval, however, these local signals must be combined into a persistent view of what the current evidence supports, what remains missing, and which action should follow. Existing methods often use such signals as separate triggers, making it difficult to preserve a coherent evidence state across a trajectory; we call this problem evidence-state fragmentation. We introduce BELIEFRAG, a closed-loop controller that updates an explicit state over sufficiency, reliability, conflict, uncertainty, evidence gaps, and acquisition cost, then chooses among retrieval, query rewriting, verification, answering, stopping, and abstention. Across six QA benchmarks with gpt-oss-120b, BELIEFRAG reaches mean token F1 0.572 with 3.89k tokens per question, outperforming fixed iterative retrieval (0.555 F1) while using 39% fewer tokens. The same quality-cost pattern transfers to Qwen3-32B, where BELIEFRAG reaches 0.552 F1 versus 0.523 for iterative retrieval while using 35% fewer tokens. Analysis shows that the main gains come from corrective re-retrieval rather than pruning alone, while several belief dimensions are redundant and calibrated answerability plays the strongest operational role. Calibration improves threshold stability across related evidence sources, although source shift can still invalidate the same decision signal.

AI clusters increasingly run large language model (LLM) inference and training on the same fabric. Prefill-decode (P-D) disaggregation creates key-value (KV) cache transfers between prefill and decode groups, whereas training collectives and all-to-all traffic benefit from near-uniform global connectivity. A static sparse topology can therefore be poorly matched to one of the two traffic patterns. We present Mode-Switching Expander (MoSE), a reconfigurable expander that treats topology design as a fixed-degree edge-allocation problem. MoSE reallocates the same sparse edge budget toward direct P-D connectivity in inference-heavy modes and restores a uniform random regular expander in training-heavy modes. We evaluate MoSE using a 1024-group flow-level topology model, shortest-path routing, and two mixed workloads. Across 20 seeds, MoSE reduces average and 95th-percentile (P95) load-aware KV communication cost by 90.8% and 91.9% relative to Static-Training in the inference-heavy mode. In the training-heavy mode, it reduces average and P95 training communication cost by 22.7% and 27.6% relative to stale Static-Inference. These results show that coarse-grained topology switching can support both workload modes without additional ports or routing changes.

Scaling Large Language Models (LLMs) via Mixture-of-Experts (MoE) enables massive parameter growth with nearly constant per-token computation. However, further scaling the parameter count requires increasingly sparse routing, where expert load imbalance becomes more severe. This imbalance reduces parameter utilization and training efficiency, and can undermine training stability, becoming a bottleneck to reliable scaling. In this work, we unify two representative auxiliary-loss-free methods as incomplete Proportional-Integral-Derivative (PID) controllers: DeepSeek's loss-free method acts as a fixed-step integral controller, while Kimi K3's Quantile Balancing functions as a generalized proportional controller. Building on this control perspective, we propose ID Balancing, an Integral-Derivative controller. It scales its integral term with load error and activates its derivative term only when imbalance worsens, enabling stronger corrections for large or worsening errors and smaller updates near balance. Evaluated across Top-$10$, Top-$5$, and Top-$3$ routing over $768$ experts, ID Balancing reduces worst-case backbone MaxVio and training-average backbone MinVio by over $50$% and $12$%, respectively, relative to the best baselines in the Top-$3$ setting. When the total parameter count increases from $18.9$B to $69.9$B (Top-$10$-of-$768$), ID Balancing's worst-case backbone MaxVio remains nearly unchanged and is approximately $89.6$% lower than that of the auxiliary-loss baseline. ID Balancing also maintains competitive language-modeling and downstream performance. The advantages of ID Balancing grow as sparsity increases, making it a promising solution for scaling larger, sparser MoE models.

Let $f$ be a nonzero holomorphic germ at $0 \in \mathbb C^n$ with $f(0)=0$, and let $\chi$ be a $C^2$ non-decreasing convex function on the left half-line. We establish sharp necessary and sufficient conditions for the local Sobolev regularity of the plurisubharmonic function $v=\chi(\log|f|).$ The criteria for the $L^p$-integrability of the classical Laplacian and for $W^{1,p}$-regularity are given by a weighted integral involving $\chi''$ and $\chi'$, respectively, and depend on $f$ only through the smallest multiplicity of $\operatorname{Div}(f)$. We also obtain the $W^{2,p}_{\mathrm{loc}}$ criterion for $1<p<\infty$. At the endpoint $p=1$, we prove that \[ v\in W^{2,1}_{\mathrm{loc}} \quad\Longleftrightarrow\quad \chi'\in L^1((-\infty,A)), \] equivalently, $v$ is locally bounded. As applications, we obtain counterexamples to Calderón-Zygmund theory and characterize a class of functions in the local Monge–Ampère domain. % and exhibit a natural family in $W^{2,1}_{\mathrm{loc}}$ whose limit fails to belong to $W^{2,1}_{\mathrm{loc}}$.

Physical reasoning from video requires inferring latent physical properties and dynamics beyond direct observation. Direct VLM inference remains unreliable on complex physical tasks without explicit modeling and validation, while predefined tool pipelines rely on task- and domain-specific priors that limit generalization across materials, dynamics, and reasoning tasks. We introduce Asking the World (ATW), a generalist agent that constructs and interrogates task-relevant executable worlds through two adaptive stages: World Modeling calibrates a world from video, while World Probing queries, simulates, and intervenes on it to obtain question-relevant evidence. Rather than prescribing the operations in either stage, ATW determines how to model and probe according to the scene and question. We develop PolyWorld Engine, a lightweight and highly programmable Warp-based multiphysics simulator for constructing and probing worlds with rigid bodies, soft bodies, cloth, ropes, fluids, and their coupled interactions. CEM-based system identification recovers task-relevant dynamics during World Modeling. The resulting world becomes an active workspace for question-directed physical experiments rather than a predetermined downstream tool. We evaluate ATW on CLEVRER, ContPhy, and three real-world scenarios. Using Gemini-3-Flash as its base VLM, ATW achieves 80.82% overall per-question accuracy on CLEVRER, improving direct Gemini-3-Flash by 46.50 points, GPT-5.5 by 13.58 points, and PhysMind by 8.27 points. On ContPhy, it reaches 70.56% overall accuracy, surpassing Gemini-3-Flash by 28.10 points and GPT-5.5 by 3.53 points. Across the three real-world scenarios, ATW achieves 71.67% accuracy, 28.33 points above GPT-5.5. These results establish agentic world modeling and probing as an effective, execution-grounded approach to generalist physical reasoning. Project page: https://asking-the-world.github.io/

Visual-token compression improves the efficiency of large vision-language models, but can expose failures that full-token evaluation misses. We study adversarial images that preserve full-token correctness yet induce errors after compression, even when both inference paths succeed on the clean image. Creating such failures is challenging because perturbing token importance can also damage the visual content needed for full-token inference. We propose Feature-Aware Token Attack (FATA), which couples attention suppression with cosine-based feature preservation on a fixed set of salient clean-image tokens. In the primary LLaVA-1.5-7B setting, FATA uses only vision-encoder gradients, without access to the deployed compressor, token budget, or downstream task. Across four visually dependent task subsets and four compressors under a controlled reconstruction protocol, FATA achieves SR = 96.3% full-token accuracy retention and CBR = 22.1% conditional blinding, compared with 89.8% and 15.7% for CAA. Ablations support the role of both objectives in balancing compressed-path failure against full-token preservation. FATA also has the lowest measured detection rate among four attacks across three evaluated detectors at a 5% false-positive rate. These findings motivate assessing adversarial robustness jointly across full-token and compressed inference.

In this article, we compute the limit Hilbert–Kunz multiplicities and limit F-signatures of all the simple singularities and the Hilbert–Kunz multiplicities of the Fermat hypersurfaces, generalizing the well-known sec z + tan z formula by Gessel and Monsky for the A1 singularities, using the theory of h-functions. We also obtain a functional equation relating the phi-function of a hypersurface to its reflection. Using limit F-invariants, we generalize both a characterization of regular local rings through F-invariants and the known cases of the Watanabe–Yoshida conjecture to characteristic zero.

We study few-step video generation, i.e., distilling a multi-step video generator, which typically requires tens of sampling steps, incurring substantial latency and compute, into a few-step student. Consistency distillation is a common recipe, in which a multi-step teacher provides the consistency targets for a few-step student. However, these teacher-guided targets are not equally trustworthy, and the content is harder to learn where it varies rapidly over time, e.g., moving foliage shadows or flowing water. We observe that supervision reliability follows the local difficulty of the content rather than semantic complexity: regions that change little yield consistent endpoint predictions, whereas regions with large temporal variation produce larger discrepancies that coincide with the largest perceptual errors. Motivated by this observation, we propose Uncertainty-Aware Consistency Distillation (UACD), which reweights consistency supervision at each spatiotemporal region using a local, parameter-free uncertainty estimate. Specifically, we construct two independently perturbed teacher-guided consistency paths, whose student endpoint predictions provide a consensus target; the discrepancy between the student's direct prediction and this target is the uncertainty proxy. We then relax the consistency penalty on high-uncertainty regions through an exponential weight, while keeping the full penalty elsewhere, since the student cannot be expected to match targets that are hard to learn. To preserve perceptual quality under aggressive step reduction, we integrate feature-space adversarial training with semantic alignment. With parameter-efficient LoRA adaptation of the 50-step Wan model, our method achieves state-of-the-art 4-step generation on VBench 2.0 (0.556 mean score) and is preferred over competing methods in a user study.

Large language model (LLM) serving requires substantial memory to store model weights and KV caches. As models grow larger and contexts become longer, memory capacity and bandwidth increasingly become bottlenecks for serving performance. Agentic workloads compound this pressure through repeated interactions over growing contexts, making it increasingly important to retain KV state for reuse. High-bandwidth flash (HBF) offers a way to expand accelerator memory capacity for large language model (LLM) serving, but its access costs and limited write endurance complicate its use. We evaluate HBF for high-throughput agentic serving across system design and scheduling choices to understand when additional capacity improves serving performance and energy efficiency. We introduce an HBM-HBF-host hierarchical storage system and buffered cache-aware scheduling, and use trace-driven simulations to analyze their effects on performance, energy consumption, and HBF write lifetime. Across the evaluated workloads, the fastest HBF-augmented systems reduce completion time by 36.1-87.7% relative to HBM-only systems. Modeled energy savings reach 59.1%, with benefits depending on the workload and weight placement. Buffered cache-aware scheduling extends estimated HBF write lifetime from 1.21 to 14.82 years in the evaluated configuration. These results demonstrate the importance of coordinating data placement and scheduling to improve serving efficiency while sustaining a practical HBF write lifetime.

Accurate assessment of color differences is essential for applications ranging from digital design to quality control. While existing color difference metrics, such as CIEDE2000, aim to approximate human perception, they may still exhibit inconsistencies with perceptual judgments. In this study, we investigate a data-driven approach to color-difference estimation based directly on human evaluations. We collect similarity judgments for 2,000 systematically generated color pairs, each rated by seven observers using a four-point ordinal scale. These judgments are then used to train regression models using different color representations, including RGB channel differences, HSI differences, and COLIBRI fuzzy linguistic categories. Experiments with five regression algorithms show that the choice of color model has a greater influence on prediction performance than the choice of regression algorithm. Using COLIBRI features alone, linear regression achieves an R2 of 0.595, outperforming RGB and HSI representations, which achieve R2 values of 0.479 and 0.493, respectively. The best performance is obtained by LightGBM using the combined representation, reaching an R2 of 0.703. The results indicate that human perceptual color differences are better captured when numerical color coordinates are complemented by graded perceptual categories, highlighting the potential of data-driven models for perceptually aligned color-difference estimation.

A surgical robot policy needs to know where each instrument's working end sits relative to the camera and to the other instrument, yet a laparoscopic operation leaves only the endoscope video, and a draped instrument hides every optical path on itself. We estimate the tool tips from distances and an IMU alone. The distances are measured by ultra-wideband carrier phase between antenna nodes on the handle side of the instruments: one per hand-held instrument, one on the endoscope, all outside the sterile barrier. Take the endoscope antenna as the reference. The two instrument antennas carry six coordinates while the three pairs give three distances, so the problem is short by three, and averaging cannot close that gap because what is missing is information, not precision. Carrier phase adds one more unknown per pair, an integer that leaves distance fixed only modulo lambda/2 = 23.1 mm. The trocar settles both difficulties: each shaft passes through a port whose position is known and whose direction the on-board IMU measures, so its antenna keeps a single degree of freedom, the insertion depth. Two unknowns now face three distances – two fix the depths and the third is left over, and that spare equation exposes a wrong integer or a wrong mounting offset instead of absorbing it. The same solve returns both tool tips in the endoscope frame, without the second carrier frequency that integer resolution usually needs, so the link never leaves a single PLL lock. In an 11-hole phantom among metal instruments the three distances hold sigma = 0.10-0.33 mm at 35-46 Hz, a sterile drape pressed onto the antennas leaves the link unchanged where an optical path would be blocked, and the logger was carried into a live rabbit appendectomy.

Global video geo-localization aims to infer the geographic location of a video worldwide, evaluating performance across four geographic hierarchies: city, state/province, country, and continent. Existing methods typically employ one-way uniform sampling to process video frames and train independent classifiers for each hierarchy, which leads to the loss of key geographic cues and prediction conflicts between hierarchies, especially for complex multi-shot edited videos. To address these limitations, we propose GeoGAT, which integrates bidirectional temporal sampling with graph attention networks (GATs). Specifically, GeoGAT extracts forward and offset-reversed frame sequences to construct complementary spatiotemporal features. These fused features are then fed into a predefined geographical hierarchy graph, where GATs perform structure-aware message passing, while a dual-constraint mechanism prunes predictions to eliminate cross-hierarchy conflicts. We construct GeoGAT10k, comprising 9,720 multi-shot edited videos from 166 cities worldwide, specifically to benchmark generalization ability on complex video structures. Experimental results on CityGuessr68k and GeoGAT10k demonstrate that GeoGAT eliminates hierarchical conflicts entirely and achieves state-of-the-art performance across all four geographic hierarchies. On CityGuessr68k, GeoGAT outperforms the strongest baseline, evaluated under both classification and retrieval protocols, by 2.6 percentage points at the city level. On the more challenging GeoGAT10k with multi-shot edited videos, the accuracy improvement exceeds 24 percentage points, validating strong generalization to complex real-world scenarios.

Satellite-ground localization estimates the planar position and yaw orientation of a ground camera within a geo-referenced satellite image. Most recent methods map ground and satellite features into a shared bird's-eye-view (BEV) space and establish spatial correspondences. However, insufficient depth constraints can assign one ground feature to different distances along a viewing direction, creating geometric ambiguity in BEV feature placement. Similar appearances at different locations can also create descriptor matching ambiguity, while existing descriptor learning lacks explicit semantic supervision to distinguish them. We propose GeoSem-BEV, a geometry-semantic constrained BEV representation learning method. Radial depth supervision constrains distance assignment, and vertical height supervision constrains height aggregation. Shared explicit semantic supervision promotes consistent semantic predictions across views and helps distinguish locations with similar semantics. These constraints improve feature placement and descriptor discriminability, enhancing state-of-the-art BEV localization models. On VIGOR with unknown orientation, GeoSem-BEV reduces mean orientation error by 37.2% and 38.1% in the cross-area and same-area settings, respectively. The corresponding errors are reduced by 10.8% and 15.6% on DReSS-D. On KITTI-CVL, it reduces same-area mean orientation error by 26.8% under 10 degree orientation noise.

Consider two orthonormal bases of a bipartite Hilbert space such that states in one basis are weakly entangled and states in the other are strongly entangled. We establish a quantitative version of the following uncertainty principle: every state that is localized in one basis must be delocalized in the other. More specifically, we lower bound the sum of the Shannon entropies of any state's coefficient distributions in the two bases by the difference between the entanglement Rényi entropies of their basis states. The result follows from new lower and upper bounds on the entanglement of superpositions that may be of independent interest. As an application, our result limits the power of weakly-entangled states in representing ground states of Hamiltonians with strongly-entangled energy eigenstates. We illustrate this application numerically for the Sachdev-Ye-Kitaev model.

Visual-inertial odometry (VIO) for aerial robots relies on high rate inertial measurement unit (IMU) propagation between visual updates. However, conventional multi state constraint Kalman filters (MSCKFs) use random walk bias assumptions and fixed noise parameters, which can limit robustness when visual information is unreliable. To address this problem, we propose LBDU-VIO, a learning-augmented MSCKF with learned continuous time bias dynamics and an IMU uncertainty model. A neural ordinary differential equation (ODE) models continuous time bias dynamics to propagate the filter's bias states, replacing their random walk model. The IMU uncertainty model predicts motion adaptive measurement noise covariances for covariance propagation. Both models are trained with pose supervision without direct labels. Experiments on real world EuRoC and TUM-VI benchmarks show lower errors than representative visual-inertial baselines, including a 25.1% reduction in mean relative position error compared with S-MSCKF on EuRoC sequences with 10s visual outage.

Generative models for tabular data are typically trained separately for each dataset, limiting knowledge transfer and requiring the storage of many specialized models. In this paper, we introduce CDMD, a tabular diffusion model trained jointly across heterogeneous datasets with different schemas and variable numbers of numerical and categorical features. Unlike existing cross-dataset tabular diffusion models that operate in continuous representation spaces, CDMD defines diffusion directly over the mixed-type feature space and is trained end-to-end. To accommodate heterogeneous categorical domains, we introduce a schema-restricted reverse-process parameterization for masked diffusion models, in which the output space dynamically adapts to each feature's vocabulary. We then compose numerical and categorical feature-level diffusion processes into a schema-dependent row-level process. A shared schema-aware Transformer denoiser captures dependencies between features and parameterizes the reverse process across varying schemas. On seven real-world datasets, a single jointly trained CDMD achieves the highest average generation quality among strong single-dataset and cross-dataset baselines, while using substantially fewer total parameters than the collection of separately trained models. Furthermore, pre-training on a corpus of 337 datasets improves generation on previously unseen datasets under both limited target data and limited adaptation epochs. These results demonstrate the potential of direct mixed-type diffusion for shared and transferable tabular data generation. Our code is available at https://github.com/ketatam/cdmd.

When optimizing an expensive black-box function sequentially, as in hyperparameter optimization, we may want to stop once the best evaluated value is certified within $\varepsilon$ of the global optimum. Such a certificate needs two ingredients: a lower confidence bound for the selected value and an upper confidence envelope over the domain, typically supplied by a Gaussian process (GP). GP-UCB-style stopping rules are valid when the kernel and constants defining this envelope are fixed before the run, but the practical temptation is to tune the envelope from the same adaptive evaluations and then certify as if it had been fixed. We use prequential e-values to make this selection auditable: starting from a predeclared set of fully specified GP/RKHS envelopes, each candidate is tested by its own one-step-ahead e-process, contradicted candidates are deleted, and certification uses the largest upper bound among the survivors. With a valid selected-point lower bound and one declared candidate having valid latent coverage and noise calibration, the rule is anytime-valid. On a 512-seed noisy RBF stress sweep, it roughly halves false-certification risk at comparable power versus fit-then-certify. Relative to random fixed GP precommitment on smooth $d=3,4$ objectives, each additional false certificate is accompanied by 3.0 and 13.5 additional correct certificates, respectively.

To a quiver of finite type one can associate two abelian categories: the category of finite dimensional modules over the corresponding affine quiver Hecke algebra and the Coulomb category of Koszul-perverse coherent sheaves. In this paper we define an exact functor from the former to the latter. This functor sends a simple to a simple or zero and is (almost) essentially surjective on simples. This implies that simple Koszul-perverse sheaves categorify the dual canonical basis.

Faulty syndrome measurements can corrupt an otherwise correct quantum-error correction step. Bivariate bicycle (BB) codes contain dependent stabilizer checks, so every valid syndrome obeys additional parity constraints, or metachecks. We study how far this built-in redundancy can identify measurement faults and when the remaining ambiguity is unavoidable, while separately checking the code's logical structure. A logical decomposition is used as a preliminary safety check: it identifies a $k/2$-dimensional annihilator subspace and a $k/2$-dimensional colon quotient, and the minimum-weight logical need not be visible from the annihilator side alone. On the measurement side, translation symmetry partitions syndrome locations into classes that carry identical metacheck information. This gives an exact characterization of the leading single-fault ambiguity, a bound on how many fault locations can be distinguished, and a family-level repair limit when the encoded dimension stays bounded while the block length grows. Under a static-data assumption, the same calculation gives the minimum number of checks that must be remeasured to remove every single-fault ambiguity. Exact finite-code calculations illustrate both regimes: all single measurement faults are distinguishable in a 72-qubit BB code, whereas the 144-qubit Gross code merges its 72 syndrome locations into 36 indistinguishable pairs. In a 108-qubit example, one logical component first appears at weight 12 while the other contains a weight-10 logical. Sustained phenomenological experiments show that joint data–measurement decoding is more robust than a separated repair stage on the more ambiguous codes. The resulting tests apply to general two-block BB codes, including non-coprime periods and repeated-root cases.

On-policy distillation (OPD) improves reasoning by providing token-level supervision from a teacher on a student's own trajectories. Existing methods primarily focus on enhancing this teacher-side guidance (e.g., by enriching teacher inputs and refining teacher feedback), yet we find that limited student perception is another critical bottleneck in multimodal OPD. By providing oracle visual facts, the performance of OPD-trained students can still be substantially improved for both weak and strong teachers. To address this bottleneck, we propose S-OPD, a simple multimodal on-policy distillation framework that explicitly strengthens student perceptual learning through two objectives. Specifically, Teacher-calibrated Policy Contrast separates student policies under original and masked images with teacher-based token-level gating, strengthening the student's reliance on visual evidence during reasoning. Policy Agreement aligns student policies under original and noise-perturbed images, further improving perceptual robustness to visual noise. Notably, our method can be seamlessly plugged into existing OPD frameworks, requiring no additional data annotations, model parameters or inference operations. Extensive experiments on eight benchmarks across student scales and distillation paradigms demonstrate consistent performance improvements, with gains of up to 4.25 points on LogicVista. When combined with existing teacher-side supervision methods, our method can yield further gains. Code is available at https://github.com/Sirilaw/S-OPD.

Toroidal discrete Wigner functions (DWFs) for finite-dimensional systems are non-unique. We completely parameterize and topologically classify the labeled single-qudit ${d\times d}$ representations whose phase-point operators are Hermitian, unit-trace, Hilbert–Schmidt orthogonal, and Weyl–Heisenberg covariant, determining the independent parameter freedom in every dimension. Our previously established stencil theorem expresses this family as descents of a doubled ${2d\times2d}$ parent Wigner representation. Here, we solve its projected-stencil admissibility conditions explicitly to obtain the full parameter space of this family. In the symplectic-Fourier representation, admissibility fixes the modulus, leaving phase data on a ${d\times d}$ base cell satisfying a parity-dependent twisted-oddness relation. This gives the parameter space ${(S^1)^{(d^2-1)/2}}$ for odd ${d}$ and ${(S^1)^{(d^2-4)/2}\times\mathbb{Z}_{2}^{3}}$ for even ${d}$. Canonical horizontal and vertical marginals reduce these spaces to ${(S^1)^{(d-1)^2/2}}$ and ${(S^1)^{d\,(d-2)/2}\times\mathbb{Z}_{2}}$, respectively. The same phase data parameterize validity-preserving rephasings of the doubled Weyl–Heisenberg displacement operators. Requiring these operators to have order dividing the Hilbert-space dimension ${d}$ replaces each ${S^1}$ factor by a discrete ${\mathbb{Z}_{d}}$ factor. The associated symplectic-Fourier characteristic functions encode the same operator information, with pointwise magnitudes independent of the valid stencil convention and hence providing convention-independent information about the represented operator within this family. This classification separates the freedom intrinsic to DWF validity from that selected by marginal and displacement-algebra requirements and makes explicit the structural distinction between odd and even dimensions.