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01.
arXiv (quant-ph) 2026-06-11

Polarization-Resolved Photon Statistics of Cavity Quantum Materials

arXiv:2606.11550v1 Announce Type: cross Abstract: By forming hybrid light-matter states, optical cavities offer a route for engineering material properties, however, unambiguously probing the effects of light-matter coupling remains difficult. Here, we show that the polarization-resolved statistics of photons transmitted through a cavity, measurable via $g^{(2)}$, provide one such diagnostic. By relating $g^{(2)}$ to matter correlation functions such as the Raman structure factor, we link photon bunching and antibunching to material properties. By applying this method to the stripy-to-antiferromagnetic transition in the Kitaev-Heisenberg spin model, we find that polarization-dependent patterns of bunching and antibunching encode the magnetic point-group symmetries of each phase and characterize the behavior at the phase boundary. Finally, we predict measuring $g^{(2)}$ for output photon pairs polarized orthogonal to the input field will isolate higher-order light-matter scattering processes that probe higher-order material correlations.

02.
arXiv (CS.CV) 2026-06-16

VigilFormer: Deformable Attention for Video Anomaly Detection with Causal Risk Inference

作者:

Video anomaly detection in surveillance settings must balance detection accuracy against real-time throughput, a tension that existing methods address either through stronger feature extractors or more efficient architectures, but rarely both. We present VigilFormer, a unified framework that combines deformable spatio-temporal attention with causal temporal modeling to detect anomalies in untrimmed surveillance video. The proposed Deformable Spatio-Temporal Encoder (DSTE) attends to a sparse set of informative locations across frames, avoiding the quadratic cost of dense attention while retaining the ability to capture irregular motion patterns. A Causal Anomaly Classifier (CAC) applies dilated causal convolutions over snippet-level features and optimizes a contrastive multiple-instance learning objective that separates anomalous and normal representations without frame-level labels. To meet deployment constraints, an Adaptive Confidence Scheduler (ACS) dynamically skips low-information frames at inference time, reducing redundant computation in static scenes. Evaluated on UCF-Crime, ShanghaiTech, and CUHK Avenue, VigilFormer achieves AUC scores of 87.83%, 97.21%, and 89.74% respectively, at 41.5 FPS on a single GPU, outperforming recent weakly-supervised methods in both accuracy and speed.

03.
arXiv (CS.CL) 2026-06-12

DSAEval: Evaluating Data Science Agents on a Wide Range of Real-World Data Science Problems

Recent LLM-based data agents aim to automate data science tasks ranging from data analysis to deep learning. However, the open-ended nature of real-world data science problems, which often span multiple taxonomies and lack standard answers, poses a significant challenge for evaluation. To address this, we introduce DSAEval, a benchmark comprising 641 real-world data science problems grounded in 285 diverse datasets, covering both structured and unstructured data (e.g., image and text). DSAEval incorporates three distinctive features: (1) Multimodal Environment Perception, which enables agents to interpret observations from multiple modalities, including text and vision; (2) Multi-Query Interactions, which mirror the iterative and cumulative nature of real-world data science projects; and (3) Multi-Dimensional Evaluation, which provides a holistic assessment across reasoning, code, and results. We systematically evaluate 13 recent advanced agentic LLMs using DSAEval. Our results show that Claude-Sonnet-4.5 achieves the strongest overall performance, MiMo-V2-Pro and GPT-5.2 lead in duration and step efficiency, respectively, and MiMo-V2-Flash is the most cost-effective. We further demonstrate that multimodal perception consistently improves performance on vision-related tasks, with gains ranging from 2.04\% to 11.30\%. Overall, while current data science agents perform well on structured data and routine data analysis workflows, substantial challenges remain in unstructured domains. Finally, we offer critical insights and outline future research directions.

04.
arXiv (quant-ph) 2026-06-16

Benchmarking Quantum Computers via Protocols, Comparing IBM's Heron vs IBM's Eagle

arXiv:2603.04377v3 Announce Type: replace Abstract: As quantum computing hardware rapidly advances, objectively evaluating the capabilities and error rates of new processors remains a critical challenge for the field. A clear and realistic understanding of current quantum performance is essential for guiding research priorities and driving meaningful progress. In this work, we apply and extend a protocol-based benchmarking methodology (Meirom, Mor, Weinstein Arxiv 2505.12441) that utilizes well-defined \underline{quantumness} thresholds. By evaluating performance at protocol level rather than the gate level, this approach provides a transparent and intuitive assessment of whether specific quantum processors, or isolated sub-chips within them, can demonstrate a practical quantum advantage. To illustrate the utility of this method, we compare two generations of IBM quantum computers: the older Eagle architecture and the newer Heron architecture. Our findings reveal the genuine operational strengths and limitations of these devices, demonstrating substantial performance improvements in the newer Heron generation. This work was made possible by IBM Quantum policies that enable independent and objective assessment of its quantum computers and sub-chips. We strongly encourage other companies to emulate the independent qubit availability and the fair pricing that allow researchers to perform such assessments.

05.
arXiv (CS.CV) 2026-06-11

DynaTok: Token-Based 4D Reconstruction from Partial Point Clouds

We address 4D reconstruction from partial point cloud sequences, where depth-sensor observations are incomplete, unordered, and lack explicit temporal correspondences. This geometry-only setting is challenging due to missing observations and ambiguous dynamics. While recent progress has largely relied on image-based methods, existing point-based approaches typically focus on single objects, assume relatively complete inputs, or require explicit correspondences. To address these limitations, we propose DynaTok, a point-based framework for correspondence-free 4D reconstruction from partial point cloud sequences without images. DynaTok encodes frames into compact latent tokens, aggregates incomplete observations over time with a Transformer-based spatiotemporal encoder, and decouples geometry and motion through residual tokens in a unified model. A flow-matching decoder then reconstructs complete, temporally consistent 4D point-cloud sequences conditioned on the latent tokens. Experiments on object- and scene-level benchmarks demonstrate improved reconstruction quality and temporal coherence from partial point cloud observations. Project page: https://wrchen530.github.io/dynatok/.

06.
arXiv (CS.CV) 2026-06-16

LentiAvatar: Pseudo-Multiview Reconstruction and Subpixel Prism Rendering for Real-Time Stereoscopic Communication

Real-time stereoscopic video communication has long been a goal of immersive telepresence, yet practical systems still require specialized capture rigs or reduce remote users to a single portrait view. We present LentiAvatar, a Gaussian head-avatar system that connects monocular avatar capture with subpixel-encoded glasses-free lenticular display for real-time autostereoscopic communication. From a monocular portrait video, LentiAvatar reconstructs a controllable head avatar and optimizes it for the lateral viewing zones induced by the display. The method uses natural head turns as pseudo-multiview (PMV) supervision to constrain regions that are otherwise weakly observed in monocular training, including hair, ears, jaw contours, and neck boundaries. Reliable side frames are yaw-binned, aligned to virtual cameras, and supervised within a strict head-and-hair domain; contour-aware losses and staged regularization further suppress ghosting, alpha leakage, and depth instability while preserving lateral detail. At runtime, LentiAvatar renders 32 virtual views and encodes them into a 4K lenticular raster with calibrated subpixel-routing masks. The live-tracker prototype sustains 10.65 FPS, and a subject-specific distilled driver raises the same display pipeline to 38.49 FPS.

07.
arXiv (CS.CL) 2026-06-15

Right or Wrong, Models Comply: Directional Blindness in LLM Moral Judgment

As language models take integrated roles across many domains, the response of LLMs to user pushback becomes a critical alignment property. Yet many existing evaluations treat compliance as unidirectional, measuring whether models resist pressure but not whether they resist it selectively. We introduce Compliance Asymmetry (A = BCR/HCR), a bidirectional diagnostic that compares beneficial output change under helpful nudges with harmful change under misleading nudges. Across 9 models and 972,000 nudge-condition responses, we find that this selectivity differs in factual and moral judgments: models follow helpful nudges more than harmful ones on factual questions (A = 1.58), but follow both directions at nearly identical rates on moral questions (A = 1.04). This phenomenon persists across model families, capability levels, and nudging types. Interestingly, we also find that chain-of-thought prompting amplifies helpful and harmful compliance together, while identity-based prompting suppresses both by nearly identical margins. These results identify direction-blind moral compliance as a distinct failure mode in current LLMs and suggest that alignment should target directionally calibrated updating rather than lower compliance alone.

08.
arXiv (math.PR) 2026-06-16

Joint convergence in Wiener chaos via transport hierarchy and Malliavin covariances

arXiv:2606.14812v1 Announce Type: new Abstract: We study the joint convergence in distribution of a sequence $X_N = I_p(f_N)$ of multiple Wiener–Itô integrals of order $p\geq 2$ that converges to a Gaussian limit $Z\sim N(0,\sigma^2)$, together with another sequence $Y_N = I_q(g_N)$ converging in law. The central finding is that the joint convergence of $(X_N, Y_N)$ is completely governed by the asymptotic behavior of the iterated Malliavin covariances $Y_{r+1,N} = \langle DX_N, DY_{r,N}\rangle_H$, $r\geq 0$: joint convergence holds as soon as these covariances converge jointly with $Y_N$, and the structure of the limiting distribution is then explicitly determined by their limits. Moreover, the convergence of the Malliavin covariances is necessary for joint convergence, as shown by a counterexample. When $q

09.
arXiv (CS.CV) 2026-06-16

ActiveSAM: Image-Conditional Class Pruning for Fast and Accurate Open-Vocabulary Segmentation

Segment Anything Model 3 (SAM 3) provides a strong frozen backbone for concept-prompted segmentation, but applying it directly to open-vocabulary semantic segmentation (OVSS) is inefficient: full-resolution decoding is typically run over the entire dataset vocabulary, whereas each image contains only a small active subset of classes. We introduce ActiveSAM, a training-free, zero-shot inference framework that turns SAM 3 into an active-vocabulary segmenter. ActiveSAM first canonicalizes and expands class prompts, then estimates an image-conditioned active set from a low-resolution presence preview. Only the retained classes are decoded at full resolution, using bucketed prompt multiplexing with the frozen SAM 3 decoder. The preview stage uses only class-presence evidence and skips unnecessary segmentation-head computation, while the final stage applies margin-aware background calibration to suppress low-confidence pixels. ActiveSAM requires no target-dataset training, no weight updates, and no oracle class-presence labels. Across eight OVSS benchmarks, ActiveSAM improves the speed-accuracy tradeoff of training-free open-vocabulary semantic segmentation, outperforming the current state-of-the-art SegEarth-OV3 by approximately +1.4 mIoU on average while running up to 5.5x faster on large-vocabulary datasets. ActiveSAM also demonstrates the strongest robustness under image corruption that simulates real-world distribution shift, making it well-suited for deployment in noisy-input domains such as autonomous driving and embodied AI. Code is available at https://github.com/VILA-Lab/ActiveSAM.

10.
arXiv (CS.LG) 2026-06-11

OmniLoc: A Geometry-Aware Foundation Model for Anchor-Free UE Localization Across Diverse Indoor Environments

arXiv:2606.11490v1 Announce Type: new Abstract: Indoor localization from wireless measurements remains challenging in large-scale deployments due to substantial variation in building geometry, the set of detectable access points (APs), and the heterogeneity of received signals. Existing learning-based methods often perform well only in limited settings and degrade under environmental shifts, making robust anchor-free localization across diverse indoor environments notoriously difficult. In this paper, we present OmniLoc, an environment-interactive foundation model for anchor-free user equipment localization across diverse indoor environments. To the best of our knowledge, OmniLoc is the first foundation-model-based approach built directly on wireless measurements for this task. OmniLoc is built on three key designs. First, a unified input tokenization module converts heterogeneous wireless measurements into a common representation that is more amenable to learning. Second, a geometry-aware Transformer performs AP-aware feature extraction by emphasizing dominant APs while aggregating complementary evidence from supporting APs. Third, a geometry-aware location estimation module conditions regression on geometric embeddings to produce geometrically consistent location predictions. We evaluate OmniLoc on both a large-scale in-house dataset and a public benchmark dataset. Results show that OmniLoc significantly outperforms existing methods, consistently improves existing backbones when its design components are integrated, and demonstrates strong generalization in cross-environment evaluations.

11.
arXiv (quant-ph) 2026-06-19

Hybrid VQE-CVQE algorithm using diabatic state preparation

arXiv:2512.04801v2 Announce Type: replace Abstract: We propose a hybrid variational quantum algorithm that has variational parameters used by both the quantum circuit and the subsequent classical optimization. Similar to the Variational Quantum Eigensolver (VQE), this algorithm applies a parameterized unitary operator to the qubit register. We generate this operator using diabatic state preparation. The quantum measurement results then inform the classical optimization procedure used by the Cascaded Variational Quantum Eigensolver (CVQE). We demonstrate the algorithm on a system of interacting electrons and show how it can be used on long-term error-corrected as well as short-term intermediate-scale quantum computers. Our simulations performed on IBM Brisbane produced energies well within chemical accuracy.

12.
arXiv (quant-ph) 2026-06-17

Impulse Decoding of Quantum LDPC Codes: Equivalence of Degeneracy and Code-Shortening

arXiv:2606.18240v1 Announce Type: new Abstract: Quantum error correction is essential for building scalable quantum computers. Within the stabilizer formalism, the Calderbank-Shor-Steane framework constructs quantum codes from pairs of classical linear codes. A distinctive feature in this setting is degeneracy, where multiple equivalent error estimates exist-a phenomenon that has no classical counterpart, and the lack of a meaningful classical coding-theoretic interpretation of which has remained a gap in the literature. In this paper, we demonstrate that degeneracy is closely related to the classical operation of shortening of a linear block code. Interestingly, the shortening here takes place at the decoder rather than at the encoder. Leveraging this insight, we present a parallel decoding scheme for quantum low-density parity-check codes, which we term impulse decoding, that significantly outperforms belief propagation with ordered statistics decoding, as well as several other existing techniques, under both code-capacity and circuit-level noise, with significantly lesser complexity. We then present another algorithm based on decoding of residual errors, which when combined with impulse decoding achieves further performance improvement under circuit-level noise.

13.
arXiv (CS.LG) 2026-06-12

Enhanced Low-Density Region Exploration in Classifier-Guided Diffusion Models Through Modified Reverse Diffusion Sampling

arXiv:2606.13347v1 Announce Type: new Abstract: Diffusion models have emerged as state-of-the-art generative models for high-fidelity image synthesis, particularly in their classifier-free guided and classifier-guided forms. However, standard classifier guidance concentrates probability mass around high-density class mean, leading to poor coverage of rare samples in the tails of the class-conditional distributions. Recent work on diffusion-based tail sampling mitigates this by training an additional low-density-seeking classifier with a synthetic-vs-real discriminator, at the cost of additional networks and training. In parallel, a number of samplers and distillation techniques accelerate or refine diffusion sampling, but do not explicitly address long-tail coverage. We propose a purely sampling-time, density-aware extension of classifier-guided conditional diffusion model that targets low-density regions without any additional training. We have applied guidance at noisy images not on predicted noise like most diffusion models. Starting from a pretrained conditional diffusion model and classifier on ImageNet, we modify the guided reverse dynamics by steering trajectories toward low-confidence regions via the modified classifier gradient, and at each time step, we also guide the sampling process toward the predicted real image. 1st guidance helps explore low-probability samples, and 2nd guidance helps to generate samples to be close to the real data manifold. The proposed sampler consistently improves ADM model recall at 64x64 resolution while maintaining a comparable FID, and with a 256x256 ADM model, we showed the results visually with different combinations of both guidance. We also showed that standard ADM classifier guidance, combined with predicted real image guidance, helps generate high perceptual quality samples with a 256x256 ADM model on ImageNet.

14.
arXiv (quant-ph) 2026-06-11

Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity

arXiv:2504.16165v2 Announce Type: replace Abstract: We investigate 1D and 2D cluster states under local decoherence to assess the robustness of their mixed-state subsystem symmetry-protected topological (SSPT) order. By exactly computing fidelity correlators via dimensional reduction of effective statistical mechanics models, we pinpoint the critical error rate for strong-to-weak spontaneous breaking of strong subsystem symmetry. Without resorting to the replica trick, we demonstrate that mixed-state SSPT order remains remarkably robust up to the maximal decoherence rate when noise respects strong subsystem symmetry. Furthermore, we propose that the mixed-state SSPT order can be detected by a constant correction to the area-law scaling of entanglement negativity, termed spurious topological entanglement negativity. This also highlights that topological entanglement negativity, a widely used diagnostic for mixed-state topological order, is generally not invariant under finite-depth quantum channels.

15.
arXiv (CS.CV) 2026-06-11

Motion Reinforces Appearance: RGB-Skeleton Gated Residual Fusion for Micro-Gesture Online Recognition

Micro-gesture analysis attracts increasing attention for inferring spontaneous emotion from subtle body movements. Micro-gesture online recognition, which localizes and classifies each gesture instance in untrimmed videos, is a core task in the 4th EI-MiGA-IJCAI Challenge. Compared with typical temporal action detection, MGR emphasizes the localization and classification of actions, requiring the model to output the start time, end time, and category of each micro-gesture. Moreover, since micro-gestures are highly spontaneous, relying solely on a single modality makes it difficult to capture the complete and accurate multi-modal cues. In this work, we propose DyFADet+, which extends DyFADet into a dual-stream RGB-skeleton framework. In our model, both modalities are projected into shared multi-scale temporal embeddings and fused through a gated residual module, which adaptively injects skeleton motion into the RGB representation rather than using naive concatenation. Finally, these fused features are decoded by a Dynamic TAD head for online classification and boundary regression. On the SMG dataset, our method achieves an F1 score of 40.88, ranking 2nd in the Micro-gesture Online Recognition track.

16.
arXiv (CS.CL) 2026-06-19

Large Language Models Hack Rewards, and Society

Reinforcement learning (RL) has become a dominant post-training paradigm, enabling large language models (LLMs) to learn from rewards. We observe that societal regulations are structurally similar to reward functions. They define measurable outcomes, thresholds, and exceptions, while often leaving institutional intent only partially specified. We hypothesise that the RL training process may exploit these gaps and therefore ask whether models' well-known tendency to hack reward functions during RL can scale into a more consequential failure mode named societal hacking: discovering loopholes in the rules society runs on. To study this phenomenon, we introduce SocioHack, a sandbox of 72 societal environments, and find that within these environments, reward hacking naturally emerges and leads to regulatory loophole discovery. Models learn to hack the social rules and generate strategies that remain technically compliant while defeating regulatory intent, and current LLM safeguards provide only limited mitigation. Therefore, collecting in-the-wild feedback for model training requires greater caution, and we need a next-generation post-training paradigm for safely iterating LLMs in real society.=

17.
arXiv (CS.AI) 2026-06-19

Analyzing Defensive Misdirection Against Model-Guided Automated Attacks on Agentic AI Systems

arXiv:2606.20470v1 Announce Type: cross Abstract: Agentic AI systems increasingly rely on language-model components to interpret instructions, process external data, invoke tools, and coordinate with other agents. These capabilities make prompt-injection and jailbreak attacks more consequential, especially as attackers adopt model-guided automation to scale probing, prompt refinement, and response evaluation. This work analyzes the resulting attack-defense setting through a probabilistic model of a target system, its defense mechanism, and the attacker's automated judge. Our analysis shows that conventional detect-and-block defenses can allow attacker success rate (ASR) to approach one as the query budget grows, since predictable refusals provide useful feedback to automated search. We then examine detect-and-misdirect, where detected malicious interactions receive controlled, non-operational responses designed to induce false-positive errors in the attacker's judge. This strategy reduces the positive predictive value of attacker-selected candidates and yields a bounded asymptotic ASR. We evaluate a proof-of-concept realization of this strategy through Contextual Misdirection via Progressive Engagement (CMPE), a lightweight conversational misdirection method designed to replace predictable refusal text with safe but strategically misleading responses in automated jailbreak settings. On jailbreak benchmarks, CMPE reduces estimated ASR upper bounds by up to two orders of magnitude and nearly eliminates verified attack success in end-to-end PAIR and GPTFuzz attack runs.

18.
arXiv (CS.CV) 2026-06-16

Learn Temporal Consistency For Robust Satellite Video Detector

Satellite video object detection (SVOD) for oriented and fine-grained objects plays an important role in satellite applications. Most existing SVOD methods only focus on one or a few coarse-grained categories of moving objects and represent objects with horizontal bounding boxes. They have difficulty extracting complete, accurate, and consistent information about objects in whole satellite videos. In this paper, we propose a satellite video object detection framework based on Temporal Consistency Learning (TCL). TCL adeptly detects oriented and fine-grained objects by leveraging the rich temporal contexts within satellite videos. The framework integrates three key modules: temporal and fine-grained feature aggregation (TFA), structure encoding (SE), and temporal consistency constraint (TCC). TFA and TCC modules facilitate consistent representation learning across frames, while the SE module encodes both appearance and structural information for precise fine-grained recognition. Experimental results on the SAT-MTB benchmark dataset demonstrate TCL's superior performance, achieving a new state-of-the-art oriented and fine-grained detection accuracy of 47.7% mAP–a 4.8% improvement over the baseline. Furthermore, our TCL framework readily accommodates existing image-based detectors, leading to enhanced detection accuracies.

19.
arXiv (CS.LG) 2026-06-16

Active Learning with Low-Rank Structure for Data Selection

arXiv:2606.16045v1 Announce Type: new Abstract: In the data selection problem, the objective is to choose a small, representative subset of data that can be used to efficiently train a machine learning model. Sener and Savarese [ICLR 2018] showed that, given an embedding representation of the data and suitable geometric assumptions, heuristics based on $k$-center clustering can be used to perform data selection. This perspective was further explored by Axiotis et. al. [ICML 2024], who proposed a data selection approach based on $k$-means clustering and sensitivity sampling. However, these methods rely on the assumption that the dataset exhibits intrinsic geometric structure that can be effectively captured by clustering, whereas many modern datasets instead possess global algebraic structure that is better exploited by low-rank approximation or principal component analysis. In this paper, we introduce a new data selection framework based on low-rank approximation and residual-based sampling, formulated through the lens of row subset selection and loss-preserving coreset construction. Given an embedding representation of the data satisfying mild regularity conditions, which can be interpreted as algebraic or angular notions of Lipschitz continuity, we show that it is possible to select a weighted subset of $\tilde{O}\left(k + \frac{1}{\varepsilon^2}\right)$ data points whose average loss approximates the average loss over the full dataset within a $(1+\varepsilon)$ relative error, up to an additive $\varepsilon \Phi_k$ term, where $\Phi_k$ denotes the optimal rank-$k$ approximation cost of the embedding matrix. We complement these theoretical guarantees with empirical evaluations, demonstrating that on a range of real-world datasets, our data selection approach achieves improved performance over prior strategies based on uniform sampling or clustering-based sensitivity sampling.

20.
arXiv (CS.CV) 2026-06-18

PorTEXTO: A European Portuguese Benchmark for Visual Text Extraction

European Portuguese (pt-PT) is largely absent from OCR benchmarks, which skew toward high-resource languages. The few benchmarks that cover pt-PT focus on historical artifacts and literature. This work addresses modern OCR applications, introducing PorTEXTO, the first benchmark for contemporary and culturally relevant pt-PT visual text extraction. To ascertain quality, we employ an annotation pipeline combining transcriptions from a frontier LVLM with exhaustive review by native speakers. We observe a sharp performance drop from synthetic to real world samples in most models, and find that, currently, specialized multilingual data is a better driver for pt-PT performance than model size or resolution budget, motivating the release of open pt-PT OCR resources.

21.
arXiv (CS.CL) 2026-06-18

Learning User Simulators with Turing Rewards

Learning to simulate human users in interactive settings could advance the training of agent assistants, evaluation of personalization systems, research in the social sciences, and more. Existing approaches generally do so by training a large language model (LLM) to match a single ground truth response, either by maximizing the log probability or by using a similarity reward. We instead propose {Turing-RL}: a Turing-Test-based reinforcement learning approach for training user simulator models. {Turing-RL} uses a discriminative Turing reward with an LLM judge to score how indistinguishable a generated response is from the real user's given the user's history, and the user simulator LLM learns to produce responses indistinguishable from what the user could have said with such rewards. Across two different domains–conversational chat and Reddit forum discussion–we find that {Turing-RL} consistently outperforms baseline methods on both LLM and human evaluation metrics. Our study suggests that optimizing for indistinguishability, rather than response matching, is effective for learning user simulators.

22.
arXiv (CS.AI) 2026-06-19

Process-Verified Reinforcement Learning for Theorem Proving via Lean

arXiv:2606.20068v1 Announce Type: new Abstract: While reinforcement learning from verifiable rewards (RLVR) typically has relied on a single binary verification signal, symbolic proof assistants in formal reasoning offer rich, fine-grained structured feedback. This gap between structured processes and unstructured rewards highlights the importance of feedback that is both dense and sound. In this work, we demonstrate that the Lean proof assistant itself can serve as a symbolic process oracle, supplying both outcome-level and fine-grained tactic-level verified feedback during training. Proof attempts are parsed into tactic sequences, and Lean's elaboration marks both locally sound steps and the earliest failing step, yielding dense, verifier-grounded credit signals rooted in type theory. We incorporate these structured rewards into a GRPO-style reinforcement learning objective with first-error propagation and first-token credit methods that balances outcome- and process-level advantages. Experiments with STP-Lean and DeepSeek-Prover-V1.5 show that tactic-level supervision outperforms outcome-only baselines in most settings, delivering improvements on benchmarks such as MiniF2F and ProofNet. Beyond empirical gains, our study highlights a broader perspective: symbolic proof assistants are not only verifiers at evaluation time, but can also act as process-level reward oracles during training. This opens a path toward reinforcement learning frameworks that combine the scalability of language models with the reliability of symbolic verification for formal reasoning.

23.
arXiv (math.PR) 2026-06-17

Order statistics for edge eigenvectors of Wigner matrices

arXiv:2606.17425v1 Announce Type: new Abstract: In this paper, we establish a general comparison theorem for the order statistics of the edge eigenvectors for generalized Wigner matrices. Consequently, we derive the Gumbel law for the maximal edge eigenvector component and prove the universality of the Gaussian fluctuations of the order statistics in an intermediate regime close to the maximum. In addition, our comparison result also implies a quantitative first order estimate for moderately small order statistics.

24.
arXiv (CS.LG) 2026-06-16

Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

arXiv:2606.16510v1 Announce Type: cross Abstract: This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters. The approach employs neural networks to construct the trial solution space, while tensor-product hat functions are adopted as test functions to enforce the variational form. To accurately resolve of sharp boundary layers, the variational form is implemented using a Petrov-Galerkin formulation. Dirichlet boundary conditions are imposed directly, while the source terms are computed using automatic differentiation. Computational experiments on standard two-dimensional problems demonstrate that the proposed method achieves high accuracy in both the maximum and L_2 norms. These results confirm the efficiency and robustness of the Petrov-Galerkin VPINN approach in accurately capturing the multiscale features of two-dimensional SPPs.

25.
arXiv (CS.AI) 2026-06-19

StaminaBench: Stress-Testing Coding Agents over 100 Interaction Turns

arXiv:2606.19613v1 Announce Type: cross Abstract: We introduce StaminaBench, a benchmark that measures the stamina of coding agents: how many consecutive interaction turns (change requests) they can handle before failing. Unlike the prevailing fraction-of-tasks-solved metric, this matches real vibe-coding where sessions run dozens or hundreds of turns. In StaminaBench, agents implement a REST API server and modify it across a tunable number of procedurally generated follow-up change requests - 100 in our experiments, resulting in codebases of up to 6,000 lines. Tests are generated fully programmatically without LLM involvement, ensuring reproducibility and reliability; change sequences are drawn from either a hardcoded or LLM-driven sampler, both constrained to a structured action space to ensure changes are valid. The agent and the server run in an isolated environment and communicate with the benchmark through HTTP, making testing fully black-box and language-agnostic. We evaluate six agent harnesses paired with seven open-source LLMs across 20 scenarios of 100 turns each and find that: (1) all the tested models fail within 5-6 turns, confirming that vibe-coding-style programming without thorough testing produces bugs; (2) passing test feedback back to the agent and allowing it to retry improves passed turn count by up to 12x; and (3) a good harness is required for strong performance: stronger models exhibit up to a 6x gap between their best and worst harness, while weaker models fail with any harness. We release the benchmark and the generated tasks to enable further research into multi-turn coding agent behavior. Benchmark code and data: github.com/amazon-science/StaminaBench.