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01.
arXiv (CS.AI) 2026-06-15

Unsupervised Learning of Efficient Exploration: Pre-training Adaptive Policies via Self-Imposed Goals

arXiv:2601.19810v2 Announce Type: replace-cross Abstract: Unsupervised pre-training can equip reinforcement learning agents with prior knowledge and accelerate learning in downstream tasks. A promising direction, grounded in human development, investigates agents that learn by setting and pursuing their own goals. The core challenge lies in how to effectively generate, select, and learn from such goals. Our focus is on broad distributions of downstream tasks where solving every task zero-shot is infeasible. Such settings naturally arise when the target tasks lie outside of the pre-training distribution or when their identities are unknown to the agent. In this work, we (i) optimize for efficient multi-episode exploration and adaptation within a meta-learning framework, and (ii) guide the training curriculum with evolving estimates of the agent's post-adaptation performance. We present ULEE, an unsupervised meta-learning method that combines an in-context learner with an adversarial goal-generation strategy that maintains training at the frontier of the agent's capabilities. On XLand-MiniGrid benchmarks, ULEE pre-training yields improved exploration and adaptation abilities that generalize to novel objectives, environment dynamics, and map structures. The resulting policy attains improved zero-shot and few-shot performance, and provides a strong initialization for longer fine-tuning processes. It outperforms learning from scratch, DIAYN pre-training, and alternative curricula. Code is available at: https://github.com/Octavio-Pappalardo/ulee-jax

02.
arXiv (CS.CL) 2026-06-15

The Coin Flip Judge? Reliability and Bias in LLM-as-a-Judge Evaluation

Authors:

LLM-as-a-Judge is now widely used to rank model outputs, train reward models, and populate public leaderboards, but its run-to-run reliability remains under-characterized. We study repeated identical evaluations on 29 tasks spanning 10 categories using two OpenAI judge models (GPT-4o-mini and GPT-4.1-mini), with 50 pairwise trials and 50 pointwise trials per question, supplemented by temperature and prompt-sensitivity ablations. Across judges, pairwise preferences flip on average 13.6% of the time, with 28% of questions exceeding a 20% flip rate and one question reaching 56%. GPT-4o-mini also exhibits a significant first-position bias (72% A-majority, p = 0.024). At the same time, mean pointwise score gaps are small (0.19–0.36 on a 10-point scale) and not statistically significant in aggregate, producing a pairwise–pointwise gap: judges frequently choose a winner even when their own scalar scores provide little evidence of a meaningful quality difference. Beyond within-judge instability, cross-judge agreement is only 76% ($\kappa = 0.51$), semantically equivalent prompt templates change majority outcomes in 25% of tested cases, and deterministic decoding reduces but does not eliminate inconsistency. A reliability curve analysis shows that, in our dataset, 11 repeated trials are needed for a majority vote to recover the 50-trial reference verdict with 95% probability on average, rising to 15 for high-variance questions. These findings suggest that single-trial LLM judging is often too noisy for high-stakes evaluation, and that multi-trial aggregation, position randomization, and explicit uncertainty reporting should be standard practice. Because both judges are from a single provider, cross-provider replication remains an important next step.

03.
arXiv (CS.CV) 2026-06-15

Efficient Online 3D Multi-Camera Multi-Object Tracking and Pose Estimation

This paper proposes a fast and online method for jointly performing 3D multi-object tracking and pose estimation using multiple monocular cameras. Our algorithm requires only 2D bounding box and pose detections, eliminating the need for costly 3D training data or computationally expensive deep learning models. Our solution is an efficient implementation of a Bayes-optimal multi-object tracking filter, enhancing computational efficiency while maintaining accuracy. We demonstrate that our algorithm is significantly faster than state-of-the-art methods without compromising accuracy, using only publicly available pre-trained 2D detection models. We also illustrate the robust performance of our algorithm in scenarios where multiple cameras are intermittently disconnected or reconnected during operation.

04.
arXiv (quant-ph) 2026-06-19

Phase locking nuclear spins in silicon with spin-orbit coupling

arXiv:2606.20340v1 Announce Type: new Abstract: Because they have such long coherence times, nuclear spins have extraordinary potential for use in quantum information processing devices. However, coherent nuclear spin control generally requires external phase references, such as microwave control fields. Here, we phase-lock a $^{29}$Si nuclear spin ensemble in a silicon quantum dot using only the internal electronic spin-orbit coupling as a phase reference. When driven with the quantum-dot electrons, the nuclear spins align themselves to a phase determined by the electronic spin-orbit coupling and the timing of the drive protocol. This enables us to measure the coherent precession and inhomogeneous dephasing of the nuclear spins. We corroborate our results with detailed numerical simulations of the many-body electron nuclear system. Our work opens new routes for coherently controlling solid-state nuclear spin ensembles.

05.
arXiv (CS.CL) 2026-06-15

ScoreGate: Adaptive Chunk Selection for Retrieval-Augmented Generation via Dual-Score Statistical Fusion

Fixed-cardinality retrieval injects a constant top-K chunks into the generator regardless of query complexity, causing over-retrieval for narrow queries and under-retrieval for compositional ones. We describe ScoreGate, a lightweight score-space decision mechanism that controls retrieval cardinality at inference time using two scores already produced by the standard pipeline: bi-encoder similarity s_i and cross-encoder reranker score r_i, with no additional model inference calls required. Its core insight is that cross-encoder affirmation can rescue semantically relevant chunks that bi-encoder retrieval ranks poorly due to vocabulary mismatch – a failure mode unaddressed by fixed-K or single-score thresholding. On MS MARCO (200 dev queries), ScoreGate achieves MRR@10 = 0.401 with 35% fewer retained chunks than Standard Top-K. On an internal benchmark (n=300, Fleiss' kappa=0.87), ScoreGate observed zero false positives (95% CI [96.4%, 100%]) at 97.77-99.34% recall, with 34.8% fewer tokens per query and only 31ms added latency. Results on both MS MARCO and real-world production traffic suggest that adaptive retrieval cardinality can improve retrieval efficiency without degrading retrieval quality.

06.
bioRxiv (Bioinfo) 2026-06-11

A high-quality chromosome-scale reference genome assembly for Asparagus racemosus var. CIM-Shakti (Shatavari), a medicinal plant of Ayurvedic importance

Asparagus racemosus Wild., commonly known as Shatavari, is an important medicinal plant in Ayurveda and is valued for its steroidal saponins, particularly shatavarin compounds, which contribute to its adaptogenic, galactagogue, immunomodulatory, and therapeutic properties. Despite its medicinal and economic importance, genomic resources for this species have remained limited, restricting molecular breeding, pathway discovery, and comparative evolutionary studies within Asparagaceae. Here, we report a high quality chromosome scale reference genome assembly of A. racemosus var. CIM Shakti generated using PacBio HiFi long read sequencing and Omni C chromatin conformation scaffolding. The pseudo haploid assembly spans 817 Mb across 53 scaffolds, with a scaffold N50 of 98.50 Mb, L50 of 5, and a largest scaffold of 113.80 Mb. Ten major chromosome scale pseudomolecules were resolved, corresponding to the haploid chromosome complement of A. racemosus. The assembly showed high gene space completeness, with BUSCO completeness of 99.8% against the Eukaryota dataset and 98.0% against the Embryophyta dataset. BlobToolKit profiling further supported assembly quality, with GC content of approximately 39 to 40% and no major evidence of contamination. EDTA based repeat annotation identified 580.93 Mb of interspersed repetitive elements, accounting for 71.06% of the 817.57 Mb genome assembly. The repeat landscape was dominated by LTR retrotransposons, particularly Gypsy elements, which accounted for 25.01% of the assembly, followed by unclassified LTR elements at 26.58% and Copia elements at 4.84%. Structural and functional annotation identified 29,199 protein coding genes represented by 29,199 transcript models, 138,433 exons, and 125,201 CDS features. The annotation was structurally robust, with an average gene length of 4,605.1 bp, 4.74 exons per transcript, and 97.80% of transcripts containing multiple exons. The CIM Shakti reference genome provides a foundational genomic resource for investigating steroidal saponin biosynthesis, sex chromosome evolution, repeat driven genome expansion, and comparative genomics in Asparagaceae. This assembly will support future studies on medicinal trait improvement, conservation genomics, and genomics assisted breeding of climate resilient Shatavari cultivars.

07.
arXiv (CS.CL) 2026-06-11

Beyond Fully Random Masking: Attention-Guided Denoising and Optimization for Diffusion Language Models

Diffusion large language models (dLLMs) offer an efficient alternative to autoregressive models through parallel decoding, yet existing post-training methods largely rely on random masking strategies that overlook intrinsic token dependencies. In this work, we present an empirical analysis of attention in dLLMs and show that tokens attending more strongly to unmasked context exhibit greater generation stability and play a critical role in reasoning. Motivated by these findings, we propose AGDO, an attention-guided denoising and optimization framework that aligns both training and optimization with attention-derived dependencies. AGDO determines the denoising order based on attention structure and emphasizes attention-critical tokens during supervised fine-tuning and reinforcement learning. Experiments on mathematical and coding benchmarks demonstrate that AGDO consistently improves reasoning performance, outperforming state-of-the-art post-training methods for dLLMs.

08.
bioRxiv (Bioinfo) 2026-06-19

Perturbation Curve models continuous transcriptional response trajectories and improves prediction of genetic modulations

Single-cell CRISPR screens, Perturb-seq, have revolutionized functional genomics by revealing biological causality. However, although perturbation assignments are typically represented as discrete labels, the cell-level effective strength of perturbations is often continuous and diverse. Current analytical frameworks struggle to decouple the variability in perturbation strength from the diversity of downstream responses. Here, we present Perturbation Curve (PertCurve), a nonlinear, curve-based computational framework that models the trajectories of transcriptomic responses by explicitly incorporating diverse perturbation magnitudes and strengths. By ordering cells by perturbation strength, we demonstrate that PertCurve accurately recapitulates the response magnitudes and reveals the distinct modularity and asynchrony patterns of downstream gene behaviors. These patterns are categorized into archetypes, including proportional, sensitive, and threshold responses. By applying this framework across CRISPRi/a modalities, we identify universal response patterns in viral infection, apoptosis, and proliferation genes, and reveal previously overlooked context-specific regulatory features in cell differentiation. Finally, incorporating PertCurve into perturbation prediction models and evaluation metrics enhances predictive performance, delivering actionable insights for refining established models.

09.
arXiv (CS.LG) 2026-06-12

Scale Buys Interpolation, Structure Buys a Horizon: Certified Predictability for Equivariant World Models

Authors:

arXiv:2606.13092v1 Announce Type: new Abstract: Scale buys interpolation; structure buys a certified horizon. A world model's average error says nothing about whether a particular prediction can be trusted, or for how long. For equivariant latent world models we give a computable, multi-step certificate of the predictable horizon: $T$-step rollout error is provably constant over each symmetry orbit (Theorem A) and stratified channel-by-channel by the predictor's Lyapunov spectrum, $T_j(\epsilon)\sim\log(1/\epsilon)/\lambda_j$. The horizon is two-sided – a matching lower bound makes approximate equivariance provably horizon-limited – and the certificate is exclusive to structure: orbit-constant error characterizes equivariance, so no non-equivariant model has it at any scale. Empirically, on 40-D Lorenz-96 only a $\mathbb{Z}_N$-equivariant network recovers the full Lyapunov spectrum ($R^2{=}0.98$); dense and recurrent baselines fail. Because the spectrum is faithful, the certificate acts, a priori: under a fixed sensing budget a $c\times$-inflated certificate provably needs $c\times$ the budget, and the equivariant certificate meets a budget its inflated dense counterpart cannot – with zero calibration data. The same read-out, unchanged, audits public pretrained world models training-free: TD-MPC2 checkpoints land on the certificate's own scope taxonomy – calibrated where strongly expansive (ratio 0.94-1.02), optimistic where weakly expansive, correctly abstaining where contracting – a map a deployed monitor replicates cell-by-cell, out-of-sample. Across the official 1M-317M multitask ladder, calibration does not improve with parameters. On V-JEPA 2-AC (1B, real robot data) the measured cross-check correctly overrides an over-promising tangent spectrum – the cross-validated audit, not the raw number, is the deployable object. Scale buys interpolation, not a calibrated horizon.

10.
arXiv (CS.AI) 2026-06-19

Uncertainty-Aware Reward Modeling for Stable RLHF

arXiv:2606.19818v1 Announce Type: cross Abstract: Reinforcement learning from human feedback (RLHF) aligns large language models by training reward models on preference data and optimizing policies to maximize predicted rewards. However, this pipeline faces two fundamental challenges: (1) reward models cannot signal when their predictions are unreliable, since they usually act as deterministic point estimators; and (2) modern group-based policy optimization can amplify unreliable reward signals, as exemplified by GRPO's uniform treatment of rewards during advantage computation. As policies explore increasingly diverse responses, these two limitations create a critical vulnerability: unreliable reward estimates may be granted disproportionate influence, triggering severe reward hacking. We propose Uncertainty-Aware Reward Modeling (UARM), which equips reward models with calibrated uncertainty via quantile-based conformal prediction and reweights GRPO advantages through heteroscedastic variance decomposition. Experiments across HelpSteer, UltraFeedback, and PKU-SafeRLHF demonstrate that UARM significantly improves reward model calibration, reduces reward hacking, and enhances downstream alignment quality compared to standard GRPO and uncertainty-agnostic baselines.

11.
medRxiv (Medicine) 2026-06-18

Personalizing Suicide Risk Assessment: Machine Learning Extraction of Cross-Modal Interactions Between Psychosocial and Demographic Factors in Veterans

Background: Veterans face an elevated risk of suicide compared to the general population, motivating national efforts to develop predictive models that can guide proactive care. Current models used by the U.S. Department of Veterans Affairs (VA) rely primarily on structured electronic health record (EHR) data, though clinical notes contain rich contextual information that can be quantified using natural language processing (NLP) to derive psychosocial variables that may improve risk detection. Machine learning methods, particularly classification and regression trees (CART), can also uncover interactions between clinical and psychosocial variables, enabling identification of patient characteristics that modify suicide risk factors. However, integrating structured and unstructured data presents challenges because NLP features often greatly outnumber traditional clinical variables, potentially biasing interaction discovery. In prior work, we addressed this imbalance by introducing a weighted CART framework that balances structured variables with NLP-derived psychosocial features from semantic lexicons (SEANCE). While effective, semantic approaches summarize language into predefined constructs and may overlook important lexical variation present in clinical narratives. Methods: In this study, we extend that framework by replacing semantic features with a high-dimensional bag-of-words (BoW) representation of clinical notes and by evaluating models across cohorts defined by structured suicide risk stratification (low, medium, high) and varying temporal lookback windows. Using a cohort of 27,241 veterans, we analyzed clinical documentation collected up to 30, 90, or 270 days prior to death (or a matched index date for controls), enabling temporally flexible risk modeling. XGBoost models were trained to balance structured and unstructured features and identify cross-modal interactions between textual and clinical variables. Results: When incorporated into generalized linear models, these interactions improved predictive performance, particularly among low- and medium-risk patients, and substantially reduced the performance gap between interpretable and more complex models. Notably, the BoW representation outperformed our prior semantic index-based approach. Discussion and Conclusions: Together, these findings demonstrate the utility of interpretable NLP methods for uncovering clinically meaningful interactions between psychosocial and demographic factors in suicide risk and establish a strong benchmark for future deep learning approaches aimed at capturing richer contextual and temporal information from clinical narratives.

12.
arXiv (CS.AI) 2026-06-15

Sensitivity Shaping for Latent Modeling

arXiv:2606.14585v1 Announce Type: cross Abstract: Generative dynamics models enable planning in challenging robotic systems, but safe deployment requires reliably detecting policy-induced out-of-distribution (OOD) transitions. Existing methods typically treat the learned dynamics as fixed and attach post hoc support surrogates. We show that these surrogates can fail when the dynamics are locally insensitive to critical action choices: unsupported control actions may produce latent predictions that resemble demonstrated transitions, suppressing OOD signals despite large true predictive errors. To address this, we introduce support-conditioned control-sensitivity regularization, which promotes sensitive local response to control input changes in learned dynamics in high-support training regions. This preserves control-induced variation while limiting unstable extrapolation due to weak empirical support. Experiments in vision-based obstacle avoidance, manipulation, and real-robot navigation show improved OOD detection and safer closed-loop planning.

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

BSViT: A Burst Spiking Vision Transformer for Expressive and Efficient Visual Representation Learning

Spiking Vision Transformers (S-ViTs) offer a promising framework for energy-efficient visual learning. However, existing designs remain limited by two fundamental issues: the restricted information capacity of binary spike coding and the dense token interactions introduced by global self-attention. To address these challenges, this work proposes BSViT, a burst spiking-driven Vision Transformer featuring a Dual-Channel Burst Spiking Self-Attention (DBSSA) mechanism. DBSSA encodes queries with binary spikes and keys with burst spikes to enhance representational capacity. The value pathway adopts dual excitatory and inhibitory binary channels, enabling signed modulation and richer spike interactions. Importantly, the entire attention operation preserves addition-only computation, ensuring compatibility with energy-efficient neuromorphic hardware. To further reduce spike activity and incorporate spatial priors, a patch adjacency masking strategy is introduced to restrict attention to local neighborhoods, resulting in structure-aware sparsity and reduced computational overhead. In addition, burst spike coding is systematically integrated across the network to increase spike-level representational capacity beyond conventional binary spiking. Extensive experiments on both static and event-based vision benchmarks demonstrate that BSViT consistently outperforms existing spiking Transformers in accuracy while maintaining competitive energy efficiency.

14.
arXiv (CS.AI) 2026-06-19

Physical Atari: A Robust and Accessible Platform for Real-time Reinforcement Learning on Robots

arXiv:2606.19357v1 Announce Type: cross Abstract: We built a robot called the Robotroller that actuates an Atari CX40+ controller and a device called the Atari Devbox that renders the game frame and the reward signal from the Arcade Learning Environment on a screen. The Robotroller and the Atari Devbox, together with an off-the-shelf camera and a desktop computer, constitute a system that can be used to study reinforcement learning algorithms in the physical world. We call the full system Physical Atari. In this paper, we detail the key decisions that make Physical Atari a robust and accessible platform. To make the system robust, we designed the Robotroller so that all movement is done through bearings, which reduces wear. Additionally, we wrote software that monitors the state of the servos at a high frequency and intervenes to limit stress. To make the system accessible, we used affordable off-the-shelf components and parts that can be manufactured using consumer 3D printers. Physical Atari can be built for under $1,000 and has been used for weeks of non-stop reinforcement learning experiments without any mechanical failures. We used it to validate that reinforcement learning algorithms can learn directly on robots and show that even small distribution shifts between learning and deployment can significantly degrade the performance of policies. Our results underscore the importance of on-device adaptation for strong performance on robots.

15.
arXiv (CS.AI) 2026-06-18

Something from Nothing: Data Augmentation for Robust Severity Level Estimation of Dysarthric Speech

arXiv:2603.15988v3 Announce Type: replace-cross Abstract: Dysarthric speech quality assessment (DSQA) is critical for clinical diagnostics and inclusive speech technologies. However, subjective evaluation is costly and difficult to scale, and the scarcity of labeled data limits robust objective modeling. To address this, we propose a three-stage framework that leverages unlabeled dysarthric speech and large-scale typical speech datasets to scale training. A teacher model first generates pseudo-labels for unlabeled samples, followed by weakly supervised pretraining using a label-aware contrastive learning strategy that exposes the model to diverse speakers and acoustic conditions. The pretrained model is then fine-tuned for the downstream DSQA task. Experiments on five unseen datasets spanning multiple etiologies and languages demonstrate the robustness of our approach. Our Whisper-based baseline significantly outperforms SOTA DSQA predictors such as SpICE, and the full framework achieves an average SRCC of 0.761 across unseen test datasets.

16.
arXiv (CS.CV) 2026-06-17

Response-Aware Multimodal Learning for Post-Treatment Visual Acuity Forecasting

Long-term visual acuity (VA) forecasting after anti-VEGF therapy is important for counseling and follow-up planning in diabetic macular edema (DME), yet remains challenging when only early post-treatment findings are available. While prior OCT-based methods mainly focus on short-term response or single-endpoint prediction, multi-horizon VA forecasting from early longitudinal data remains insufficiently under-explored. In this study, we assembled a real-world cohort of 188 anti-VEGF–treated DME patients with paired baseline and month-1 OCT scans, along with tabular OCT-derived biomarkers and non-imaging clinical variables. Using only these early data, we formulate a multi-horizon VA forecasting problem aimed at predicting visual outcomes at 3, 6, 12, 18, and 24 months, reflecting clinically meaningful follow-up intervals. We propose ReVA, a response-aware multimodal framework that combines baseline and month-1 OCT features with tabular variables to capture disease status and early treatment response. ReVA integrates spatial OCT attention, dependency-aware tabular encoding, and cross-modal fusion to predict patient-specific long-term VA trajectories. The proposed framework achieves MAE=0.1246, RMSE=0.1621, and R^2=0.6064 for 24-month VA prediction, with consistent performance across all forecast horizons. Our findings show that incorporating early treatment-response signals enables clinically meaningful long-term visual acuity forecasting, supporting data-driven decision support for routine anti-VEGF management. Code and pretrained models will be released on https://github.com/nguyenpbui/ReVA.

17.
arXiv (CS.AI) 2026-06-18

SHIFT: Semantic Harmonization via Index-side Feature Transformation for Multilingual Information Retrieval

arXiv:2606.18801v1 Announce Type: cross Abstract: With the rapid expansion of massive multilingual corpora, Multilingual Information Retrieval (MLIR) has emerged as a critical technology for global information access. MLIR enables users to retrieve semantically relevant documents from multilingual text collections using a single-language query. However, recent multilingual dense retrieval models often exhibit a strong preference for documents in the same language as the query. This leads to severe language bias, where top-ranked results are dominated by documents of specific languages, even when documents in other languages contain more semantically relevant information. To address this issue, we propose SHIFT, a training-free method applicable in the indexing stage. Specifically, SHIFT utilizes parallel translation pairs to estimate a relative language vector for each target language with respect to a source language. Subsequently, SHIFT corrects the language-specific offset by subtracting this relative language vector from document embeddings during indexing. Our comprehensive evaluation across four MLIR benchmarks and diverse dense retrieval models confirms that SHIFT can effectively mitigate language bias and enhance MLIR performance.

18.
arXiv (CS.AI) 2026-06-17

Extracting Semantics: LLM-Guided Automatic Population of Robot Ontology from URDF

arXiv:2606.17073v1 Announce Type: cross Abstract: While commonsense knowledge may suffice for virtual agents, embodied robots interacting with humans require grounded and semantically rich representations of both their environment and their own physical embodiment. In cognitive robotics, ontologies are effective for integrating such heterogeneous knowledge to enable explainable reasoning, even during continuous knowledge updates. Yet, their manual construction remains a bottleneck. We present a preliminary approach for the automatic generation of robot semantic abstractions by transforming Unified Robot Description Format (URDF) models into populated ontologies. Although URDF files provide structural and kinematic descriptions, their identifiers often require commonsense interpretation to recover meaningful semantics, a task at which Large Language Models (LLMs) excel. Our pipeline leverages LLMs to infer semantic relationships by prompting them with concepts from an existing ontology, ensuring the final classification remains aligned with the formal model. To improve reliability, the pipeline combines majority voting across multiple LLM queries along with syntactic and schema-level validation to ensure that generated outputs conform to the expected representation format and ontology constraints. We evaluate the approach on multiple robot descriptions and discuss the generated abstractions. Initial results indicate that the proposed method can effectively bridge the gap between low-level robot descriptions and the structured, grounded knowledge representations required for human-robot interaction.

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

CzechDocs: A Multiway Parallel Dataset of Formatted Documents for Minority Languages in Czechia

We present CzechDocs, a multiway parallel dataset of formatted documents (HTML, DOCX, and PDF) covering Czech and minority languages used in Czechia-primarily Ukrainian and English, with smaller portions of Vietnamese, Russian and other languages. The dataset is designed to support the evaluation of machine translation systems that aim to preserve document formatting during translation. We provide a comparison of the most common approaches to format-preserving machine translation on a validation subset of the dataset. This validation split, together with the evaluation toolkit, is publicly released for further research. A held-out test split will be reserved for a future shared task focused on document-level translation with formatting preservation.

20.
arXiv (math.PR) 2026-06-19

On creating convexity in high dimensions

arXiv:2502.10382v3 Announce Type: replace-cross Abstract: Given a subset $A$ of $\mathbb{R}^n$, we define \begin{align*} \mathrm{conv}_k(A) := \left\{ \lambda_1 s_1 + \cdots + \lambda_k s_k : \lambda_i \in [0,1], \sum_{i=1}^k \lambda_i = 1 , s_i \in A \right\} \end{align*} to be the set of vectors in $\mathbb{R}^n$ that can be written as a $k$-fold convex combination of vectors in $A$. Let $\gamma_n$ denote the standard Gaussian measure on $\mathbb{R}^n$. We show that for every $\varepsilon > 0$, there exists a subset $A$ of $\mathbb{R}^n$ with Gaussian measure $\gamma_n(A) \geq 1- \varepsilon$ such that for all $k = O_\varepsilon(\sqrt{\log \log(n)})$, $\mathrm{conv}_k(A)$ contains no convex set $K$ of Gaussian measure $\gamma_n(K) \geq \varepsilon$. This result acts as a complement to the recent affirmative resolution of Talagrand's convexity conjecture by Hua, Song, and Tudose, which states that a universal dilation of the threefold Minkowski sum $A+A+A$ of a large set $A$ guarantees a large convex subset. Our approach utilises concentration properties of random copulas and the application of optimal transport techniques to the empirical coordinate measures of vectors in high dimensions.

21.
arXiv (CS.AI) 2026-06-16

Auditing Reward Hackability in Code RL Training Environments

arXiv:2606.16062v1 Announce Type: new Abstract: We measure the rate at which code RL environments accept incorrect solutions as correct. On a 49-task sample of SWE-bench Verified, 28.5% of tasks have test suites weak enough that a Docker-verified incorrect patch passes them. On 20 R2E-Gym tasks across 6 repositories, the same pipeline at single-shot exploit generation yields 25.0%. A random-effects meta-analysis over 134 frontier model submissions to SWE-bench Verified finds, within the same human-rated difficulty stratum, model Pass@1 is +14.14 percentage points higher on flagged-hackable tasks than on robust ones (95% CI [+11.80, +16.48]; one-sided p < 10^-6; I^2 = 0%; 123 of 134 models positive). We then describe a procedure for hardening the broken tasks. An inline LLM judge with a Docker gold-sanity gate runs each generated test against the gold solution before the judge is consulted. On the 11 broken tasks in the audit, the gate flags 65 of 105 decisive LLM-generated tests as failing on the gold patch itself, a 61.9% per-augmentation defect rate the LLM judge alone misses. With diversity-biased retry, the loop converges 9 of 11 tasks to a gated upgrade.

22.
arXiv (CS.LG) 2026-06-16

Towards Data-Efficient Cross-Device Generalization of Grad-Shafranov Equilibria via Transfer Learning Neural Operator

arXiv:2606.15512v1 Announce Type: new Abstract: Real-time reconstruction of magnetohydrodynamic equilibria is essential for plasma shaping, stability assessment and feedback control in magnetic confinement fusion. However, Grad-Shafranov equilibrium calculations remain largely device-specific and iterative, limiting their use in latency-constrained control settings. Existing neural approaches can accelerate individual equilibrium predictions, but they do not generally provide reusable models across changing plasma boundaries or tokamak geometries. Here we show that equilibrium reconstruction can be recast as a cross-device operator learning problem. We develop a domain-specific neural operator framework that maps geometry and profile parameters directly to the poloidal flux field, replacing repeated solve-on-demand computation with amortized operator inference. Using the analytically tractable Solov'ev family as a controlled Grad-Shafranov testbed, we generate equilibria across eight geometrically distinct tokamak-like configurations and benchmark five neural operator architectures under four transfer-learning strategies. Single-geometry pretraining gives poor transfer to unseen devices, whereas multi-geometry pretraining enables data-efficient adaptation. The Wavelet Neural Operator gives the strongest cross-geometry performance, reaching mean relative L2 errors below 4% with 100 labelled target equilibria and below 2% with full fine-tuning. The predicted magnetic fields satisfy the divergence-free constraint to numerical precision, and four architectures achieve millisecond or sub-millisecond inference. These results identify neural operator pretraining as a route towards reusable, real-time equilibrium inference across fusion device configurations.

23.
arXiv (math.PR) 2026-06-18

Denoising Distances in Metric Measure Spaces

arXiv:2606.18301v1 Announce Type: cross Abstract: Recent work studied the problem of finding clusters and denoising pairwise distances from noisy distances of points sampled on a manifold. We study the same problems in more general metric measure spaces under \lowerphiregularity{}. We give an algorithm that extracts large localized clusters around every sampled point and uses them to denoise distances to any fixed accuracy, with near-linear running time in the dense fixed-accuracy regime. We also show how to achieve much higher accuracy with a non-efficient algorithm. This suggests that unlike the Riemannian case, denoising to higher accuracy in more general metric spaces has a statistical-computational gap.

25.
arXiv (math.PR) 2026-06-17

Critical spectral behavior and large deviations for geometric $\alpha$-stable processes

arXiv:2606.17501v1 Announce Type: new Abstract: In this paper, we study the Schrödinger-type operator associated with geometric stable processes on $\mathbb{R}^{d}$, especially the differentiability of spectral function. Let $\mathcal{H}$ be the generator of the geometric stable process and $\mu$ a smooth measure on $\mathbb{R}^{d}$. Then the spectral function $C(\theta)$ is defined as $C(\theta) = -\inf \sigma(-\mathcal{H} - \theta \mu)$, where $\sigma(\mathcal{A})$ denotes the spectrum of $\mathcal{A}$ and $\theta$ is a real parameter. Since the geometric stable process exhibits severe local singularities in its Lévy measure, its transition semigroup lacks ultracontractivity, which invalidates classical methods for proving the differentiability. To overcome this obstacle, we use the compact embedding of the extended Dirichlet space into $L^2(\mu)$. As a primary application of this differentiability, we establish a large deviation principle for a positive continuous additive functional associated with the smooth measure $\mu$.