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

Trusted Uncertainty in Large Language Models: A Unified Framework for Confidence Calibration and Risk-Controlled Refusal

Deployed language models must decide not only what to answer but also when not to answer. We present UniCR, a unified framework that turns heterogeneous uncertainty evidence including sequence likelihoods, self-consistency dispersion, retrieval compatibility, and tool or verifier feedback into a calibrated probability of correctness and then enforces a user-specified error budget via principled refusal. UniCR learns a lightweight calibration head with temperature scaling and proper scoring, supports API-only models through black-box features, and offers distribution-free guarantees using conformal risk control. For long-form generation, we align confidence with semantic fidelity by supervising on atomic factuality scores derived from retrieved evidence, reducing confident hallucinations while preserving coverage. Experiments on short-form QA, code generation with execution tests, and retrieval-augmented long-form QA show consistent improvements in calibration metrics, lower area under the risk-coverage curve, and higher coverage at fixed risk compared to entropy or logit thresholds, post-hoc calibrators, and end-to-end selective baselines. Analyses reveal that evidence contradiction, semantic dispersion, and tool inconsistency are the dominant drivers of abstention, yielding informative user-facing refusal messages. The result is a portable recipe of evidence fusion to calibrated probability to risk-controlled decision that improves trustworthiness without fine-tuning the base model and remains valid under distribution shift.

02.
arXiv (quant-ph) 2026-06-12

From 2D Yang-Mills to Calogero-Sutherland via a colored particle

arXiv:2606.13388v1 Announce Type: cross Abstract: We study Yang-Mills theory coupled to a particle on a cylinder, where gauge invariance and compactness reduce the dynamics to a finite dimensional quantum system. In the Abelian case, this yields a model equivalent to the Landau problem on a torus, with a degenerate ground state structure. We generalize this construction to non-Abelian gauge groups and show that, for SU(N), the system reduces to a one dimensional quantum many body problem with a singular Calogero-Sutherland-type interaction.

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

Reliability of Probabilistic Emulation of Physical Systems

arXiv:2606.12997v1 Announce Type: new Abstract: Two dominant approaches have emerged for generating probabilistic forecasts of physical systems: generative models, such as diffusion or flow matching; and ensembles of deterministic models with stochasticity injected, trained using the continuous ranked probability score (CRPS) loss. While both approaches have demonstrated strong predictive accuracy, the reliability of their uncertainties has not been systematically assessed. We address this gap by developing a framework to evaluate both approaches across diverse 2D spatiotemporal physical systems, under matched model size and computational budget. We assess the reliability of probabilistic emulation by inspecting the empirical coverage of predictive intervals, while also considering accuracy and computational efficiency metrics. CRPS-trained ensembles typically achieve more reliable uncertainties on both single-step prediction and autoregressive rollouts, demonstrating better coverage than the standard alternative of training generative models in a latent space. Moreover, the CRPS approach offers significantly faster inference. When generative models are trained in ambient rather than a compressed latent space, which is often infeasible for high-dimensional problems, they exhibit comparable coverage to CRPS-trained ensembles, though with substantially larger inference latency. In contrast, when CRPS-trained ensembles are trained in latent space they do not show a marked degradation in coverage with respect to ambient space. Both generative models and CRPS-trained ensembles demonstrate good predictive accuracy. To facilitate future research and application, we release AutoCast, a modular framework implementing both generative models and CRPS-trained ensembles, alongside AutoSim, a flexible dataset generation package for rapid prototyping.

04.
arXiv (CS.AI) 2026-06-12

GeoNatureAgent Benchmark: Benchmarking LLM Agents for Environmental Geospatial Analysis Across Frontier and Open-Weight Foundation Models

arXiv:2606.12821v1 Announce Type: new Abstract: Environmental scientists spend disproportionate effort on data wrangling rather than analysis, and AI agents that automate geospatial workflows remain unvalidated: no benchmark evaluates agents operating through structured tool calling against real APIs. We introduce the GeoNatureAgent Benchmark, the first benchmark for environmental analysis agents that operate via structured tool calls to a production-style geospatial API. It comprises 93 tasks across 18 categories, covering municipality analysis, multi-turn conversation, spatial reasoning, cross-indicator synthesis, error handling and recovery, ranking, comparison, multilingual understanding, habitat analysis, and task rejection. Tasks are evaluated against an open, self-hostable API serving three environmental indicators across Spain and Portugal via sixteen tools. We evaluate seven LLMs (Claude Sonnet 4, DeepSeek V3.2, GLM-5, Gemini 2.5 Pro, Qwen3-235B, GPT-OSS-120B, Llama 4 Scout) under three temperature-1.0 seeds, reporting capability and per-case cost as orthogonal axes. We find: (1) Claude Sonnet 4 leads at 60.8% +/- 0.8%, followed by DeepSeek V3.2 at 56.3% +/- 3.1%, with no other model above 51%; (2) the cost-accuracy Pareto frontier is occupied mostly by open-weight models, with DeepSeek V3.2 offering 93% of Claude's capability at 11x lower cost ($0.011/case); (3) comparison tasks remain universally unsolved (0% on close-value comparisons), exposing systematic reasoning limits; and (4) structured tool calling against a real API is more discriminative than general-purpose GIS benchmarks, with accuracies 25-35 points lower. We further show extensibility by integrating BigEarthNet V2 land cover for Portugal alongside Spanish CO2 and erosion indicators. The benchmark, harness, and self-hostable API are publicly available.

05.
arXiv (math.PR) 2026-06-12

Dimension-free Markov–Bernstein inequalities for product measures

作者:

arXiv:2606.13575v1 Announce Type: cross Abstract: We study dimension-free Markov–Bernstein inequalities for polynomials with respect to product probability measures. In the Gaussian case, for $p\ge4$, we prove that \[ \|\nabla f\|_{L^p(\gamma^n)} \le C(p)d^{\frac12+\theta_p} \|f\|_{L^p(\gamma^n)} \] for every polynomial $f$ of degree at most $d$, where $\theta_p\le \frac{2}{3p}$ and $\theta_p=0$ whenever $p$ is an even integer. Thus, for even integer exponents, we establish the sharp dependence on the degree conjectured by Eskenazis–Ivanisvili. For general $p\ge4$, the estimate improves upon their dimension-free inequality. We also obtain dimension-free Markov–Bernstein inequalities with sharp dependence on the degree for even integer exponents beyond the Gaussian setting. We first prove such estimates for the uniform distribution on the unit cube and then extend them to products of absolutely continuous measures with unimodal densities. Finally, we treat products of one-dimensional Freud measures with densities proportional to $e^{-|t|^{2m}}$.

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

Extremal representations of functions of matrices and applications to multivariate prediction

arXiv:2606.19359v1 Announce Type: cross Abstract: Motivated by two seminal results of multivariate prediction theory by Helson and Lowdenslager and by Wiener and Masani we prove extremal representations of functions of matrices and derive their prediction-theoretic consequences. We also sketch a way to obtain matricial inequalities from our results. The main goal of the paper is the computation of the infimum of a set of values of the form $tr(A \Delta A^*)$, where $\Delta$ is a given non-negative Hermitian $n \times n$ matrix and the choices for $A$ exhauste a certain set of $n \times n$ matrices. In particular, we focus on norm-bounded unit spheres with certain types of properties of unitary invariance, what allows an application of the theory of majorization.

07.
arXiv (CS.LG) 2026-06-16

The Information-Theoretic Benefit of Shared Representations under Orthogonality Constraints

arXiv:2606.16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models. Empirically, exploiting similarity across different problems, instead of solving them individually, can significantly improve overall performance. While the generalization and sample complexity properties of multitask learning have been widely studied, the parametric complexity of joint approximation in comparison to separate approximation remains less well understood. The question is particularly relevant in modern deep learning, where models are increasingly required to satisfy structural constraints such as equivariance, conservation laws, or orthogonality. We prove lower and upper bounds on the description-length for separate and joint approximation classes, respectively, in uniform norm. We build a class of orthogonal functions by composing a shared hard feature, realized by a Rademacher-Haar wavelet series, with Sawtooth-Walsh readouts to enforce orthogonality of output coordinates. The dyadic tree structure of the Rademacher-Haar wavelet concentrates the approximation hardness in the common feature component, while the readouts act as task-specific heads. Using an information-theoretic framework, we obtain a sharp gap between the optimal approximation rates achievable by joint and separate coding. Finally, we realize this separation in a neural network model using Heaviside activations via reduction to triangle-wave approximation. Our results show that even under an orthogonality constraint joint approximation requires strictly fewer bits in compositional architectures, provided the tasks share a latent hard feature. This provides theoretical insight into the description-length-efficiency of compositional multi-output architectures and clarifies how neural networks can retain expressivity under geometric constraints.

08.
arXiv (CS.LG) 2026-06-12

Let's Ask Gauss: Improved One-Run Privacy Auditing

arXiv:2606.12733v1 Announce Type: new Abstract: Privacy auditing provides an important safeguard by estimating the actual information leaked by a model, thus ensuring that theoretical privacy guarantees hold in practice. We study empirical privacy auditing for differentially private (DP) machine learning, focusing on efficient one-run methods for mechanisms such as DP-SGD. Prior one-run approaches threshold training examples or "canaries" into binary membership guesses, which discards useful information. We show that, in the white-box DP-SGD setting, canary-aligned signals naturally form a sequence of random variables whose normalized sum is asymptotically Gaussian. Leveraging this distributional perspective, we develop a DP-auditing framework that leads to tighter privacy lower bounds from a single training run.

09.
arXiv (CS.AI) 2026-06-19

QueryGaussian: Scalable and Training-Free Open-Vocabulary 3D Instance Retrieval

arXiv:2606.19733v1 Announce Type: cross Abstract: Efficiently retrieving specific 3D instances from large-scale scenes via natural language prompts remains a formidable challenge in multimedia analysis. Existing approaches predominantly follow a "scene-level embedding" paradigm, which requires distilling high-dimensional semantic features into every 3D primitive. This strategy suffers from a fundamental architectural bottleneck: memory and computational costs scale linearly with scene complexity, inevitably triggering out-of-memory (OOM) failures in city-scale environments. To address this barrier, we propose QueryGaussian, a training-free framework for expeditious and scalable open-vocabulary 3D instance retrieval. Unlike holistic semantic distillation, QueryGaussian employs an instance-level query mechanism that decouples semantic understanding from geometric representation. Specifically, we leverage pre-trained 2D vision models to interpret user prompts and lift segmentation masks into 3D via a concurrent maximum-weight association strategy, ensuring semantic-visual consistency. To mitigate projection ambiguity, we introduce a temporal fusion module with multi-stage adaptive density clustering. Experimental results demonstrate that QueryGaussian not only matches the accuracy of state-of-the-art methods but also delivers a decisive efficiency leap, reducing GPU memory usage by over 70% and accelerating inference by 180x. Crucially, QueryGaussian enables expeditious instance retrieval on city-scale scenes containing tens of millions of Gaussians using consumer-grade hardware.

10.
arXiv (CS.CV) 2026-06-15

Relational Retrieval: Leveraging Known-Novel Interactions for Generalized Category Discovery

In this study, we tackle Generalized Category Discovery (GCD) via a Relational Retrieval perspective, explicitly coupling labeled and unlabeled data through bidirectional knowledge transfer. While existing methods treat these sources separately, missing valuable interaction opportunities, we propose Relational Pattern Consistency (RPC) that enables mutual enhancement. RPC employs One-vs-All classifiers for soft ID/OOD decomposition, then introduces two mechanisms: (i) for known-class preservation, we transfer semantic behavioral alignment; (ii) for category discovery, we leverage the insight that samples from the same category maintain invariant relationships with known-class prototypes, transforming unreliable pseudo-labeling into well-defined relational pattern matching. This bidirectional design allows labeled data to guide unlabeled learning while discovering novel categories through their collective relational signatures. Extensive experiments demonstrate RPC achieves state-of-the-art performance on both generic and fine-grained benchmarks.

11.
arXiv (CS.CL) 2026-06-12

Operads for compositional reasoning in LLMs

Question decomposition, i.e. breaking a complex query into simpler sub-queries whose answers are composed to produce a final answer, is a widely used strategy for improving LLM reasoning, yet it currently lacks a rigorous mathematical foundation. In this paper, we propose operads, mathematical structures that model many-in, one-out operations and compositions thereof, as a natural framework for describing question decomposition. We define the questions operad $Q$, in which operations correspond to question templates and composition corresponds to substitution of sub-answers, and show how QA models can be interpreted as algebras over $Q$. Beyond reframing existing practice, this operadic perspective points toward new methods, in particular a notion of operadic consistency, which measures whether a QA model's answers agree across the partial collapses of a question decomposition tree. Empirical evaluation of operadic consistency is reported in our companion paper (Bottman, Liu, and Richardson, 2026), which finds it strongly correlated with accuracy across twelve LLMs and four multi-hop QA datasets and outperforming standard temperature-based self-consistency baselines. We argue that operads are the natural mathematical home for question decomposition, and that invariants such as operadic consistency open new directions for analyzing and improving the reliability of multi-step reasoning.

12.
arXiv (CS.CL) 2026-06-16

Agentic Reinforcement Learning for Search Misaligns Instruction-Tuning

Agentic reinforcement learning (RL) trains large language models to use tools, but its impact on alignment is poorly understood. We study how agentic RL for search affects the alignment of instruction-tuned (IT) models. We find that RL-trained models inherit refusal reasoning by deflecting harmful requests into benign search queries, but this breaks down under a simple diagnostic trigger that elicits a search call before refusal can occur. Under this condition, RL models produce multi-step unsafe search actions and reasoning, reducing search query safety by up to 68.6% in Qwen and Llama models relative to their IT counterparts. The effect generalises across model families, scales, and RL algorithms. To understand why, we identify linear directions in the residual stream that control search query safety, and show that RL training progressively shifts search behaviour toward the harmful end of this direction. We thus propose representation-guided RL training, which adds a reward penalty based on projection toward the harmful search direction. Training on benign data alone, it restores IT-level alignment without reducing task accuracy and requires no additional training data. Together, our work provides the first framework for diagnosing, mechanistically analysing, and mitigating alignment degradation in agentic RL for search.

13.
arXiv (CS.LG) 2026-06-11

SEDULity: A Proof-of-Learning Framework for Distributed and Secure Blockchains with Efficient Useful Work

arXiv:2512.13666v2 Announce Type: replace-cross Abstract: The security and decentralization of Proof-of-Work (PoW) have been well-tested in existing blockchain systems. However, its tremendous energy waste has raised concerns about sustainability. Proof-of-Useful-Work (PoUW) aims to redirect the meaningless computation to meaningful tasks such as solving machine learning (ML) problems, giving rise to the branch of Proof-of-Learning (PoL). While previous studies have proposed various PoLs, they all, to some degree, suffer from security, decentralization, or efficiency issues. In this paper, we propose a PoL framework that trains ML models efficiently while maintaining blockchain security in a fully distributed manner. We name the framework SEDULity, which stands for a Secure, Efficient, Distributed, and Useful Learning-based blockchain system. Specifically, we encode the template block into the training process and design a useful function that is difficult to solve but relatively easy to verify, as a substitute for the PoW puzzle. We show that our framework is distributed, secure, and efficiently trains ML models. We further demonstrate that the proposed PoL framework can be extended to other types of useful work and design an incentive mechanism to incentivize task verification. We show theoretically that a rational miner is incentivized to train fully honestly with well-designed system parameters. Finally, we present simulation results to demonstrate the performance of our framework and validate our analysis.

14.
arXiv (CS.CL) 2026-06-11

A PubMed-Scale Dataset of Structured Biomedical Abstracts

Structured abstracts are important for biomedical literature processing, by facilitating information retrieval, text mining, and knowledge synthesis. However, a vast portion of abstracts indexed in PubMed remain unstructured, presenting a significant bottleneck for downstream text-processing workflows and applications. To resolve this limitation, we introduce Structured PubMed, a comprehensive corpus of section-labeled biomedical abstracts compiled from the complete PubMed database, encompassing over 23.2 million research-article records. The corpus is divided into two distinct subsets: a collection of 5.9 million author-structured abstracts parsed from official XML files, and an automatically labeled collection of 17.2 million originally unstructured abstracts structured via a verbatim-extraction Large Language Model pipeline. Every record is harmonized under a unified five-section schema and mapped to its original PubMed identifier, publication type, and publication date. This dataset can be utilized to train sentence-classification models, benchmark text-segmentation architectures, and perform large-scale, section-specific information extraction at an unprecedented PubMed-wide scale.

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

BrainFusionNet: a deep learning and XAI model to understand local, global, and sequential features of MRI images for improved brain tumour detection

The noise of Magnetic Resonance Imaging MRI poses challenges for Deep Learning DL when tumor boundaries are obscured tumor location and appearance are complex Therefore we develop BrainFusionNet that combines Convolutional Neural Networks CNNs Vision Transformers ViT and Gated Recurrent Units GRUs to extract spatial contextual and sequential features from MRI images for improved brain tumor classification Furthermore explainable AI such as SHAP LIME and GradCAM are integrated to visualise and highlight image regions that contribute to BrainFusionNets decisionmaking process The proposed BrainFusionNet model is evaluated on two publicly available MRI datasets Kfold validation suggests 98 accuracy on both datasets The model was compared with the six stateoftheart SOTA CNNs and transfer learning Among the SOTA CNNs DenseNet121 and VGG16 achieved the highest accuracy of 96 The novelty of BrainFusionNet is that the hybrid model effectively extracts local and global features from MRI images even in smallscale tumor regions and small tumor sizes The model has a balanced sequential CNN architecture to capture lowlevel and deeperlayer features a customized ViT that captures local features stabilizes gradient flow and reduces the risk of vanishing gradients during MRI image training The CNN and ViT outputs are fed into a GRU for final classification Furthermore we analyze pixel intensities to determine whether MRI image quality affects image classification Our findings are very novel in image interpretation as we found that the distribution of pixel intensities in MRI images affects DL performance

16.
arXiv (CS.CV) 2026-06-12

Iterative Visual Thinking: Teaching Vision-Language Models Spatial Self-Correction through Visual Feedback

Vision-language models (VLMs) achieve strong singleshot spatial grounding, yet lack any mechanism to observe and correct their own predictions. We find that naively prompting a VLM to iterate over rendered visualizations of its predictions causes catastrophic failure: Acc@0.5 on referring expression comprehension collapses from 79.6% to 48.7% (a 31 percentage point drop), revealing a fundamental gap between grounding capability and self-correction ability. We propose Iterative Visual Thinking (IVT), a closed-loop framework in which the model predicts a bounding box, observes the prediction rendered on the image, and iteratively refines through visual feedback. A two-phase training recipe closes the self-correction gap: first, we exploit the base model's own predictions as realistic errors and prompt a teacher VLM to generate corrective reasoning traces, yielding supervised data without human annotation; second, we apply Group Relative Policy Optimization (GRPO) with a simple IoU reward to stabilize multi-step refinement. On a mixed benchmark spanning RefCOCOg, Ref-Adv, and Ref-L4 (505 test samples), SFT warm-up with IVT surpasses the single-shot base model on every metric: Acc@0.5 rises to 82.0% (+2.4pp), Acc@0.7 to 74.1% (+3.2pp), and Acc@0.9 to 48.3% (+2.8pp). GRPO further reduces per-step IoU degradation by 5x, stabilizing the refinement trajectory. All training uses only 2,400 samples on a single GPU, demonstrating that spatial self-correction is a learnable capability that can be instilled at modest scale.

17.
arXiv (CS.CL) 2026-06-12

KCSAT-ML: Probing Reasoning Models with Nationwide-Cohort Human Difficulty

Math reasoning benchmarks have proliferated, yet most lack a per-item difficulty signal grounded in actual human performance. We introduce KCSAT-ML, a decade (2014-2025) of Korean College Scholastic Ability Test (KCSAT; Suneung) mathematics: 664 problems with a 339-item core set carrying official per-item error rates from nationwide cohorts of hundreds of thousands of examinees. We pair the benchmark with Difficulty-aligned Reasoning Gain (DRG): a score-orthogonal metric that asks whether a model's mistakes concentrate on the items humans found hard, or on items humans found easy. Together they expose, across a wide range of VLMs (and LLMs via OCR), three patterns: (i) low-budget accuracy collapses on the high-human-error tail at every model size; (ii) test-time scaling (TTS) raises token use roughly linearly with cohort error rate, while accuracy gains follow a non-monotonic curve; (iii) within a single family, TTS flips between anti-scaling on the hardest items and overthinking on easier ones – two faces of the same alignment failure. On DRG, models with near-identical accuracy can sit at near-opposite values: one model gets wrong what humans also find hard, while another solves the hardest items yet fails on items humans find easy – a contrast that aggregate accuracy hides. Our code and dataset builder will be open-sourced at https://github.com/naver-ai/KCSAT-ML.

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

FreoStream:Enhancing Stream Guardrails via Future-Aware Reasoning and Safety-Aligned Optimization

arXiv:2606.13737v1 Announce Type: cross Abstract: Stream guardrails enable token-level safety detection before full responses are generated. However, they often make overly conservative judgements and block those sensitive but safe tokens, which is known as over-refusal. Due to lack of full context, they also fail to detect implicitly harmful content from jailbreaking. To address these challenges, we propose FreoStream, a novel streaming guardrail framework. Specifically, FreoStream fine-tunes a LoRA module to perform Future-Aware Reasoning when the base guardrail detects unsafe tokens. The reasoning process follows a Future-Reason-Judge paradigm: predict the future, reason about the full context and give the final judgement. This design can effectively reduce over-refusal by incorporating the future information. Moreover, we introduce the Safety-Aligned Optimization module that extracts the safety-aligned component from the reasoning gradients to update the base guardrail model, thereby enhancing streaming safety detection. Extensive experiments on various safety benchmarks demonstrate that FreoStream achieves lower over-refusal rates and better jailbreak defense compared to existing streaming guardrails.

19.
arXiv (math.PR) 2026-06-11

Patterned matrices with random walk entries

arXiv:2512.04612v3 Announce Type: replace Abstract: It is well known that the weak limit of a suitably scaled continuous-time random walk (CTRW) is the Brownian motion. We investigate the convergence of certain patterned random matrices whose entries are independent CTRWs and their time-changed versions, in a non-commutative probability framework. For the Wigner link function, the limits are free Brownian motion and its time-changed version driven by an inverse stable subordinator. For the symmetric circulant and the circulant with CTRW entries, we use their explicit eigenvalue expressions to define some empirical processes that converge weakly to a Brownian motion and a complex Brownian motion, respectively. For matrices with iid entries, and for elliptic matrices, the algebraic limits are equal in $*$-distribution to processes whose marginals are circular and elliptic variables, respectively. A random time-changed variant of these results is also established.

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

Speaker Verification with Speech-Aware LLMs: Evaluation and Augmentation

arXiv:2603.10827v2 Announce Type: replace-cross Abstract: Speech-aware large language models (LLMs) can accept speech inputs, yet their training objectives largely emphasize linguistic content or specific fields such as emotions or the speaker's gender, leaving it unclear whether they encode speaker identity. First, we propose a model-agnostic scoring protocol that produces continuous verification scores for both API-only and open-weight models, using confidence scores or log-likelihood ratios from the Yes/No token probabilities. Using this protocol, we benchmark recent speech-aware LLMs and observe weak speaker discrimination (EERs above 20% on VoxCeleb1). Second, we introduce a lightweight augmentation that equips an LLM with ASV capability by injecting frozen ECAPA-TDNN speaker embeddings through a learned projection and training only LoRA adapters. On TinyLLaMA-1.1B, the resulting ECAPA-LLM achieves 1.03% EER on VoxCeleb1-E, approaching a dedicated speaker verification system while preserving a natural-language interface.

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

Understanding LLM Reasoning for Abstractive Summarization

Reasoning has substantially improved Large Language Models (LLMs) on analytical tasks such as mathematics and code generation, but its value for abstractive summarization remains unclear. To address this gap, we adapt general reasoning strategies to the summarization setting and conduct a large-scale comparative study of 8 reasoning strategies and 3 Large Reasoning Models (LRMs) across 8 diverse datasets, evaluating both summary quality and factual faithfulness. Our results show that reasoning is not a universal solution and its effectiveness depends strongly on the strategy and the summarization setting. In particular, we find a trade-off between summary quality and factual faithfulness. Explicit reasoning strategies often improve reference-based quality, but may weaken factual grounding, whereas implicit reasoning in LRMs shows the opposite tendency. We further find that increasing an LRM's internal reasoning budget does not reliably improve summarization and can even reduce factual consistency. These findings suggest that, for summarization, more reasoning is not always better. Effective reasoning should preserve faithful compression rather than induce over-elaboration. Our source code is publicly available.

22.
arXiv (math.PR) 2026-06-18

Functions of Bounded Variation and Point Processes

arXiv:2606.08304v2 Announce Type: replace-cross Abstract: We investigate the relationship between the analytical properties of functions of bounded variation and the statistical behavior of hyperuniform point processes. We establish several characterization formulas for the jump part of the gradient of a bounded variation function, extending and unifying previous results by Beretti–Gennaioli and Dávila. In particular, we provide new expressions for the $L^2$-jump of the gradient using both difference quotients and Fourier transform methods. Furthermore, we connect these analytic structures to the theory of hyperuniform point processes. By analyzing the variance of linear statistics associated with bounded variation functions, we provide asymptotic estimates that depend on the specific classification of the hyperuniformity of the point process. The results show how the regularity and jump discontinuities of a function dictate the growth rate of fluctuations in point processes. Finally, we introduce an averaged quadratic BMO-type oscillation functional over translated and rotated cube partitions, similar to the one recently studied by Ambrosio et al., and prove, using results from point process, that it converges to an explicit dimensional constant times the $L^2-$jump, giving in particular a further new characterization of the perimeter of a set.

23.
arXiv (CS.CL) 2026-06-11

Evolving Agents in the Dark: Retrospective Harness Optimization via Self-Preference

AI agents rely on a harness of skills, tools, and workflows to solve complex problems. Continually improving this harness is essential for adapting to new tasks. However, existing optimization methods typically require ground-truth validation sets, yet such labeled data is difficult to acquire in practical deployment settings. To address this problem, we introduce Retrospective Harness Optimization (RHO), a self-supervised method that optimizes the agent harness using only past trajectories. Specifically, RHO selects a diverse coreset of challenging tasks from past trajectories and re-solves them in parallel. The agent analyzes these rollouts using self-validation and self-consistency, then generates candidate harness updates and selects the most effective one by its own pairwise self-preference. We evaluate RHO across three diverse domains, spanning software engineering, technical work, and knowledge work. Notably, a single optimization round improves the pass rate on SWE-Bench Pro from 59% to 78% without any external grading. Furthermore, our analysis demonstrates that RHO effectively targets prior failure modes. As a result, the optimized harness alters the agent's behavior patterns and sustains higher accuracy during long-horizon sessions.

24.
arXiv (CS.AI) 2026-06-11

Sparsified Kolmogorov-Arnold Networks for Interpretable Quantum State Tomography

arXiv:2606.11814v1 Announce Type: cross Abstract: Machine-learning approaches to quantum state tomography can achieve high reconstruction fidelity, but the physical structure used by the trained model often remains implicit. Here we ask whether a sparsified Kolmogorov-Arnold Network (KAN) can be used not only as a regressor, but also as an inspectable reconstruction rule whose internal organization can be checked against known Pauli structure. We study a controlled three-qubit GHZ-family benchmark in which all 63 non-identity Pauli expectation values are used to reconstruct three GHZ-subspace variables: the population imbalance $z$, the real off-diagonal component $c$, and the imaginary off-diagonal component $s$. Under finite-shot sampling and depolarizing noise, external ablation identifies the extended 12-channel GHZ-relevant Pauli set from the 63 measurements, with exact top-12 recovery across the tested shot counts and depolarizing-noise strengths. These support patterns remain stable across multi-seed random-initialization and noise-level analyses, and collapse under random-label controls. The dominant pruned input-hidden-output pathways organize Z-type population observables and X/Y off-diagonal observables in a pattern consistent with the analytic GHZ Pauli grouping, and sparse formula recovery recovers the canonical signed Pauli relations. The contribution of the KAN is therefore pathway-level structural interpretability within a neural reconstruction model, rather than superior sparse regression. Together with negative controls, these probes provide a consistency chain for auditing learned reconstruction rules against known physical structure.

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

PCBSchemaGen: Reward-Guided LLM Code Synthesis for Printed Circuit Boards (PCB) Schematic Design with Structured Verification

arXiv:2602.00510v2 Announce Type: replace Abstract: Most LLM code-synthesis benchmarks rely on unit tests as the reward oracle, but PCB schematic design has none: correctness is defined by structured physical constraints over real IC packages and pin-level assignments, per-task golden references are unavailable, and SPICE simulation does not validate schematic-level correctness. We introduce PCBSchemaGen, a training-free inference-time framework that turns a frozen LLM into a verifiable, repairable PCB schematic generator. The framework induces a domain schema from IC datasheets to ground LLM decoding, pairs it with a deterministic 5-layer continuous-reward verifier with pin-level error localization, and refines candidates through a Thompson Sampling arm-acquiring bandit. We evaluate on 2 PCB benchmarks covering 227 real-IC tasks across 22 unified circuit domains, including a public-schematic-derived suite that serves as a fully held-out generalization test (verifier, KG library, and prompts frozen before any evaluation). Under our framework, an open-weight 31B model (Gemma-4-31B) passes 81.3% of PCBBench tasks on average, and the same framework transfers across both benchmarks with zero verifier code changes; a Circuitron-style inference-time prompting baseline on the same Gemma-4-31B backbone collapses on hard system-level designs. This suggests inference-time refinement under a deterministic structural verifier is a general recipe for reference-free LLM code synthesis in domains without unit-test oracles. Our benchmarks and deterministic verifier are publicly available at https://github.com/HZou9/PCBSchemaGen_v2.