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01.
arXiv (math.PR) 2026-06-25

Pointwise Hurst Estimation via Scale Accumulation: A Noise-Robust Approach for Rough Volatility

作者:
Jokubas Petkevicius↗

arXiv:2606.25771v1 Announce Type: cross Abstract: We introduce an estimator for the pointwise, time-varying Hölder exponent (Hurst parameter) of a stochastic process, based on the geometry accumulation integral G_Lambda(t) = integral from Lambda to 1 of |eth_s X(t)| s^{-1} ds, where eth_s X(t) = (X(t+s)-X(t))/s is the scale derivative at resolution s. We prove consistency, noise robustness with explicit threshold Lambda* = sigma^{1/H}, and a CLT at rate (log Lambda)^{-1/2}. The estimator is pointwise in time, defined at finite resolution, and eliminates microstructure noise by scale separation. Existing estimators give a global H from integrated variance; this gives a time-varying H(t) directly from the price path.

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

AdaSR: Adaptive Streaming Reasoning with Hierarchical Relative Policy Optimization

作者:
Junlong Tong↗Wenqi Xu↗Yingqi Fan↗Anhao Zhao↗Xuan Lu↗Yang Tan↗Xiaoyu Shen↗

Large reasoning models typically follow a read-then-think paradigm: they observe the complete input, reason over a static context, and then produce the answer. Yet many real-world scenarios are inherently dynamic, such as audio and video stream, where information arrives as a continuous stream and models must reason, update, and respond under partial observations. Recent streaming reasoning methods allow models to think while reading, but they largely rely on supervised imitation of pre-constructed trajectories, which limits their flexibility. In this paper, we propose AdaSR, an adaptive streaming reasoning framework that enables models to reason during input streaming and perform final deliberation once the stream is complete, learning when to think, and how much computation to allocate across different stages. To optimize this hierarchical reasoning process, we introduce Hierarchical Relative Policy Optimization (HRPO), which decomposes policy optimization into streaming reasoning and deep reasoning phases, providing more fine-grained advantage assignment instead of uniformly distributing a single sequence-level advantage over all tokens. HRPO integrates format, accuracy, and adaptive thinking rewards to enforce valid reasoning protocols, preserve final task performance, and encourage latency-aware computation allocation. Experiments show that AdaSR achieves a better balance among reasoning accuracy, computational efficiency, and streaming latency compared with supervised fine-tuning baseline. We release our code at https://github.com/EIT-NLP/StreamingLLM/tree/main/AdaSR.

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03.
arXiv (math.PR) 2026-06-18

Finite free perpetuities

作者:
Julia Le Bihan↗Bartosz Ko{\l}odziejek↗

arXiv:2606.19115v1 Announce Type: new Abstract: We introduce and study finite free perpetuities, defined as monic polynomial solutions of degree $n$ to the affine fixed-point equation \[ p(z) = \mathbb{E}\!\left[ A^{n}\,p\!\left(\frac{z-B}{A}\right)\mathbf{1}_{\{A\neq0\}} \right] + \mathbb{E}\!\left[ (z-B)^n\mathbf{1}_{\{A=0\}} \right], \] where $A$ and $B$ are complex-valued random variables with finite moments up to order $n$. Equivalently, if $p(z)=\mathbb{E}[(z-X)^n]$, then $p$ encodes a truncated moment version of the classical perpetuity equation $X\stackrel{d}{=}AX+B$ with $X$ and $(A,B)$ independent. This places finite free perpetuities between classical perpetuities and free-probabilistic fixed-point laws. We prove existence and uniqueness under weak conditions, and we identify a broad class of admissible pairs $(A,B)$ for which the resulting polynomial has only real, nonnegative zeros. Our approach uses finite free additive and multiplicative convolutions together with a probabilistic representation via the $U$-transform. As a motivating example, we exhibit an explicit family of finite free perpetuities expressed in terms of Jacobi polynomials and show that their empirical root distributions converge to a free-beta-prime law. More generally, for admissible sequences of parameters, we prove weak convergence of the empirical root distributions of finite free perpetuities to the law of a free perpetuity characterized by the corresponding free fixed-point equation. This yields a finite-degree polynomial model approximating free perpetuities and clarifies the connection between classical affine recursions, finite free convolutions, and free probability.

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04.
arXiv (quant-ph) 2026-06-24

On estimating Schatten norm and power distances between quantum states

作者:
Yupan Liu↗Qisheng Wang↗

arXiv:2505.00457v3 Announce Type: replace Abstract: We study the computational complexity of estimating the quantum Schatten $\alpha$-norm distance $T_\alpha(\rho_0,\rho_1)$, given $poly(n)$-size state-preparation circuits of $n$-qubit quantum states $\rho_0$ and $\rho_1$. This quantity serves as a lower bound on the trace distance and, for $\alpha > 1$, is interchangeable with its powered version $\Lambda_\alpha(\rho_0,\rho_1)$. For any constant $\alpha > 1$, we develop an efficient rank-independent quantum estimator for $T_\alpha(\rho_0,\rho_1)$ with time complexity $poly(n)$, achieving an exponential speedup over the prior best results of $\exp(n)$ due to Wang, Guan, Liu, Zhang, and Ying (TIT 2024). When $01$, QSD$_{\alpha}$ is $\sf BQP$-complete. 2. For any $1 \leq \alpha(n) \leq 1+negl(n)$, QSD$_\alpha$ is $\sf QSZK$-complete, implying that no efficient quantum estimator for $T_\alpha(\rho_0,\rho_1)$ exists unless ${\sf BQP}={\sf QSZK}$. This $\sf QSZK$-hardness result also extends to the promise problem defined by $\Lambda_\alpha(\rho_0,\rho_1)$ for constant $0

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05.
arXiv (CS.LG) 2026-06-12

Detecting Explanatory Insufficiency in Learned Representations: A Framework for Representational Vigilance

作者:
Jacques Raynal↗Pierre Slangen↗Elsa Raynal↗Jacques Margerit↗

arXiv:2606.13172v1 Announce Type: new Abstract: Learned representations are central to modern machine learning and are commonly evaluated through predictive performance, robustness, uncertainty estimation, or generalization. However, a learned representation may remain operationally successful while progressively failing to organize persistent residual structures that are not fully captured by conventional evaluation metrics. This article introduces VER, the Vigilant Evaluator of Representations, a conceptual framework for monitoring representational adequacy in learned representations. VER does not propose a new learning algorithm, loss function, or model architecture. Instead, it formalizes a diagnostic process through which persistent residual structures may be identified, analyzed, and interpreted as potential indicators of explanatory insufficiency. The framework distinguishes representational inadequacy from ordinary prediction error, uncertainty, noise, and distribution shift. It introduces a monitoring sequence based on representation identification, explanatory-domain delimitation, residual-structure detection, explanatory-resistance evaluation, and vigilance signaling. VER is intended as a contribution to representation diagnostics in machine learning. Its objective is not to replace existing evaluation methods but to complement them by treating representational adequacy as an explicit object of inquiry. A path toward empirical evaluation through representational-vigilance benchmarks is also outlined.

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

SPATIA: Multimodal Generation and Prediction of Spatial Cell Phenotypes

作者:
Zhenglun Kong↗Mufan Qiu↗John Boesen↗Xiang Lin↗Sukwon Yun↗Tianlong Chen↗Manolis Kellis↗Marinka Zitnik↗

Understanding how cellular morphology, gene expression, and spatial context jointly shape tissue function is a central challenge in biology. Image-based spatial transcriptomics technologies now provide high-resolution measurements of cell images and gene expression profiles, but existing methods typically analyze these modalities in isolation or at limited resolution. We address the problem by introducing SPATIA, a multi-level generative and predictive model that learns unified, spatially aware representations by fusing morphology, gene expression, and spatial context from the cell to the tissue level. SPATIA also incorporates a spatially conditioned generative framework with confidence-aware OT reweighting and morphology-profile alignment for modeling target-state morphology distributions. Specifically, we propose a confidence-aware flow matching objective that reweights weak optimal-transport pairs based on uncertainty. We further apply morphology-profile alignment to encourage biologically meaningful image generation, enabling the modeling of microenvironment-dependent phenotypic transitions. We assembled a multi-scale dataset consisting of 25.9 million cell-gene pairs across 17 tissues. We benchmark SPATIA against 18 models across 12 tasks, spanning categories such as phenotype generation, annotation, clustering, gene imputation, and cross-modal prediction. SPATIA achieves improved performance over state-of-the-art models, improving generative fidelity by 8% and predictive accuracy by up to 3%.

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

Shift-Invariant Attribute Scoring for Kolmogorov-Arnold Networks via Shapley Value

作者:
Wangxuan Fan↗Ching Wang↗Siqi Li↗Nan Liu↗

arXiv:2510.01663v2 Announce Type: replace-cross Abstract: For many real-world applications, understanding feature-outcome relationships is as crucial as achieving high predictive accuracy. While traditional neural networks excel at prediction, their black-box nature obscures underlying functional relationships. Kolmogorov–Arnold Networks (KANs) address this by employing learnable spline-based activation functions on edges, enabling recovery of symbolic representations while maintaining competitive performance. However, KAN's architecture presents unique challenges for network pruning. Conventional magnitude-based methods become unreliable due to sensitivity to input coordinate shifts. We propose ShapKAN, a pruning framework using Shapley value attribution to assess node importance in a shift-invariant manner. Unlike magnitude-based approaches, ShapKAN quantifies each node's actual contribution, ensuring consistent importance rankings regardless of input parameterization. Extensive experiments on synthetic and real-world datasets demonstrate that ShapKAN preserves true node importance while enabling effective network compression. Our approach improves KAN's interpretability advantages, facilitating deployment in resource-constrained environments.

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08.
arXiv (CS.AI) 2026-06-18

AI-Driven Assessment of Human Tutors: Linking Training Performance to Real-Life Practice

作者:
Danielle R. Thomas↗Marie Cynthia Abijuru Kamikazi↗Clara Brandt↗Conrad Borchers↗Kenneth R. Koedinger↗

arXiv:2606.18617v1 Announce Type: cross Abstract: There exist numerous tutor training platforms. However, few provide AI-driven training and evaluation for human tutors based on real-life performance. We present an AI-driven system that assesses both open responses during training and authentic real-life tutoring. Unlike platforms that only assess learning through online training or simulations, our system utilizes Generative AI (Gemini-2.5-pro) to analyze transcriptions of authentic tutoring, measuring the transfer of tutor skills to real-life application. Human tutors instructing students remotely in math (N=86) completed six scenario-based lessons, averaging a significant 7.4% learning gain. Using mixed-effects models across 405 session-to-lesson pairs, we found that training performance significantly predicted real-life transcript scores with an effect size of 0.25 SD. Model comparison (AIC/BIC) indicated averaging open response and multiple choice performance during training predicted real-life tutor performance best, although open responses were comparatively more predictive. Exploratory analysis showed that after training, tutors were significantly more likely to encounter pedagogical opportunities to apply their skills (61.1% to 68.9%) and demonstrated higher execution quality within those opportunities (65.5% to 68.1%). Interrupted time series analysis suggested that these tutor improvements were part of a gradual trend over time rather than an immediate intervention effect of training. We illustrate an AI-driven method to link tutor training with real-life assessment. In doing so, we contribute open datasets, AI prompts, and scoring rubrics to support transparency and reproducibility.

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09.
arXiv (CS.AI) 2026-06-11

GPO: Learning from Critical Steps to Improve LLM Reasoning

作者:
Jiahao Yu↗Zelei Cheng↗Xian Wu↗Xinyu Xing↗

arXiv:2509.16456v3 Announce Type: replace Abstract: Large language models (LLMs) are increasingly used in various domains, showing impressive potential on different tasks. Recently, reasoning LLMs have been proposed to improve the reasoning or thinking capabilities of LLMs to solve complex problems. Despite the promising results of reasoning LLMs, enhancing the multi-step reasoning capabilities of LLMs still remains a significant challenge. While existing optimization methods have advanced the LLM reasoning capabilities, they often treat reasoning trajectories as a whole, without considering the underlying critical steps within the trajectory. In this paper, we introduce Guided Pivotal Optimization (GPO), a novel fine-tuning strategy that dives into the reasoning process to enable more effective improvements. GPO first identifies the `critical step' within a reasoning trajectory - a point that the model must carefully proceed to succeed at the problem. We locate the critical step by estimating the advantage function. GPO then resets the policy to the critical step, samples the new rollout and prioritizes the learning process on those rollouts. This focus allows the model to learn more effectively from pivotal moments within the reasoning process to improve the reasoning performance. We demonstrate that GPO is a general strategy that can be integrated with various optimization methods to improve reasoning performance. Besides theoretical analysis, our experiments across challenging reasoning benchmarks show that GPO can consistently and significantly enhance the performance of existing optimization methods, showcasing its effectiveness and generalizability in improving LLM reasoning by concentrating on pivotal moments within the generation process.

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10.
arXiv (quant-ph) 2026-06-19

Effective Faraday interaction between light and Helium-3 nuclear spins in a multi-pass cell

作者:
Kaiwen Yi↗Yida Sha↗Zejia Lin↗Matteo Fadel↗Xiang Peng↗

arXiv:2606.20328v1 Announce Type: new Abstract: Helium-3 nuclear spins form an exceptionally stable quantum system with extremely long coherence time, offering exciting opportunities for quantum technologies. In particular, nuclear spin-squeezed states promise enhanced precision for sensing tasks and tests of new physics. A central challenge for all these applications is the realization of a controllable light-nuclear spin interface. Here we experimentally demonstrate such an interface by exploiting metastability-exchange collisions in a low-pressure helium-3 gas cell at room temperature. A radio-frequency discharge produces a small population of metastable atoms that both enables efficient optical pumping and mediates an effective Faraday interaction between the collective nuclear spin and an optical probe. We quantitatively characterize the strength of this interaction as a function of the nuclear polarization, applied magnetic field, and probe-beam parameters. Moreover, we show that using a multi-pass cell enhances this interaction by effectively increasing the optical depth. Extrapolating to a tenfold increase of the probe power used in the present experiment, we project a measurement-induced squeezing rate of 0.52 s$^{-1}$. Our results provide a practical pathway for optical access to helium-3 nuclear spins and open prospects for generating long-lived, macroscopic nuclear spin-squeezed states for quantum metrology.

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

GENIE: A Fine-Grained Measure for Novelty

作者:
Ramya Namuduri↗Manya Wadhwa↗Anshun Asher Zheng↗Greg Durrett↗Junyi Jessy Li↗

Large Language Models have consistently demonstrated a lack of creativity and diversity across tasks. Prior work has focused on addressing whether models are capable of generating creative outputs. Here, we aim to consider novelty and investigate what makes model-generated content novel or not novel in a task-specific manner. We propose a fine-grained evaluation metric GENIE to measure the novelty of responses along task-specific features with respect to a population of responses. We show that unlike GENIE, holistic metrics struggle to capture the high-dimensionality of novelty and do not provide insight on which properties they target. Finally, we use GENIE to measure the effectiveness of mitigation methods that address creativity to better understand where these methods can improve novelty.

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12.
arXiv (quant-ph) 2026-06-25

Anomalous topological superradiant phases

作者:
You-Qi Lu↗Yu-Yu Zhang↗Zi-Xiang Hu↗

arXiv:2606.25635v1 Announce Type: new Abstract: We present a novel set of light-matter topology realized by implementing a finite-component quantum Rabi array with a photonic analog of the Su-Schrieffer-Heeger (SSH) configuration. We demonstrate how complex light-matter couplings with species-dependent phases lead to the closure of superradiance-induced band gap in a manner that differs from that in the SSH model. We uncover an topological superradiant phase transition from a normal phase to a topological superradiant electromagnet phase, which is characterized both by a local order parameter and a global topological invariant. Novel superradiance-enhanced edge states emerge with significantly amplified excitations superior to those in topological normal phase. Strikingly, tuning light-atom coupling induces novel topological superradiant electric and magnetic phases, exhibiting chiral edge-mode excitation at opposite boundaries. Our proposed setup offers a tunable platform for topological quantum optics, advancing applications in topological superradiant lasers.

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13.
arXiv (quant-ph) 2026-06-16

Exactly Solvable Quantum Model with Spin-Dependent Coulomb Interaction

作者:
Jiang-Lin Zhou↗Yu-Xuan Zhang↗Choo Hiap Oh↗Jing-Ling Chen↗

arXiv:2501.05103v5 Announce Type: replace Abstract: In this work, we report an exactly solvable quantum model featuring a spin-dependent Coulomb interaction, described by the spin vector potential \(\vec{\mathcal{A}} = k (\vec{r} \times \vec{S}) / r^2\) together with a Coulomb-type scalar potential \(\varphi = \kappa / r\) . The model is governed by the Schrödinger-type Hamiltonian \(\mathcal{H}_S = \vec{\Pi}^2 / (2M) + q \varphi\) in nonrelativistic quantum mechanics and by the Dirac-type Hamiltonian \(\mathcal{H}_D = c \vec{\alpha} \cdot \vec{\Pi} + \beta M c^2 + q \varphi\) in relativistic quantum mechanics, where \(\vec{\Pi} = \vec{p} - (q/c)\vec{\mathcal{A}}\) is the canonical momentum. We demonstrate two main results: (i) Just as the Coulomb-type scalar potential \(\mathcal{S}_Maxwell = \{\vec{\mathcal{A}} = 0,\ \varphi = \kappa / r\}\) is a local exact solution of Maxwell's equations on $r\neq0$, the gauge potential \(\mathcal{S}_YM = \{\vec{\mathcal{A}} = k (\vec{r} \times \vec{S}) / r^2,\ \varphi = \kappa / r\}\) constitutes a local exact solution of the Yang–Mills equations on the punctured region $r\neq0$. (ii) Both Hamiltonians \(\mathcal{H}_S\) and \(\mathcal{H}_D\) can be solved exactly in the presence of this spin-dependent Coulomb interaction. The resulting energy spectra are derived, and they naturally reduce to those of the ordinary hydrogen atom when the spin-dependent terms are neglected. Finally, we clarify the quantization conditions and the fixed-background interpretation of the model.

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

StaminaBench: Stress-Testing Coding Agents over 100 Interaction Turns

作者:
Vlad Sobal↗Shuo Yang↗Yuting Zhang↗Wei Xia↗Stefano Soatto↗

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.

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

Every Act Has Its Price: Compressed Moral Composition in Frontier LLMs

作者:
Weijia Zhang↗Ruiqi Chen↗Yunze Xiao↗Weihao Xuan↗

Existing LLM moral benchmarks usually ask which isolated moral act, value, or foundation a model prefers. This is useful but incomplete. Realistic judgments often require a model to combine several moral signals within the same option. We introduce **Moral Trolley Arena**, a two-stage blind ELO benchmark for measuring how LLMs compose moral evidence. The single-scene arena first calibrates individual moral acts from a 229-scenario corpus across five Moral Foundations Theory foundations; the composite arena then combines calibrated acts into two-act moral items over a controlled intensity grid and measures the resulting composite preferences. Across ten frontier models, composite judgments are largely predicted by component act strength, but the relation is consistently compressed rather than simply additive. Models also show non-additive intensity anchoring, bounded foundation-specific residuals after component control, and highly convergent composite preference surfaces across providers. These results suggest that moral audits should measure composition rules for moral evidence, not only rankings over isolated acts.

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

RL-Index: Reinforcement Learning for Retrieval Index Reasoning

作者:
Yongjia Lei↗Nedim Lipka↗Zhisheng Qi↗Utkarsh Sahu↗Koustava Goswami↗Franck Dernoncourt↗Ryan A. Rossi↗Yu Wang↗

arXiv:2606.16316v1 Announce Type: cross Abstract: Retrieving external knowledge is essential for solving real-world tasks, yet it remains challenging when the relationship between a query and its relevant knowledge involves implicit and complex reasoning beyond surface-level semantic or lexical matching (e.g., mathematical problems relying on the same theorem or coding requiring deep reasoning). Existing approaches primarily rely on query-side reasoning (e.g., query rewriting), which introduces significant online latency and underutilizes the opportunity to perform reasoning over the knowledge corpus itself (i.e., index-side reasoning). In this paper, we propose RL-Index, an agentic indexing framework that formulates retrieval index reasoning as a reinforcement learning problem. Instead of performing reasoning at query time, RL-Index shifts reasoning to the indexing stage by augmenting documents with LLM-generated rationales that explicitly encode the latent query-knowledge relationship. To optimize the quality of these rationales, we employ Group Relative Policy Optimization (GRPO) and use retrieval similarity as a verifiable reward signal, enabling direct optimization of indexing decisions for retrieval effectiveness. Extensive experiments on the BRIGHT benchmark demonstrate that RL-Index consistently improves both retrieval and downstream question-answering performance, while significantly reducing online inference latency. Moreover, the learned rationale augmentation generalizes across diverse retrievers and generators, highlighting its robustness as a plug-and-play indexing strategy across different retrieval systems.

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17.
Nature (Science) 2026-06-08

Distributed control circuits across a brain-and-cord connectome

作者:
Alexander S. Bates↗

Just as genomes revolutionized molecular genetics, connectomes (maps of neurons and synapses) are transforming neuroscience. To date, the only organisms with complete connectomes are worms1–3, sea squirts4, and comb jellies5 (103–104 synapses). By contrast, the fruit fly is more complex (108 synaptic connections), with a brain that supports learning and spatial memory6,7 and an intricate ventral nerve cord analogous to the vertebrate spinal cord8–12. Here we report the first densely-reconstructed adult fly connectome that unites the brain and ventral nerve cord, and we leverage this resource to investigate principles of neural control. We show that effector neurons (motor neurons, endocrine cells, and efferent neurons targeting the viscera) are primarily influenced by sensory neurons in the same body part, forming local feedback loops. These local loops are linked by long-range circuits involving ascending and descending neurons organized into behavior-centric modules. Single ascending and descending neurons are often positioned to influence the voluntary movements of multiple body parts, together with the endocrine cells or visceral organs that support those movements. Brain regions involved in learning and navigation supervise these circuits. These results reveal an architecture that is distributed, parallelized, and embodied, reminiscent of distributed control architectures in engineered systems13,14.

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

Variational Autoencoder Layer

作者:
Gananath R↗

arXiv:2606.25900v1 Announce Type: new Abstract: Variational Autoencoders (VAEs) belong to a family of autoencoders with probabilistic properties, making them well suited for generating data by producing a smooth and continuous latent space. Despite being introduced over a decade ago, the method continues to be widely adopted in both research and industry for diverse applications. While VAEs are typically used as standalone models, this paper introduces a novel approach to integrate them as a neural network layer. Furthermore, a new training strategy is proposed for models incorporating these layers, and their performance is thoroughly analyzed.

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20.
arXiv (CS.AI) 2026-06-16

Entropy-Gated Latent Recursion

作者:
Soham Bhattacharjee↗Dushyant Singh Chauhan↗Salem Lahlou↗Martin Takac↗Nils Lukas↗

arXiv:2606.16620v1 Announce Type: cross Abstract: Inference-time scaling has become the dominant lever for improving language-model reasoning, but existing methods derive rollout diversity from a single source: stochastic token-level sampling. We argue that this single-axis sampling space is fundamentally limiting, and identify a second, fully deterministic and complementary axis: the layer span $L$ at which a frozen model's top decoder layers are recursively re-applied at high-uncertainty tokens. Different choices of $L$ produce distinct rollouts that solve different subsets of problems, with no stochasticity. We instantiate this axis through Entropy-Gated Latent Recursion (EGLR), a training-free decoding procedure that re-applies the top-$L$ layers for at most $K_{\max}$ iterations until the next-token distribution converges. Combined with $T$ temperature samples, EGLR turns a single-axis stochastic rollout pool into an $L\times T$ Cartesian sampling space at almost the same per-rollout cost. We characterize this space across $8$ instruction-tuned models and $6$ math reasoning benchmarks, and show that the $L$-axis is genuinely complementary to temperature: on MATH-500 with Qwen2.5-3B-Instruct, the joint $L\times T$ oracle reaches $91.6\%$, $+8.2$ percentage points beyond the temperature-only oracle ($83.4\%$) and $+10.4$ points beyond the layer-only oracle ($81.2\%$), confirming that the two axes capture genuinely complementary problems. The expanded rollout pool provides richer per-prompt candidates for any downstream procedure that consumes rollouts, including self-consistency, best-of-$N$ with verifiers, and group-relative RL training (GRPO), opening a new direction for inference-time scaling that does not rely on stochastic noise.

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22.
arXiv (CS.LG) 2026-06-17

From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

作者:
Prashant K. Jha↗

arXiv:2503.05598v2 Announce Type: replace-cross Abstract: This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, including DeepONet, PCANet, and the Fourier Neural Operator, highlighting their underlying representations, computational structures, and comparative performance. These architectures are demonstrated on three canonical PDE problems: the Poisson equation, a linear elasticity problem, and a hyperelasticity problem. To make the presentation self-contained, key foundational topics are introduced, including finite-dimensional representations of function spaces, singular-value decomposition, and sampling from infinite-dimensional function spaces. Beyond forward modeling, the review discusses the use of neural operators as surrogate models within a Bayesian inverse-problem framework, including prior specification, forward-map approximation, and posterior computation. The performance of the three neural-operator architectures is evaluated on in-distribution samples, out-of-distribution samples, and Bayesian inference tasks. The review also discusses challenges related to prediction accuracy and generalization, outlining emerging strategies such as residual-based error correction and multi-level training. The review concludes by positioning neural operators within broader scientific-computing workflows and by identifying directions for reliable, scalable operator learning.

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23.
arXiv (CS.AI) 2026-06-16

SkillVetBench: LLM-as-Judge for Multi-Dimensional Security Risk Evaluation in Open-Source LLM Agent Skills

作者:
Ismail Hossain↗Sai Puppala↗Md Jahangir Alam↗Tanzim Ahad↗Sajedul Talukder↗

arXiv:2606.15899v1 Announce Type: cross Abstract: Open-source LLM agent ecosystems are growing rapidly, yet the security of community-contributed skills - modular tool definitions that extend agent capabilities - remains largely unvetted. The gap we fill: existing scanners operate at the code layer and are structurally blind to instruction-layer and multi-agent risk - natural-language directives that hijack an agent, exfiltrate data through encoded side channels, or chain harm across pipelines - so what is needed is a semantic, multi-dimensional vetting system rather than another signature matcher. We present SKILLVETBENCH, a live public leaderboard on Hugging Face that uses an LLM-as-Judge to vet agent skills. What is new: SARS (Skill Agentic Risk Score), a five-dimensional agentic-risk metric with a principled weighted formula for instruction-following systems. What is integrated: full CVSS v4.0 vector decomposition and a ClawHub dual-view that places our LLM-generated review beside the official marketplace verdict. What is demonstrated: drawing on our companion benchmark paper [ 1], the LLM-as-Judge stage achieves zero false negatives across 78 confirmed-malicious skills and zero false positives across 22 benign controls, while the best static baseline (SKILLSIEVE) still misses 15%; for instruction-layer categories such as Prompt Injection and Memory Poisoning, conventional tools miss between 89% and 100% of threats (e.g., CODEBERT detects none of nine memory-poisoning skills). Detection rates vary from 35% to 95% across four LLM evaluators, motivating ensemble scoring in production deployments.

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24.
arXiv (CS.AI) 2026-06-12

Structured vs. Unstructured Pruning: An Exponential Gap

作者:
Davide Ferre'↗Fr\'ed\'eric Giroire↗Frederik Mallmann-Trenn↗Emanuele Natale↗

arXiv:2603.02234v3 Announce Type: replace-cross Abstract: The Strong Lottery Ticket Hypothesis (SLTH) states that large, randomly initialized neural networks contain sparse subnetworks capable of approximating a target function at initialization without training, suggesting that pruning alone is sufficient. Pruning methods are typically classified as unstructured, where individual weights can be removed from the network, and structured, where parameters are removed according to specific patterns, as in neuron pruning. Existing theoretical results supporting the SLTH rely almost exclusively on unstructured pruning, showing that logarithmic overparameterization suffices to approximate simple target networks. In contrast, neuron pruning has received limited theoretical attention, despite its practical appeal for direct hardware speedups. In this work, we consider the problem of approximating a single bias-free ReLU neuron by pruning hidden units of a randomly initialized two-layer ReLU network, effectively isolating the intrinsic limitations of neuron pruning. We show that achieving an $\varepsilon$-approximation requires a starting network size of $\Omega(1/\varepsilon)$ for neuron pruning, whereas weight pruning succeeds with only $O(\log(1/\varepsilon))$ hidden units, revealing an exponential separation between the two approaches.

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25.
arXiv (CS.LG) 2026-06-11

Point-Identification of a Robust Predictor Under Latent Shift with Imperfect Proxies

作者:
Zahra Rahiminasab↗Reza Soumi↗Arto Klami↗Samuel Kaski↗

arXiv:2603.15158v2 Announce Type: replace Abstract: Addressing the domain adaptation problem becomes more challenging when distribution shifts across domains stem from latent confounders that affect both covariates and outcomes. Existing proxy-based approaches that address latent shift rely on a strong completeness assumption to uniquely determine (point-identify) a robust predictor. Completeness requires that proxies have sufficient information about variations in latent confounders. For imperfect proxies the mapping from confounders to the space of proxy distributions is non-injective, and multiple latent confounder values can generate the same proxy distribution. This breaks the completeness assumption and observed data are consistent with multiple potential predictors (set-identified). To address this, we introduce latent equivalent classes (LECs). LECs are defined as groups of latent confounders that induce the same conditional proxy distribution. We show that point-identification for the robust predictor remains achievable as long as multiple domains differ sufficiently in how they mix proxy-induced LECs to form the robust predictor. This domain diversity condition is formalized as a cross-domain rank condition on the mixture weights, which is substantially weaker assumption than completeness. We introduce the Proximal Quasi-Bayesian Active learning (PQAL) framework, which actively queries a small, targeted set of diverse domains that satisfy this rank condition. PQAL can recover the point-identified predictor, demonstrates robustness to varying degrees of shift and outperforms previous methods on synthetic data and semi-synthetic dSprites, IHDP, ACS Folktables datasets.

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