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02.
arXiv (math.PR) 2026-06-11

Heat kernel estimates for Markov processes with blowing-up jump kernels

Authors:
Soobin Cho↗Panki Kim↗Renming Song↗Zoran Vondra\v{c}ek↗

arXiv:2512.24807v2 Announce Type: replace Abstract: In this paper, we establish sharp two-sided heat kernel estimates for a large class of purely discontinuous symmetric Markov processes on closed subsets $F$ of $\mathbb{R}^d$, whose jump kernels blow up on a Borel subset $\Sigma$ of $F$. We assume that $F\setminus \Sigma$ is a $\kappa$-fat set and is dense in $F$. To the best of our knowledge, this is the first work establishing sharp heat kernel estimates for jump processes whose jump kernels blow up on part of the state space. The jump kernels under consideration take the form $J(x,y)=|x-y|^{-d-\alpha}{\mathcal B}(x,y)$, where $\alpha\in (0,2)$ and the function ${\mathcal B}(x,y)$ blows up at a subset $\Sigma$ of $F$. A fundamental obstacle is that the tails of the jump measures are not uniformly bounded, and hence standard techniques in heat kernel analysis do not provide a priori off-diagonal estimates. To overcome this difficulty, we develop a new approach based on weighted integral estimates for the heat kernel that are sensitive to both the blow-up behavior of the jump kernel and the geometry of $F\setminus \Sigma$. Examples of processes falling within our general framework include traces of isotropic $\alpha$-stable processes in $C^{1,\rm Dini}$ sets, processes in Lipschitz sets arising in connection with the nonlocal Neumann problem, and a large class of resurrected self-similar processes in the closed upper half-space.

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

Planning with the Views via Scene Self-Exploration

Authors:
Kangrui Wang↗Linjie Li↗Zhengyuan Yang↗Shiqi Chen↗Zihan Wang↗Li Fei-Fei↗Jiajun Wu↗Leonidas Guibas↗Lijuan Wang↗Manling Li↗

Can VLMs predict how each camera move changes the view, and plan many such moves ahead? We call this capability view planning, requiring (1)understanding how a single action transforms the view, and (2)composing many such transformations across multi-turn plans to identify a target view. We probe both abilities in our proposed ViewSuite, a 3D point-cloud environment on real ScanNet scenes. Across 13 frontier VLMs, a critical planning gap emerges: they possess basic view-action knowledge but fail to compose it across multi-turn plans, with the gap widening as viewpoint distance grows. To close this gap, we propose an iterative framework that alternates self-exploration with view graph distillation. The key insight is that all exploration trajectories, regardless of their outcome, collectively form a view graph that compactly captures how viewpoints connect across a scene. Distilling this graph into diverse supervised tasks reshapes the policy distribution and overcomes the sparse rewards that stall pure RL. This improves Qwen2.5-VL-7B from 2.5% to 47.8% on interactive view planning, surpassing GPT-5.4 Pro (18.5%) and Gemini 3.1 Pro (21.4%). Self-exploration emerges as a promising path toward VLMs that can actively reason and plan in 3D space. Code and Data are at https://viewsuite.github.io.

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04.
arXiv (CS.LG) 2026-06-11

A theory of learning data statistics in diffusion models, from easy to hard

Authors:
Lorenzo Bardone↗Claudia Merger↗Sebastian Goldt↗

arXiv:2603.12901v2 Announce Type: replace-cross Abstract: While diffusion models have emerged as a powerful class of generative models, their learning dynamics remain poorly understood. We address this issue first by empirically showing that standard diffusion models trained on natural images exhibit a distributional simplicity bias, learning simple, pair-wise input statistics before specializing to higher-order correlations. We reproduce this behaviour in simple denoisers trained on a minimal data model, the mixed cumulant model, where we precisely control both pair-wise and higher-order correlations of the inputs. We identify a scalar invariant of the model that governs the sample complexity of learning pair-wise and higher-order correlations that we call the diffusion information exponent, in analogy to related invariants in different learning paradigms. Using this invariant, we prove that the denoiser learns simple, pair-wise statistics of the inputs at linear sample complexity, while more complex higher-order statistics, such as the fourth cumulant, require at least cubic sample complexity. We also prove that the sample complexity of learning the fourth cumulant is linear if pair-wise and higher-order statistics share a correlated latent structure. Our work describes a key mechanism for how diffusion models can learn distributions of increasing complexity.

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05.
arXiv (quant-ph) 2026-06-19

A Quantum Encoding of Traveling Salesperson Tours via Route Generation, Cost Phases, and a Reversible Valid-Permutation Oracle

Authors:
Alexander Johannes Stasik↗Franz Georg Fuchs↗

arXiv:2603.21283v3 Announce Type: replace Abstract: For a traveling salesperson problem (TSP) of n cities, we present a compact quantum encoding based on a time-register representation of tours. A candidate route is represented as a sequence of n-1 city labels over discrete time steps, with one fixed start city and the remaining cities encoded in binary registers. We describe three ingredients of the construction: uniform route generation over the route register, a reversible validity oracle, and a phase oracle that encodes the total tour cost. The validity oracle checks both that the non-start city labels form a permutation and, for incomplete graphs, that every directed edge used by the route exists. The cost oracle then accumulates the start-edge, intermediate-transition, and return-edge costs into a tour-dependent phase for valid routes. This yields a coherent superposition of candidate routes with feasibility and tour-length information embedded directly in the quantum state. The complete construction uses O(n log n) qubits, while a naive implementation has worst-case elementary-gate complexity O(n^3 log n). The encoding is compatible with amplitude amplification or spectral filtering techniques such as the quantum singular value transform (QSVT) or Grover's algorithm. However, due to the exponentially small fraction of valid tours, the overall complexity remains exponential even when combined with amplitude amplification.

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

SHARD: Safe and Helpful Alignment via Self-Reframing Distillation

Authors:
Viswonathan Manoranjan↗Amogh Gupta↗Anvesh Rao Vijjini↗Thomas Hofweber↗Snigdha Chaturvedi↗

Large language models often struggle with sensitive prompts. They may refuse outright, provide generic safety boilerplate, or fail to address the user's legitimate informational needs that can be answered safely. We introduce SHARD, a self-reframing distillation method to improve safe-helpfulness. It first rewrites sensitive prompts to surface benign intent using philosophical guidelines, then reframes its original responses into safe, more helpful ones, and finally fine-tunes the model on its self-reframed responses. Across DNA and the English subset of LINGUASAFE, SHARD improves helpfulness for most model families while preserving safety. It also remains competitive with distillation from a larger teacher model, suggesting that models can internalize safe and helpful behavior elicited from their own. Warning: This paper contains content that may be offensive or harmful.

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

MineExplorer: Evaluating Open-World Exploration of MLLM Agents in Minecraft

Authors:
Tianjie Ju↗Yueqing Sun↗Zheng Wu↗Wei Zhang↗Yaqi Huo↗Xi Su↗Qi Gu↗Xunliang Cai↗Gongshen Liu↗Zhuosheng Zhang↗

Multimodal large language models (MLLMs) have shown strong capabilities in perception, reasoning, and action generation. However, their ability to sustain exploration in dynamic open worlds remains unclear. Existing embodied and game-based benchmarks often compress interaction into short-horizon tasks or entangle success with domain-specific game mechanics. In this paper, we introduce MineExplorer benchmark for evaluating open-world exploration capabilities of MLLM agents in Minecraft. We first filter atomic tasks whose solutions rely heavily on Minecraft-specific knowledge to better reflect general open-world reasoning. Then we organize the benchmark around a ReAct-style capability formulation and compose atomic tasks into implicit multi-hop tasks. To further construct reliable instances, MineExplorer uses a multi-agent synthesis workflow that jointly designs task graphs, sandbox scenes, and rule-based milestone evaluators. Human evaluation shows that the multi-agent synthesis workflow produces significantly more reliable instances than a single-agent baseline. Experiments with advanced MLLM agents show that open-world exploration remains challenging, as strong models can handle many single-hop tasks but degrade sharply when hidden prerequisites must be coordinated over longer trajectories. Further analysis finds that task difficulty tracks agent completion, and larger models or thinking modes do not consistently translate into better performance. Code and dataset are available at https://github.com/Jometeorie/MineExplorer.

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08.
arXiv (CS.CL) 2026-06-16

Equity with Efficiency: An Empirical Study of Tokenizers for Multilingual Large Language Models

Authors:
Kieron Seven Jun Wei Lee↗Muhammad Reza Qorib↗Andrew Ivan Soegeng↗Hwee Tou Ng↗

Multilingual large language models (LLMs) depend on subword tokenization to bridge discrete text and continuous neural representation. State-of-the-art multilingual LLMs often use Byte-level Byte-Pair Encoding (BPE) tokenizers that structurally favor high-resource languages and Latin scripts. For speakers of underrepresented languages, particularly those across Southeast Asia, this bias inflates inference costs and widens cross-lingual capability gaps. We present the first systematic comparison of equitable tokenizers on a unified benchmark spanning 11 Southeast Asian languages. Beyond tokenizer-level analysis of compression efficiency and cross-lingual equity, we assess downstream task performance through controlled 1.5B-parameter language model training using the same training data. Our results show that Parity-aware BPE lies on the Pareto frontier of the efficiency-equity trade-off, achieving strong compression parity at competitive cost. Morphology-Driven Byte Encoding delivers the best semantic reasoning performance through morphologically richer representations, albeit at a higher computational expense. Byte Latent Transformer underperforms on downstream tasks, possibly because its architectural assumptions misalign with the constraints of limited low-resource training data. Together, our findings demonstrate that cross-lingual fairness and tokenization efficiency are not fundamentally at odds, and offer practical guidance for designing equitable multilingual models.

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

SpatialSV: Internalizing Interpretable 3D Spatial Awareness in MLLMs via Task-Oriented Visual Supervision

Authors:
Jiayu Tang↗Yuchen Zhou↗Chao Gou↗

Unlocking the spatial intelligence of multimodal large language model (MLLMs) is crucial for understanding and interacting with the 3D world. Prevailing approaches typically inject spatial priors via external tools, which impose significant inference overhead, or rely on latent feature distillation, which remains uninterpretable and lacks fine-grained geometric constraints. To address these issues, we propose SpatialSV, a framework designed to internalize robust 3D spatial awareness within MLLMs while simultaneously offering inherent interpretability. Deviating from passive feature imitation, SpatialSV employs task-oriented visual supervision, compelling the model to actively lift its 2D visual features into explicit 3D representations, including depth maps, camera poses, and point clouds. Crucially, this 2D-to-3D lifting process provides a transparent window into the model's representations: the resulting 3D reconstructions serve as an intuitive proxy for visualizing and diagnosing the quality of the model's intrinsic spatial knowledge. Extensive experiments across multiple models and benchmarks demonstrate the effectiveness of SpatialSV in enhancing and interpreting MLLMs' spatial intelligence. Furthermore, the framework exhibits strong generalization in semi-supervised settings, validating its potential to leverage unlabeled visual data for scalable, interpretable spatial representation learning.

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10.
arXiv (CS.AI) 2026-06-16

Shachi: A Modular, Controllable Framework for LLM-Based Agent-Based Modeling of Emergent Collective Behavior

Authors:
So Kuroki↗Yingtao Tian↗Kou Misaki↗Takashi Ikegami↗Takuya Akiba↗Yujin Tang↗

arXiv:2509.21862v3 Announce Type: replace Abstract: How collective behaviors emerge from the interactions of individual LLM-driven agents is a central question in artificial life, yet controlled study of these emergent dynamics has been hindered by the lack of a principled simulation framework for systematic experimentation. To address this, we introduce Shachi, a principled methodology and modular framework that decomposes an agent's cognition into core components: Configuration for intrinsic identity, Memory for contextual continuity, and Tools for extended capabilities, all orchestrated by an LLM reasoning engine. This decomposition treats each cognitive component as an independently controllable variable, enabling perturbation studies that trace how micro-level cognitive traits propagate into population-level dynamics. We investigate behavioral patterns across a 10-task benchmark spanning three levels of collective complexity. Shachi enables memory transfer across environment transitions, producing history-dependent behavioral shifts, and allows agents to simultaneously inhabit multiple environments, revealing cross-environment interference invisible in single-environment studies. Furthermore, in a real-world U.S. tariff shock case study, locally interacting agents with individually controlled cognitive components produce macro-level market dynamics directionally consistent with observed real-world outcomes. Our work provides a rigorous, open-source simulation framework for LLM-based ABM, aimed at fostering cumulative scientific inquiry into the emergent collective behaviors of interacting artificial agents.

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11.
arXiv (CS.AI) 2026-06-16

PrologMCP: A Standardized Prolog Tool Interface for LLM Agents

Authors:
Agnieszka Mensfelt↗Adarsh Prabhakaran↗Adrian Haret↗Vince Trencsenyi↗Kostas Stathis↗

arXiv:2606.14935v1 Announce Type: new Abstract: Frontier reasoning-tuned language models still fail on deductive tasks at depth, and the cost of improved performance through extended internal reasoning scales poorly. Symbolic delegation offers a complementary route: a language model translates the problem, while a solver performs the inference. However, current autoformalization pipelines for logic programming are typically bespoke integrations tied to particular tasks or agents. We introduce PrologMCP, a task-agnostic, open-source server that exposes Prolog as a stateful tool through the Model Context Protocol (MCP). Its compact tool interface, structured error reporting, and per-session isolation make the translate-run-inspect-repair loop a reusable primitive for MCP-capable agents. We evaluate a formalizer agent enhanced with PrologMCP against standard and reasoning LLMs (Claude Sonnet 4.6, GPT-4.1, and o4-mini) on two subsets of PARARULE-Plus: a general-purpose sample and a more challenging one targeting a specific failure mode of natural-language reasoning. On the general sample, the formalizer matches or exceeds reasoning LLMs (accuracy 1.00 vs.\ 1.00 / 0.998), with the largest gains over standard models (0.762 for GPT-4.1). On the challenging subset, the formalizer remains near-perfect (1.00 / 0.99) while reasoning LLMs drop to 0.95 / 0.94. These results suggest that delegating inference to Prolog via MCP is a robust and inspectable alternative to extended natural-language reasoning.

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

Metabolic quantum limit to the information capacity of magnetoencephalography

Authors:
E. Gkoudinakis↗S. Li↗I. K. Kominis↗

arXiv:2511.06401v3 Announce Type: replace-cross Abstract: Magnetoencephalography measures the magnetic fields generated by neural currents using quantum sensors such as superconducting quantum interference devices and atomic magnetometers. Here we combine the energy resolution limit of magnetic sensing with the metabolic power available to neural currents to derive a technology-independent bound on the information capacity of MEG. The bound factorizes into geometry, metabolism, and Planck's constant, and gives an estimated maximum information rate of 2.2~Mbit/s for representative human-brain parameters. Further, we show that the externally measurable magnetic field has a finite angular bandwidth, with high multipole components being geometrically attenuated and falling below the quantum-limited noise floor. This yields an information-limited spatial scale of order $1~cm$ and renders the accessible measurement space effectively finite-dimensional. The energy resolution limit therefore defines an information-theoretic Nyquist scale for magnetoencephalography, beyond which denser spatial sampling provides redundant measurements rather than additional recoverable information. Since the energy resolution limit also makes the noise variance grow linearly with measurement bandwidth, temporal and spatial bandwidths compete, producing a fundamental spatio-temporal trade-off. These results show how quantum-limited measurements constrain the observable complexity and information content of noninvasive brain imaging, providing a quantitative link between fundamental physics and neuroscience.

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13.
arXiv (CS.CV) 2026-06-24

CrossFusion: A Multi-Scale Cross-Attention Convolutional Fusion Model for Cancer Survival Prediction

Authors:
Rustin Soraki↗Huayu Wang↗Sitong Liu↗Joann G. Elmore↗Linda Shapiro↗

Cancer survival prediction from whole slide images (WSIs) is a challenging task in computational pathology due to the large size, irregular shape, and high granularity of the WSIs. These characteristics make it difficult to capture the full spectrum of patterns, from subtle cellular abnormalities to complex tissue interactions, which are crucial for accurate prognosis. To address this, we propose CrossFusion, a novel multi-scale feature integration framework that extracts and fuses information from patches across different magnification levels. By effectively modeling both scale-specific patterns and their interactions, CrossFusion generates a rich feature set that enhances survival prediction accuracy. We validate our approach across six cancer types from public datasets, demonstrating significant improvements over existing state-of-the-art methods. Moreover, when coupled with domain-specific feature extraction backbones, our method shows further gains in prognostic performance compared to general-purpose backbones. The source code is available at: https://github.com/RustinS/CrossFusion

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14.
arXiv (math.PR) 2026-06-11

The $K$-th nearest neighbor random walk on a Poisson point process gets trapped

Authors:
Anne-Laure Basdevant↗David Coupier↗Jean-Baptiste Gou\'er\'e↗Marie Th\'eret↗

arXiv:2606.11271v1 Announce Type: new Abstract: The $K$-th nearest neighbor random walk $(X_n)_{n \geq 0}$ on a homogeneous Poisson point process $\chi$ on $\R^d$ ($d\geq 1$), starts at the origin and at each step picks its next Poisson point among its closest neighbors according to i.i.d. labels having the same distribution as $K$. Our main result (Theorem 1) states that the number of Poisson points visited by $(X_n)_{n \geq 0}$ admits an exponential decay whenever the random variable $K$ has a bounded support (BS). In particular, the $K$-th nearest neighbor random walk visits finitely many Poisson points if and only if $K$ satisfies Assumption (BS). To prove it, we introduce the key notion of pioneer point which allows us to deal with the region of $\R^d$ already explored by $(X_n)_{n \geq 0}$. Still under Assumption (BS), we also prove an exponential decay for the Euclidean length of the trajectory performed by $(X_n)_{n \geq 0}$ (Theorem 2). Finally, and quite surprisingly, we exhibit an example of label distribution with bounded support for which the $K$-th nearest neighbor random walk discovers new Poisson points after a number of steps whose tail distribution is at least polynomial (Theorem 3).

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15.
arXiv (math.PR) 2026-06-24

Toeplitz Determinants and Admissible Correlation Intervals

Authors:
Thomas Erben↗

arXiv:2606.24603v1 Announce Type: new Abstract: For a homogeneous one-dimensional random field, positive semidefiniteness of finite Toeplitz correlation matrices imposes non-trivial constraints on admissible correlation coefficients. The widths of the corresponding admissible intervals are closely related to determinants of principal Toeplitz submatrices. Using the classical Desnanot–Jacobi determinant identity, I derive a simple determinantal representation for the widths of admissible correlation intervals. As an immediate consequence, I recover the product expressions for admissible interval widths previously stated by Schneider & Hartlap (2009). The argument places these relations into the general framework of classical Toeplitz determinant theory.

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16.
arXiv (quant-ph) 2026-06-17

Coherent Dark State Formation of a Lead-Vacancy Spin Qubit in Diamond

Authors:
Yiyang Chen↗Koyo Hirai↗Tzyy Zheng Neo↗Eiki Ota↗Takashi Taniguchi↗Masashi Miyakawa↗Shinobu Onoda↗Toshiharu Makino↗Mutsuko Hatano↗Takayuki Iwasaki↗

arXiv:2605.27841v2 Announce Type: replace Abstract: A lead-vacancy (PbV) center in diamond exhibits coherent emission above the liquid helium temperature, making it highly attractive for quantum network applications. Here, we report the magneto-optical and spin properties of PbV centers in diamond. We record a spin lifetime of 12 ms at 7.5 K under large off-axis magnetic field. Furthermore, we observe formation of the coherent dark state by coherent population trapping and estimate a spin dephasing time of 177 ns at 6.5 K. This work demonstrates the outstanding thermal robustness of the PbV spin compared to other group-IV centers above 4 K.

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17.
arXiv (CS.AI) 2026-06-24

AI-Driven Analytics of Team-Teaching Talk: Acoustic Patterns across Experience, Cohorts and the Learning Design

Authors:
Yuchen Liu↗Roberto Martinez-Maldonado↗Riordan Alfredo↗Paola Mejia-Domenzain↗Dwi Rahayu↗Sadia Nawaz↗

arXiv:2606.09831v2 Announce Type: replace-cross Abstract: As classroom cohorts expand, team teaching is increasingly used to integrate the expertise and pedagogical perspectives of multiple teachers. Yet, there is limited empirical understanding of how team teaching unfolds in practice, particularly regarding differences in teachers' contributions across experience levels, student cohorts, and learning task design. Prior research on team teaching has largely relied on retrospective self-reports or small-scale observations, offering limited insight into the micro-level processes through which team teaching is enacted. Teacher talk offers a scalable lens on these processes. While research in individual teaching contexts shows that acoustic features of speech (e.g., voice quality, intonation, and loudness) can shape student learning, evidence from team-teaching settings remains scarce. Moreover, capturing such features through manual observation or transcription is especially challenging in team-teaching classrooms, where multiple teachers speak across extended sessions and spatial locations, limiting scalability without automation. Grounded in spatial pedagogy theory and team-teaching research, this paper presents an AI-based speech processing approach to analyse classroom talk in team-teaching settings. We analysed 36 recorded undergraduate and postgraduate sessions involving 12 teachers. Spatial pedagogy behaviours were coded and acoustic features extracted to examine variation across teachers' experience, student cohorts, and the learning task design. The results reveal systematic differences, most notably in loudness dynamics: high-experience teachers, undergraduate classes and collaborative learning tasks exhibited greater loudness variation, suggesting more frequent modulation of volume to foreground key information and support classroom interaction and engagement.

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

Sub-Token Routing for KV Cache Compression

Authors:
Wei Jiang↗Wei Wang↗

Transformer inference often requires a large KV cache, especially for long-context language modeling and multimodal generation. Existing compression methods usually reduce cache cost by selecting, evicting, quantizing, or compressing cached tokens, or by reducing the visual-token sequence before language-model inference. We introduce sub-token routing, a KV-compression method that adds a finer control axis inside retained tokens. It splits each retained value vector into groups and keeps only selected groups, while leaving query and key states unchanged. The method is designed to work after token-level reduction. First, a token-reduction method determines which tokens are retained. Then, sub-token routing compresses the value states inside those retained tokens. Experiments under matched KV budgets show that adding sub-token routing improves token-level reduction performance in both LLM and VLM settings, including Quest on LLaMA-2-7B and Qwen2.5-7B, and FastV/VisionZip across LLaVA and Qwen-VL models. The gains are larger at smaller KV budgets, suggesting that value-group routing is especially useful when further token removal becomes costly. Overall, token-level reduction and sub-token routing provide complementary ways to reduce KV cost.

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

A Geometric Family of Correlations Containing the Quantum Singlet

Authors:
E. Aldo Arroyo↗

arXiv:2606.12045v1 Announce Type: new Abstract: We introduce a geometrically constrained hidden-variable framework that generates a family of correlations parametrized by a boundary function, within which the quantum singlet correlation appears as a particular member. Exact expressions for the correlation function are derived. Several structural results are established, including admissibility conditions, symmetry properties, a universal stationary point of the associated CHSH function, and an exact relation between the CHSH value at $\nu=\pi/4$ and a geometric contrast measure defined on the underlying hidden-variable distributions. Rather than treating the quantum singlet correlation as an isolated target to be reproduced, the present framework places it within a broader geometric structure of correlations. These results suggest the existence of a nontrivial geometric structure underlying the family of correlations and motivate the search for a principle capable of selecting the quantum singlet solution from within that family.

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

Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

Authors:
Baicheng Li↗Haizhao Yang↗Shijun Zhang↗

arXiv:2606.16975v1 Announce Type: cross Abstract: In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks. We first show that any function in $W^{2,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy, measured in the $W^{1,\infty}$-norm, by a fixed-size neural network using the Elementary Universal Activation Function ($\mathrm{EUAF}$). To extend this result to $W^{s,\infty}((a,b)^d)$ for $s\in\mathbb{N}$, we introduce a smooth activation $\mathrm{DUAF}_{\infty}$ from the family of Differentiable Universal Activation Functions ($\mathrm{DUAF}_n$). We prove that any function in $W^{s,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy in the $W^{s-1,\infty}$-norm by a fixed-size $\mathrm{DUAF}_{\infty}$-activated network. We further construct sigmoidal variants $\widetilde{\mathrm{DUAF}}_n$ and show that, for every $1\leq s\leq n$, fixed-size $\widetilde{\mathrm{DUAF}}_n$-activated networks still approximate any $f\in W^{s,\infty}((a,b)^d)$ with arbitrary accuracy in the $W^{s-1,\infty}$-norm. In all these results, the width and depth bounds are computed explicitly, and the proposed activations are elementary.

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

GRACE: Step-Level Benchmark for Faithful Reasoning over Context

Authors:
Hoang Pham↗Dong Le↗Anh Tuan Luu↗

Many reasoning tasks require models to reason over input context, from document-grounded question answering to rule-based deduction. Chain-of-Thought (CoT) prompting produces traces that appear transparent, yet individual steps can silently deviate from the source evidence, even when the final answer is correct. Existing methods detect hallucinations at the response level but fail to identify where in the chain a failure occurs or what type it is. We introduce GRACE, the first human-annotated step-level faithfulness benchmark with a data-driven error taxonomy for context-grounded textual reasoning. GRACE covers CoT traces from 10 models across 4 source datasets, with each step annotated for faithfulness, error category, and natural language explanation. A data-driven taxonomy, discovered bottom-up via unsupervised clustering, organizes failures into two tracks: GRACE-Inference (deductive errors) and GRACE-Grounding (factual grounding errors), with four categories each. The evaluation set is human-annotated and challenging by design. Our experiments reveal substantial headroom for current models. In addition, integrating step-level faithfulness signals into reinforcement learning pipelines improves both downstream accuracy and reasoning reliability.

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22.
arXiv (CS.CL) 2026-06-18

UniECG: Understanding and Generating ECG in One Unified Model

Authors:
Jiarui Jin↗Haoyu Wang↗Xiang Lan↗Jun Li↗Hongyan Li↗Shenda Hong↗

Electrocardiogram (ECG) interpretation is a fundamental skill in medical education, yet students often need more than static examples to connect waveform evidence with diagnostic reasoning. This paper presents UniECG as a step toward interactive ECG education. UniECG supports two complementary learning interactions: given an ECG signal or image, it generates an evidence-based explanation; given a textual learning objective, it generates a corresponding ECG signal example for case-based learning. The model follows a two-stage design. First, it learns grounded ECG explanation from ECG signal–image–text data. Second, it introduces special ECG generation tokens and aligns their hidden representations with a pretrained text-conditioned ECG diffusion model, enabling controllable signal-level ECG generation. We evaluate UniECG through grounded ECG explanation and generation-oriented qualitative analysis, examining its potential to support explanation and case-based learning. UniECG is intended as an educational aid and a research step toward interactive AI-assisted ECG learning, rather than a clinically validated diagnostic system.

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23.
arXiv (CS.CL) 2026-06-15

Fractured Chain-of-Thought Reasoning

Authors:
Baohao Liao↗Hanze Dong↗Yuhui Xu↗Doyen Sahoo↗Christof Monz↗Junnan Li↗Caiming Xiong↗

Inference-time scaling techniques have significantly bolstered the reasoning capabilities of large language models (LLMs) by harnessing additional computational effort at inference without retraining. Similarly, Chain-of-Thought (CoT) prompting and its extension, Long CoT, improve accuracy by generating rich intermediate reasoning trajectories, but these approaches incur substantial token costs that impede their deployment in latency-sensitive settings. In this work, we first show that truncated CoT, which stops reasoning before completion and directly generates the final answer, often matches the full CoT sampling while using dramatically fewer tokens. Building on this insight, we introduce Fractured Sampling, a unified inference-time strategy that interpolates between full CoT and solution-only sampling along three orthogonal axes: (1) the number of reasoning trajectories, (2) the number of final solutions per trajectory, and (3) the depth at which reasoning traces are truncated. Through extensive experiments on five diverse reasoning benchmarks and several model scales, we demonstrate that Fractured Sampling consistently achieves superior accuracy-cost trade-offs, yielding steep log-linear scaling gains in Pass@k versus token budget. Our analysis reveals how to allocate computation across these dimensions to maximize performance, paving the way for more efficient and scalable LLM reasoning. Code is available at https://github.com/BaohaoLiao/frac-cot.

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24.
arXiv (CS.AI) 2026-06-19

On the Limitations of Ray-Tracing for Learning-Based RF Tasks in Urban Environments

Authors:
Armen Manukyan↗Hrant Khachatrian↗Edvard Ghukasyan↗Theofanis P. Raptis↗

arXiv:2507.19653v2 Announce Type: replace-cross Abstract: We study the realism of Sionna v1.0.2 ray-tracing for outdoor cellular links in central Rome. We use a real measurement set of 1,664 user-equipments (UEs) and six nominal base-station (BS) sites. Using these fixed positions we systematically vary the main simulation parameters, including path depth, diffuse/specular/refraction flags, carrier frequency, as well as antenna's properties like its altitude, radiation pattern, and orientation. Simulator fidelity is scored for each base station via Spearman correlation between measured and simulated powers, and by a fingerprint-based k-nearest-neighbor localization algorithm using RSSI-based fingerprints. Across all experiments, solver hyper-parameters are having immaterial effect on the chosen metrics. On the contrary, antenna locations and orientations prove decisive. By simple greedy optimization we improve the Spearman correlation by 5% to 130% for various base stations, while kNN-based localization error using only simulated data as reference points is decreased by one-third on real-world samples, while staying twice higher than the error with purely real data. Precise geometry and credible antenna models are therefore necessary but not sufficient; faithfully capturing the residual urban noise remains an open challenge for transferable, high-fidelity outdoor RF simulation.

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25.
arXiv (CS.CL) 2026-06-16

LLM Judges Have Dark Current: A Psychometric Datasheet for LLM-as-a-Judge Evaluation

Authors:
Hiroyasu Usami↗Keisuke Hara↗Ayato Tsuboi↗Naohiko Matsuda↗

LLM-as-a-judge systems are now routinely used for open-ended model evaluation, where human preference annotation is costly, slow, and difficult to reproduce. Yet these judges are often reported as scalar accuracy, win-rate, or agreement devices. We argue that a judge should instead be reported as a measurement instrument. We introduce a Judge Datasheet protocol that measures dark current under true-vacuum inputs, stable cross-sensitivity to same-quality surface variation, positional false preference, target sensitivity on a controlled quality ladder, and the criterion or operating point induced by tie instructions. The direction-stability decomposition reveals that apparent Delta0 preference can be stable surface response or disguised position bias. In a three-judge open-weight case study, Llama-3.1-8B shows high dark current and presentation-conflicted Delta0 behavior, Qwen2.5-14B is vacuum-clean and target-sensitive but mixes stable and positional over-discrimination, and Qwen2.5-32B is vacuum-clean with low stable cross-sensitivity and low positional false preference. A strict tie criterion eliminates Qwen32B Delta0 false preference but absorbs marginal Delta1 target signals into ties while preserving Delta5 sensitivity. The results show that prompting moves the criterion, not the resolution. We do not claim that the downstream mechanism hypothesis that motivated this work is confirmed; the contribution is a metrological protocol for measuring the measuring device before downstream claims are made.

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