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01.
arXiv (quant-ph) 2026-06-19

Inhibited radiative decay enhances single-photon emitters

arXiv:2511.23301v2 Announce Type: replace Abstract: Quantum networks and modular quantum computers require efficient spin-photon interfaces, often realized using optical resonators that enhance radiative decay on a desired transition. However, this requires small mode volumes and high quality factors, which limits multiplexing capacity and demands precise frequency tuning. Here, we demonstrate an alternative approach that circumvents these bottlenecks for upscaling. Using a W1 silicon photonic crystal waveguide with a tailored photonic bandgap, we selectively inhibit unwanted decay pathways, thereby redirecting emission to the desired transition. This enables efficient photon collection over a large frequency range, allowing the resolution and individual addressing of tens of erbium dopants. Their lifetimes are preserved, or even increased, compared to bulk material. The extended mode volume of the devices enables the use of lower dopant concentrations, thereby improving emitter coherence. Our approach can be combined with Purcell enhancement and applied to other spin-qubit platforms, opening intriguing perspectives for photonic quantum technologies.

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

Lifted Schrödinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions

arXiv:2605.24795v2 Announce Type: replace-cross Abstract: We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics. Since the direct Schrödinger bridge between Gaussian mixtures is generally not available in closed form, we introduce a lifted path-space construction in which each trajectory is augmented with a source–target component label. Consequently, the problem decomposes into Gaussian component-to-component Schrödinger bridges with explicit marginal, drift, and cost formulas, while the mixture-level assignment reduces to a finite-dimensional entropic coupling problem with a Sinkhorn scaling form. We then analyze the projection obtained by discarding or forgetting the label. By construction, the projected law satisfies the original Gaussian-mixture endpoint constraints, but its relative entropy generally differs from the lifted relative entropy by a nonnegative conditional label-information gap. This gap reveals a path-space obstruction: the lifted optimizer cannot, in general, be identified with the direct unlabeled Schrödinger bridge after projection. We also derive the posterior-averaged Markov drift associated with the projected marginal flow, prove a kinetic-energy upper bound, and identify a common path-potential condition under which the projection gap vanishes. Several numerical illustrations showing density and shape control are recorded for a self-contained exposition.

03.
Science (Express) 2026-05-21

Nodeless superconducting gap and electron-boson coupling in (La,Pr,Sm)3Ni2O7 films | Science

作者: 未知作者

The discovery of superconductivity in Ruddlesden-Popper (RP) bilayer nickelate films under ambient pressure provides an opportunity to directly investigate electronic energy scales of the superconducting state and the pairing mechanism. We report angle-resolved photoemission spectroscopy measurements of superconducting (La,Pr,Sm) 3 Ni 2 O 7 thin films by developing an ultra-high vacuum cryogenic sample quenching and transfer technique. A superconducting gap of ~18 meV with coherence peaks is observed along the Brillouin zone diagonal. The finite gap persists across the entire Brillouin zone, revealing the absence of gap nodes. A kink is observed in the energy-momentum dispersion at ~70 meV below Fermi level, indicating an electron-boson coupling. The simultaneous observation of a nodeless superconducting gap and electron-boson coupling provides insight into the pairing symmetry and gluing mechanism in RP bilayer nickelates.

04.
arXiv (CS.LG) 2026-06-15

The Program Is Still There: A Conservation Law for Program Discovery

arXiv:2606.13799v1 Announce Type: cross Abstract: Finding the shortest program that generates a sequence is uncomputable, and for six decades that fact has been mistaken for a wall around finding any generating program. It is not a wall but a price, and this paper measures it. For every algorithm that learns about a candidate program only through its score, a class spanning Levin search, evolutionary methods, simulated annealing, and the cross-entropy method, we define the coupling width of a search problem and prove an unconditional worst-case lower bound, exponential in that width with base one less than the domain size. From it follows a conservation law: structural knowledge injected into a search trades one for one against the search it removes, and their sum can never fall below the length of the program sought. Levin's 1973 upper bound and the lower bound proved here are the two ends of one conserved quantity, closing on each other as the instruction set grows. The only escape is to read a candidate's structure rather than its score, and its price, which we prove for generic targets, is incompleteness. A deterministic engine built on this theory recovers a generating program, certified by compressing its data and predicting an unseen continuation, for 2,383 of 3,914 sequences across four independent populations, including 244 of the 256 elementary cellular automata, with measured discovery cost rising along program length more than an order of magnitude inside the score-oracle worst case.

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

A Computational Audit of Demographic Association Encoding in ClinicalBERT Language Predictions

Transformer-based clinical language models are increasingly integrated into high-stakes clinical decision support pipelines, yet the computational mechanisms through which demographic associations encoded in medical documentation propagate into model probability distributions remain empirically underspecified. We present a systematic computational audit of representational bias in ClinicalBERT (Alsentzer et al., 2019), a BERT-based model pretrained on MIMIC-III discharge summaries, employing two complementary probing methodologies: Log Probability Bias Analysis (LPBA), which quantifies demographic descriptor-induced shifts in masked token probability distributions across behavioral and evaluative semantic categories, and Masked Language Model-based analysis (MLM), which probes internal representational structure for demographic agency attribution encoding across 98 real clinical sentence templates and eight intersectional race-gender combinations. Corpus frequency analysis operationalizes the distinction between statistical disparity and bias amplification by benchmarking model outputs against empirical term frequencies in the MIMIC-III training corpus. Of 32 statistically significant findings, 65.6% contradict observed corpus distributions, rising to 80% for Black patients and 87.5% for agency attribution under MLM probing, providing direct empirical evidence that representational bias in ClinicalBERT operates predominantly through model-internal amplification rather than training data inheritance. Keywords: natural language processing, clinical documentation, algorithmic auditing, representational bias, health equity 1

06.
arXiv (CS.LG) 2026-06-18

Stochastic Thermodynamics and SDE-based Generative Models

作者:

arXiv:2606.18290v1 Announce Type: cross Abstract: SDE-based generative models, including diffusion models and the Schrödinger bridge, have found broad applications in signal processing tasks such as speech enhancement, image restoration, and time-series generation. This note presents a modeling framework for such models within the context of stochastic thermodynamics. The main results of this note are trajectory-level definitions of work, heat, and entropy production, along with a generalized Jarzynski identity and a second-law-like inequality. The proposed framework extends the original Jarzynski setup to accommodate time-dependent bath temperature and nonconservative driving forces. This thermodynamic perspective may deepen our understanding of diffusion models and the Schrödinger bridge from a nonequilibrium statistical mechanics viewpoint.

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

OneFocus: Enabling Real-World X-ray Security Screening with a Unified Vision-Language Model

X-ray contraband detection is critical for security in large-scale logistics and transportation, yet conventional detectors struggle to adapt to emerging contraband types and lack fundamental visual understanding. Vision-language models (VLMs) offer strong generalization but are hindered by the scarcity of high-quality X-ray image-caption data. To bridge this critical gap, we present MMXray, a meticulously curated benchmark of 52,124 image-caption pairs spanning 28 fine-grained classes of X-ray contraband. To enrich MMXray with realistic occlusion patterns, we further introduce CleanDET, a dedicated synthesis dataset containing clean foreground contraband images from 28 categories and background images with diverse density levels, together with AnyContraSyn, a controllable synthesis method designed to operate on CleanDET. We also develop OnePipe, an extensible pipeline for systematic data curation. Built on MMXray, we propose OneFocus, a unified VLM that supports four core tasks: visual question answering, contraband localization, classification, and image understanding. OneFocus achieves state-of-the-art performance in X-ray contraband understanding and demonstrates robust cross-domain generalization, establishing a strong vision-language baseline for security screening.

08.
arXiv (CS.LG) 2026-06-11

Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations

arXiv:2605.04853v2 Announce Type: replace Abstract: We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error. A base low-regularity integrator provides a consistent first-order approximation to nonlinear dispersive PDEs, while a lightweight neural network, operating on a low-dimensional latent manifold, learns the residual defect that analytical methods cannot close. An explicit time-step scaling on the neural correction ensures that its Lipschitz contribution remains $\mathcal{O}(\tau)$, yielding a Gronwall stability factor bounded uniformly in the step size and independent of the spatial resolution. The network is trained end-to-end through a solver-in-the-loop objective that unrolls the full iteration and penalises trajectory error in a Bourgain-type norm, aligning learning with multi-step solver dynamics rather than isolated one-step targets. Under stated assumptions, the global error satisfies $C(\varepsilon_{net}+\delta)\,\tau^\gamma\ln(1/\tau)$, where $\varepsilon_{net}$ measures the network approximation quality and $\delta$ the training shortfall. Experiments on three dispersive benchmarks with rough data show that HIN-LRI improves accuracy over analytical integrators, splitting methods, and neural PDE surrogates, with stable spatial refinement, effective out-of-distribution transfer, and modest online overhead.

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

Weakly Supervised Segmentation as Semantic-Based Regularization

Weakly supervised semantic segmentation (WSSS) trains dense pixel-level segmentation models from partial or coarse annotations such as bounding boxes, scribbles, or image-level tags. While recent work leverages foundation models such as the Segment Anything Model (SAM) to generate pseudo-labels, these approaches typically depend on heuristic prompt choices and offer limited ways to incorporate prior knowledge or heterogeneous labels. We address this gap by taking a neurosymbolic perspective: integrating differentiable fuzzy logic with deep segmentation models. Weak annotations and domain-specific priors are unified as continuous logical constraints that fine-tune SAM under weak supervision. The refined foundation model then produces improved pseudo-labels, from which we train a second-stage prompt-free segmentation model. Experiments on Pascal VOC 2012 and the REFUGE2 optic disc/cup segmentation dataset show that our logic-guided fine-tuning yields higher-quality pseudo-labels, leading to state-of-the-art segmentation accuracy that often exceeds densely supervised baselines.

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

CODA-BENCH: Can Code Agents Handle Data-Intensive Tasks?

Advanced agents are increasingly demonstrating the potential to operate as autonomous engineers, creating a growing demand for evaluation benchmarks that capture the complexity of real-world development. Such environments typically involve both complex code and large-scale data (i.e., file system). However, existing benchmarks usually evaluate code-centric or data-centric capabilities in isolation, leaving a clear gap with real development scenarios. In this paper, we bridge this gap by introducing CODA-BENCH, the first benchmark to jointly evaluate code and data intelligence in a data-intensive environment. We construct a data-intensive Linux sandbox based on the Kaggle ecosystem (containing hundreds of datasets), where agents must actively explore complex file hierarchies to identify relevant resources and generate code for data-driven analytical tasks. CODA-BENCH comprises 1,009 tasks spanning 31 communities, with each task environment containing an average of 980 files, simulating realistic data scale and noise. Evaluations of advanced agents reveal that even top-performing systems struggle to effectively integrate data discovery with code execution, achieving a success rate of only 61.1%. These results highlight a substantial gap in current agentic capabilities for data-intensive tasks and point to promising directions for future research.

11.
Nature (Science) 2026-06-09

How ice forms is a mystery — now scientists are cracking the case

Theories about how ice crystals grow in cooling liquids are wildly inaccurate when compared with experimental data, but studies are starting to illuminate the earliest moments in freezing. Theories about how ice crystals grow in cooling liquids are wildly inaccurate when compared with experimental data, but studies are starting to illuminate the earliest moments in freezing.

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

Generalizing Beyond Suboptimality: Offline Reinforcement Learning Learns Effective Scheduling through Random Solutions

arXiv:2509.10303v2 Announce Type: replace-cross Abstract: Online reinforcement learning (RL) approaches have demonstrated strong performance on Job Shop Scheduling (JSP) and Flexible JSP (FJSP) problems by learning scheduling policies through direct interaction with simulated environments. However, these methods often require extensive training interactions, limiting their sample efficiency and practical applicability. Motivated by this challenge, we introduce Conservative Discrete Quantile Actor-Critic (CDQAC), an offline RL algorithm that learns effective scheduling policies directly from static, suboptimal datasets. CDQAC couples a quantile-based critic with delayed policy updates to estimate the return distribution of machine-operation pairs. Extensive experiments on JSP and FJSP benchmarks demonstrate that CDQAC consistently outperforms the data-generating heuristics, surpasses state-of-the-art offline and online RL baselines, and is highly sample efficient, requiring only 1 to 5% of the original dataset to learn high-quality policies. Our analysis suggests that, in scheduling, offline RL performance is governed mainly by state-action coverage rather than the quality of individual trajectories. Scheduling couples a dense reward aligned with the makespan objective with equal-length trajectories across heuristics, enabling effective learning from a broad range of behaviors. Consistent with this observation, datasets generated by a simple random heuristic with broader coverage let it outperform policies trained on datasets produced by stronger heuristics such as Genetic Algorithms.

13.
arXiv (CS.AI) 2026-06-17

Patients With Personality: Realistic Patient Simulation through Controlled Diversity and Selective Disclosure

arXiv:2606.17441v1 Announce Type: cross Abstract: Simulating realistic patient interactions is a key requirement to testing clinical applications of LLMs at scale without time-consuming and expensive user studies. However, existing approaches often lack realism and controllability, often oversharing information unprompted, and failing to capture the wide variability of patient behavior. Here, we introduce PatientsWithPersonality (PWP), a patient simulation framework that generates realistic yet diverse virtual patient responses through explicit personality parametrization over a latent patient state. Grounded in HEXACO, a six-dimensional personality space used to quantify and parameterize human behavioral traits, our approach enables fine-grained control over conversational style, cooperativeness, and information disclosure within a unified framework. In a clinician evaluation, PWP is judged nearly as realistic as recorded human actors and clearly ahead of prior simulators, while being flagged as "too informative" far less often. Conditioning on HEXACO axes yields personas whose configured traits are recoverable by both clinicians and an autorater, span a substantially wider behavioral footprint than the closest baseline, and prevent oversharing. Altogether, our framework paves the way for more accurate and informative LLM benchmarking through our realistic and steerable patient simulator.

14.
arXiv (CS.CL) 2026-06-15

"I Didn't Make the Micro Decisions": Measuring, Inducing, and Exposing Goal-Level AI Contributions in Collaboration

As large language models (LLMs) increasingly shape how users form, refine, and extend their goals, attributing contributions in human-AI collaboration becomes critical for users calibrating their own reliance and for evaluators assessing AI-assisted work. Yet existing methods focus on final artifacts, missing the process through which goals themselves are jointly shaped. We introduce a goal-level attribution framework, CoTrace, that decomposes explicit goals into verifiable requirements and traces both direct contributions and indirect influences across dialogue turns. Applying CoTrace to 638 real-world collaboration logs, we find that while models account for only 11-26% of goal-shaping contribution, they contribute substantially more on introducing lower-level concrete requirements, and make various kinds of indirect contributions. Through controlled simulations, we show that interaction design choices significantly affect model goal-shaping behavior. In a user study, exposing participants to goal-level analyses shifts their perceived contributions by nearly 2 points on a 5-point scale, revealing systematic miscalibration in how users understand their own AI-assisted work.

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

Rubric-Guided Self-Distillation: Post-Training Without Rubric Verifiers

arXiv:2606.12507v1 Announce Type: new Abstract: Rubrics have emerged as an alternative to RLVR in open-ended domains where a single ground-truth final answer is not available. Existing rubric-based training methods rely on an LLM verifier that scores each rollout against rubrics. This introduces substantial training-time overhead, exposes optimization to verifier-specific biases, and reduces rubric feedback to a sparse end-of-trajectory signal. We propose Rubric-Guided Self-Distillation (RGSD), a verifier-free training method in which the base policy, conditioned on the rubric, serves as the teacher for the unconditioned student. RGSD distills the rubric-conditioned teacher distribution into the student token-by-token, replacing sparse trajectory-level rewards with dense per-token learning signals and removing the LLM judge from the training loop entirely. Across Qwen-2.5 (3B, 7B) and Qwen3-Thinking (4B, 8B) models on medical and science domains, RGSD achieves rubric satisfaction comparable to judge-based GRPO while using one on-policy rollout per prompt and no training-time verifier calls. Ablations show that raw rubrics provide a stronger teacher enrichment signal than self-generated reference responses, while a stronger GRPO judge can outperform RGSD in some settings, positioning RGSD as a complementary verifier-free alternative when verifier cost or reliability is the bottleneck.

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

ReproRepo: Scaling Reproducibility Audits with GitHub Repository Issues

Reproducing research results from papers and released code is central to scientific progress. Existing works have introduced benchmarks to evaluate whether LLM agents can assist with reproducibility, but they are difficult to scale due to their reliance on substantial manual effort for data curation and evaluation. We introduce ReproRepo, a scalable framework for reproducibility evaluation that leverages human-raised GitHub issues as naturally occurring supervision on realistic reproduction blockers. We instantiate ReproRepo on 1,149 recent machine learning papers from major conferences and evaluate four frontier model-agent configurations. Our results show that LLM agents, even without executing code, can identify many real-world reproducibility problems from paper-repository pairs: the best agent in our study, namely Codex with GPT-5.5, surfaces at least one semantically related human-reported blocker for ~90% of papers in the study. Further analysis shows that agents are particularly effective for surfacing visible failures and identifying the right semantic region, but may still be insufficient in exact localization. ReproRepo can serve as a reusable, scalable framework for future evaluations of LLM agents on real-world reproducibility auditing. Our code is released at https://github.com/LithiumDA/ReproRepo.

17.
arXiv (CS.CL) 2026-06-11

Kuramoto Attention: Synchronizing Self-Attention on the Torus

We introduce Kuramoto attention, a self-attention layer in which each hidden coordinate is an angle. The layer scores tokens by gated cosine similarity, attends over previous phase states, and updates each token by the tangent component of the attention-weighted circular mean. Because the values are the raw phase states, this update is exactly the Kuramoto coupling term $\sum_u A_{t,u}\sin(\theta_u-\theta_t)$, with the attention matrix acting as an adaptive, content-dependent coupling kernel. Equivalently, the gated score is a learned metric on the torus that selects which tokens couple, and the update pulls each token toward the circular mean of the tokens it selects, tightening their phase agreement. The same two ingredients, an invariant similarity score and an on-manifold mean, define such a layer on any compact group; the torus is the abelian case, where both are closed-form. The softmax weights solve an entropy-regularized phase-retrieval problem, and rotary position enters as a position-dependent phase drift in the score. On enwiki8 character-level language modeling, the layer trains as a functional language model whose bits-per-character stays close to a strong matched RoPE+SwiGLU transformer: within $0.02$ BPC at one million parameters ($1.637\pm0.010$ versus $1.616\pm0.004$) and level on the median at five million ($1.448$ versus $1.452$ over five seeds) with the transformer ahead on the mean ($1.468$ versus $1.456$). These experiments establish that the constrained geometric structure is a viable language model at this scale; the structure itself, and its synchronization reading, is the contribution. Ablations isolate the load-bearing components, and the result gives a compact bridge between self-attention and phase synchronization.

18.
arXiv (CS.LG) 2026-06-12

The Mathematics of AI Winters: The mathematical Taxonomy of Paradigm Fragility in AI Winter

arXiv:2606.12610v1 Announce Type: new Abstract: Two major periods of reduced funding and confidence in artificial intelligence research, commonly called the first and second AI winters, are usually explained through engineering failure, commercial disappointment, and inflated expectations. This article develops a complementary thesis: that the dominant paradigms of those periods also met genuine formal barriers, including limitations of representation, optimisation, computational complexity, statistical learnability, and high-dimensional approximation. The contribution is synthetic rather than archival. We do not claim that particular theorems mechanically caused the winters; rather, we show that several central disappointments of early AI were aligned with mathematically precise bottlenecks. We analyse these bottlenecks through the perceptron impossibility results of Minsky and Papert, the complexity-theoretic hardness of exact neural-network training established by Blum and Rivest, minimax rates for nonparametric estimation in high dimension due to Stone, vanishing-gradient analyses by Hochreiter and by Bengio and collaborators, and classical statistical learning theory in the tradition of Vapnik and Chervonenkis, Valiant, and Blumer and collaborators. We then relate these barriers to the later breakthroughs that mitigated, rather than eliminated, them.

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

Wasserstein Policy Learning for Distributional Outcomes

arXiv:2606.19117v1 Announce Type: cross Abstract: Offline policy learning has received growing attention in causal inference. The primary objective is to learn a policy (individualized treatment rule) as a mapping from covariates to treatment that maximizes the empirical welfare defined as the mean of scalar-valued potential outcomes. In this paper, we study offline policy learning with distribution-valued outcomes, where each potential outcome is a probability measure on $\mathbb{R}$ and the reward is defined through a utility functional applied to the Wasserstein barycenter of induced outcome distributions. We establish statistical guarantees for the policy learning framework based on both Inverse Probability Weighting (IPW) and Doubly Robust (DR) estimators. By handling the challenging uniform deviation over the product of the combinatorial policy class and the infinite-dimensional quantile domain, we prove that the finite-sample regret has leading dependence $\widetilde{\mathcal{O}}(\sqrt{\mathrm{N-dim}(\Pi)/N})$. In the one-dimensional Wasserstein setting and under the stated regularity conditions, the leading regret rate is still governed by the policy-class complexity. Moreover, we provide a minimax lower bound establishing the sharpness of the leading dependence on $N$ and $\mathrm{N-dim}(\Pi)$.

21.
arXiv (CS.LG) 2026-06-12

Circuit Synchronization Precedes Generalization: Causal Evidence from Fourier Structure in Grokking Transformers

arXiv:2606.12966v1 Announce Type: new Abstract: Grokking – where a transformer on modular arithmetic suddenly transitions from near-chance to near-perfect validation accuracy – is attributed to a Fourier circuit, but its timing, causal structure, and controllability remain poorly understood. We introduce the Frequency Synchronization Degree (FSD), a normalised, permutation-tested metric for Fourier circuit synchronisation requiring no prior circuit knowledge. Across nine modular addition configurations (primes p in {53, 71, 97, 113, 131}, three seeds), FSD synchronises 500-3,000 steps before grokking (mean lead +1,722 steps; all nine positive, sign-test p~0.004), and precedes a restricted-logit loss baseline (Nanda et al.'s excluded loss) in all nine cases, making it the earliest available predictor. We provide direct causal evidence that the inter-phase gap is a regularisation phenomenon: forking training at the FSD-ceiling step and varying weight decay lambda produces strictly monotone earlier grokking, with Delta_t proportional to 1/lambda. This law replicates across three primes (p in {53,97,131}; R^2=1.00 and R^2=0.99 for two clean cases), captured as Delta_t ~ C/lambda, consistent with (1/lambda)*log(||W_mem||/tau). Architecture ablations show an attention-only model groks with a strong FSD precursor; an MLP-only model never groks; a single-layer model's FSD lags, confirming the precursor is a multi-block circuit property.

22.
arXiv (CS.LG) 2026-06-15

How Task Structure Limits Multi-Agent Success: An Information-Theoretic Analysis

arXiv:2606.13733v1 Announce Type: cross Abstract: Multi-agent systems (MAS) were expected to overcome the limitation of single-agent systems (SAS) through collaboration. However, under typicality conditions on the task's constraint graph and bounded inter-agent communication, we prove that the success probability of a MAS is closely tied to the connectivity of task constraints, where each agent has limited information-processing capacity. Specifically, the success probability decays exponentially with an information bottleneck that emerges from partitioning the task's constraint graph among agents. We define this quantity as the minimum cut cost $C_{\min}$ of the potential constraint graph of each task. This information-theoretic bound applies to both open systems with external feedback and closed systems without. We validate our theory on both synthetic experiments and real-world empirical data from SWE-bench submissions. From our framework, effective MAS design should incorporate task-inherent constraints alongside engineering optimization, and when $\Cmin$ is high, practitioners should restructure tasks rather than simply scaling agents or communication.

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

Resource-Aware LLM Reasoning for Mobile Edge General Intelligence

arXiv:2509.23248v3 Announce Type: replace Abstract: The rapid advancement of large language models (LLMs) has enabled an emergence of agentic artificial intelligence (AI) with powerful reasoning and autonomous decision-making capabilities. This integration with edge computing has led to the development of Mobile Edge General Intelligence (MEGI), which brings real-time, privacy-preserving reasoning to the network edge. However, deploying LLM-based agentic AI reasoning in MEGI environments poses significant challenges due to the high computational demands of reasoning and the limited resources of edge devices. To address these challenges, we propose a joint optimization framework for efficient LLM reasoning deployment in MEGI. First, we systematically review enhancement methods to identify mechanisms suitable for edge adaptation. Subsequently, we present a distributed framework that synergizes reasoning enhancement via adaptive CoT prompting with scalable deployment through a distributed MoE architecture. An important innovation of this approach involves modeling reasoning depth as a dynamic network resource variable, which is optimized jointly with expert activation and transmission power. This mechanism allows the system to dynamically regulate expert networks and reasoning complexity according to task requirements and device capabilities. Experimental evaluations in mobile edge environments demonstrate that the proposed framework effectively balances reasoning quality and resource efficiency. The results show that with less than one second of additional inference time, both accuracy and latency satisfaction rate can reach 90\%, validating the practical viability of deploying sophisticated LLM reasoning in resource-constrained MEGI systems.

24.
arXiv (math.PR) 2026-06-17

A Tanaka-Type Formula for Compact Sets and Equilibrium Measures of L\'{e}vy Processes

arXiv:2606.17472v1 Announce Type: new Abstract: Tanaka's formula is a classical identity for Brownian motion, and Tsukada (2018) extended it to L\'{e}vy processes not necessarily symmetric. From a potential-theoretic point of view, this formula shows that the invariant function for the process killed upon hitting a singleton can be decomposed into the sum of a martingale part and a local time. In this paper, we generalize this singleton setting and derive a Tanaka-type formula for a compact set $B$. To this end, we introduce the equilibrium measure, defined as the rescaled limit of the $q$-capacity measures, and show that the invariant function for the process killed upon hitting $B$ can be represented as the integral, with respect to the equilibrium measure, of the invariant functions associated with processes killed upon hitting singletons, up to an additive constant called the Robin constant. Moreover, when $B$ is an interval, we obtain explicit representations of the equilibrium measure, the Robin constant, and the martingale part for recurrent stable processes as well as for recurrent spectrally negative L\'{e}vy processes. Finally, we discuss how an analogous Tanaka-type formula can also be established for transient L\'{e}vy processes.

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

Deep Q-Learning on Hölder Spaces

作者:

arXiv:2606.16846v1 Announce Type: cross Abstract: We study the operator-theoretic core of Q-learning in continuous-time stochastic control with continuous states and actions. In value-based reinforcement learning, each Q-learning or DQN update is built from a Bellman optimality target; our analysis isolates this target in a diffusion setting and studies its regularity and approximation complexity. Under uniform ellipticity and Hölder-regular coefficients, we show that a Bellman update maps bounded inputs into an anisotropic regularity class, smoothing the state variable while leaving only Lipschitz dependence on the action variable. This yields a compact family of Bellman iterates and motivates a tensor-product DeepONet architecture adapted to the mixed regularity of the problem. We then derive explicit approximation and resource bounds, together with a stiffness–complexity trade-off as the time step $\delta \to 0$. The resulting theory makes a direct contribution to Q-learning theory at the level of Bellman target regularity and approximation in continuous stochastic control. At the same time, we do not claim a full convergence theorem for practical sampled Q-learning with exploration, replay, and stochastic gradient updates.