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01.
arXiv (math.PR) 2026-06-18

Kemeny's constant minimization for reversible Markov chains via structure-preserving perturbations

arXiv:2510.24679v4 Announce Type: replace-cross Abstract: Kemeny's constant measures the efficiency of a Markov chain in traversing its states. We investigate whether structure-preserving perturbations to the transition probabilities of a reversible Markov chain can improve its connectivity while maintaining a fixed stationary distribution. Although the minimum achievable value for Kemeny's constant can be estimated, the required perturbations may be infeasible. We reformulate the problem as an optimization task, focusing on solution existence and efficient algorithms, with an emphasis on the problem of minimizing Kemeny's constant under sparsity constraints.

02.
arXiv (CS.CV) 2026-06-16

On the Adversarial Robustness of Multimodal LLM Judges

Multimodal Large Language Models (MLLMs) are increasingly used as automated judges, e.g., for image quality and safety assessment. However, their adversarial robustness remains largely unexplored, threatening the fairness and reliability of automated judging. To bridge this gap, we introduce RobustMLLMJudge, the first general framework for evaluating the adversarial robustness of general-purpose MLLMs when functioning as judges. It covers diverse attacks against popular judge approaches across quality and safety evaluation scenarios. Using RobustMLLMJudge, we reveal that i) different MLLM judges are highly vulnerable to score-inflating adversarial attacks; and ii) although effective, these attack methods face a critical challenge due to unique constraints in the evaluation protocols of MLLM judges. We further propose MGSIA, namely Manifold-Guided Semantic Induction Attack, a novel method that bypasses these constraints to enable more effective and transferable attacks on MLLM judges. The core idea of MGSIA is to combine affirmative semantic induction with high-score manifold alignment: it maximizes the probability that judges yield affirmative responses (e.g., "Yes") to binary semantic queries, while regularizing adversarial representations toward high-score centers estimated from proxy protocols. Together, these objectives yield transferable score-inflating perturbations. Extensive experiments demonstrate the superiority and generalizability of MGSIA in deceiving advanced MLLM judges under different evaluation scenarios, highlighting the need for robust MLLM judges. Code and data will be made available at https://github.com/mala-lab/RobustMLLMJudge.

03.
arXiv (CS.LG) 2026-06-19

Comparative Study of Neural Surrogate Architectures for Autoregressive Prediction of Internal Battery States

arXiv:2606.20053v1 Announce Type: new Abstract: The Doyle-Fuller-Newman (DFN) model resolves internal electrochemical states in lithium-ion batteries with high fidelity. However, the numerical solution of its governing equations is computationally prohibitive for real-time deployment, limiting scalability from individual cells to pack and fleet-scale applications. While machine learning surrogates can substantially reduce inference latency through GPU acceleration, most existing approaches learn solution approximations tied to specific operating conditions rather than learning generalizable state-evolution dynamics. This work presents a systematic comparison of four neural network architectures (MLP, ResNet, U-Net, FNO) formulated as autoregressive state-transition operators that predict full DFN internal states across a wide range of operating conditions. To ensure a controlled architectural comparison, all models are trained under a unified framework using multi-step unrolling and current-conditioning, isolating the impact of spatial inductive bias. Results demonstrate that the U-Net's multi-scale feature hierarchy achieves a mean final-step nRMSE of 3% averaged across all internal state variables after 300-step autoregressive rollouts, while providing a 5.38x speed-up over the numerical solver. These findings highlight spatial inductive bias as a critical determinant of surrogate performance, advancing the development of surrogates for internal state observability for next-generation battery management systems and digital twins.

04.
arXiv (CS.LG) 2026-06-16

ExpRL: Exploratory RL for LLM Mid-Training

arXiv:2606.17024v1 Announce Type: new Abstract: Sparse reward reinforcement learning (RL) has become a standard tool for improving LLM reasoning, but its success depends critically on the coverage present in the base model. In practice, models are often primed for RL through mid-training on curated reasoning traces that teach useful primitive skills such as decomposition, verification, or self-correction. Although effective, this strategy requires manually specifying what the model should learn, and it remains unclear whether such primitive coverage is enough for much harder problems, which require combining these skills into broader solution strategies. We study a more automated approach: RL-based mid-training using large corpora of human-written question-answer data. Rather than treating reference solutions as targets to imitate, our method, ExpRL, uses them as reward scaffolds: references are hidden from the policy and used only to construct problem-specific grading rubrics for judging on-policy reasoning traces. The policy samples from the original problem prompt, while an LLM judge compares the sampled reasoning trace against the reference solution and assigns outcome-level or process-level dense rewards. This lets ExpRL reinforce partial progress, useful intermediate reductions, and productive reasoning behaviors that sparse final-answer rewards often fail to upweight. On challenging math reasoning tasks, ExpRL yields stronger RL priming than SFT, sparse-reward GRPO, and self-distillation, and provides a better initialization for subsequent sparse-reward RL. Additional mixed-domain experiments further suggest that ExpRL can extend beyond the original math-only setting.

05.
arXiv (CS.CV) 2026-06-17

TextMesh4D: Zero-shot Text-to-4D Mesh Generation

Large-scale, high-quality dynamic 3D (4D) assets are essential for learning physically grounded representations, but remain costly to capture and annotate at scale. This limits the viability of supervised 4D learning and motivates zero-shot text-to-4D generation leveraging pretrained diffusion priors. To model complex dynamics, prior methods typically adopt implicit 3D representations (e.g., NeRFs or 3DGS) for their deformation capacity. However, their implicit nature provides limited control over surface topology, which hinders high-fidelity geometry and makes temporally coherent surface reconstruction challenging. To address these limitations, we explore zero-shot text-to-4D mesh generation. However, a structural mismatch arises when combining diffusion-based guidance with topology-constrained meshes: the guidance is noisy and spatially inconsistent, while meshes impose severe topological constraints, making direct vertex-level deformation unstable. In this paper, we introduce TextMesh4D, the first zero-shot framework for text-to-4D that directly generates dynamic meshes by addressing the above challenge at two complementary levels. Geometrically, we shift deformation modeling from vertices to faces via a Jacobian Deformation Field (JDF), enabling topology-aware surface reconstruction through an integrability-enforcing integration formulation. Semantically, we propose a Local-Global Semantic Regularizer (LGSR) that preserves identity over time by jointly constraining local deformation plausibility and global shape consistency. Extensive experiments demonstrate state-of-the-art temporal consistency, structural fidelity, and visual quality, while remaining efficient on a single 24GB GPU.

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

Leveraging systems' non-linearity to tackle the scarcity of data in the design of Intelligent Fault Diagnosis Systems

arXiv:2606.20323v1 Announce Type: new Abstract: Deep Transfer Learning (DTL) allows for the efficient building of Intelligent Fault Diagnosis Systems (IFDS). On the other hand, DTL methods still heavily rely on large amounts of labelled data. Obtaining such an amount of data can be challenging when dealing with machines or structures faults. This document proposes a novel approach to the design of vibration-based IFDS using DTL in condition of strong data scarcity. A periodic multi-excitation level procedure leveraging intrinsic non-linearities of real-world systems is used to produce images that can be conveniently analysed by pre-trained Convolutional Neural Networks (CNNs) to diagnose faults. A new data visualization method and its augmentation technique are proposed in this paper to tackle the typical lack of data encountered during the design of IFDS. Experimental validation on a railway pantograph structure provides effective support for the proposed method.

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

Cross-modal Identity Mapping: Minimizing Information Loss in Modality Conversion via Reinforcement Learning

Large Vision-Language Models (LVLMs) often omit or misrepresent critical visual content in generated image captions. Minimizing such information loss will force LVLMs to focus on image details to generate precise descriptions. However, measuring information loss during modality conversion is inherently challenging due to the modal gap between visual content and text output. In this paper, we argue that the quality of an image caption is positively correlated with the similarity between images retrieved via text search using that caption. Based on this insight, we further propose Cross-modal Identity Mapping (CIM), a reinforcement learning framework that enhances image captioning without requiring additional annotations. Specifically, the method quantitatively evaluates the information loss from two perspectives: Gallery Representation Consistency and Query-gallery Image Relevance. Supervised under these metrics, LVLM minimizes information loss and aims to achieve identity mapping from images to captions. The experimental results demonstrate the superior performance of our method in image captioning, even when compared with Supervised Fine-Tuning. Particularly, on the COCO-LN500 benchmark, CIM achieves a 20% improvement in relation reasoning on Qwen2.5-VL-7B.

08.
medRxiv (Medicine) 2026-06-12

An integrative multi-omics framework identifies epigenetic dysregulation of HAND2 as a potential primary driver of impaired enteric neural crest cell differentiation in Hirschsprung Disease

Hirschsprung disease (HSCR) is a congenital neurodevelopmental disorder characterized by segmental aganglionosis due to impaired developmental processes of enteric neural crest cells (NCCs). Despite being the leading genetic cause of functional intestinal obstruction in early childhood, HSCR represents a paradigmatic challenge in precision medicine: its multifactorial etiology, complex gene-environment interactions and limited resolution of single-modality analyses have long hindered mechanistic understanding and therapeutic translation. Here, we applied an integrative multi-omics approach combining genetic, phenotypic, epigenomic and transcriptomic analyses of matched ganglionic and aganglionic formalin-fixed paraffin-embedded (FFPE) patient tissues, complemented by patient-specific in vitro models. Beyond established genetic contributors, our integrative approach reveals novel regulatory pathways predominantly affecting enteric NCC differentiation, with convergent evidence pointing to epigenetic dysregulation as a primary disease mechanism. Notably, we identified over 1,300 differentially methylated positions between ganglionic and aganglionic FFPE samples, with HAND2 emerging as a key candidate due to multiple hypermethylated sites and consistently reduced expression levels in aganglionic tissues and in vitro models, suggesting a potential role in HSCR pathophysiology. We propose that our multi-omics approach offers a powerful and comprehensive framework for dissecting disease mechanisms. Beyond advancing biological understanding, this strategy holds promise for paving the way for molecularly informed patient stratification and supporting the development of personalized treatment and postoperative management strategies.

09.
arXiv (CS.LG) 2026-06-16

Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning

arXiv:2606.14970v1 Announce Type: new Abstract: Fine-tuning large language models (LLMs) has become a central application of modern optimization, enabling pretrained models to adapt to diverse downstream tasks and domain-specific data. A major obstacle in large-scale fine-tuning is the memory overhead of backpropagation, which requires storing activations, gradients, and optimizer states. Zeroth-order (ZO) optimization offers a memory-efficient alternative, but its performance is highly sensitive to the stepsize and smoothing parameter, often requiring costly task-specific tuning. Parameter-free (PF) optimization addresses this issue by adapting algorithmic parameters without prior knowledge of problem-dependent constants. Moreover, large-scale fine-tuning can benefit from geometry-aware updates that account for the heterogeneous structure of parameter blocks, which can be modeled through methods that exploit linear minimization oracle (LMO). In this work, we study PF adaptation for LMO-based ZO optimization and introduce $\texttt{AdaNAGED}$, a method that unifies gradient-free training, adaptive tuning, and non-Euclidean update geometry. We establish convergence guarantees and validate the method on large-scale LLM fine-tuning task with $\texttt{OPT}-1.3\mathrm{B}$ model.

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

DeXposure-Claw: An Agentic System for DeFi Risk Supervision

Decentralized finance exposes supervisors to fast-moving, networked credit risks. General-purpose LLM agents fit this setting poorly: they over-read weak evidence and recommend high-stakes interventions, while existing evaluations offer no regulator-aligned way to measure the resulting false alarms. We introduce DeXposure-Claw, a forecast-grounded agentic supervision system that routes LLM decisions through structured evidence: (1) DeXposure-FM, a graph time-series foundation model, forecasts future exposure networks; (2) deterministic monitors and stress scenarios then turn those forecasts into typed alerts, attribution signals, and scenario evidence; and (3) data-health and confidence gates constrain escalation before DeXposure-Claw emits auditable supervisory tickets with rationales. We further develop DeXposure-Bench, a six-axis evaluation harness, whose decision axis scores tickets against a regulator-aligned absolute-loss ground truth and an explicit false-intervention rate. Experiments on five years of weekly real data fully support our system. Code is at https://github.com/EVIEHub/DeXposure-Claw.

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

SupraBench: A Benchmark for Supramolecular Chemistry

Supramolecular chemistry, which includes the study of non-covalent host-guest assemblies, has advanced various applications. However, designing host-guest systems remains time-consuming, requiring days of dry-lab verification per candidate pair. Although LLMs have emerged as a fast alternative with strong performance on molecular binding tasks, no benchmark currently systematically evaluates LLMs for host-guest reasoning across fundamental supramolecular chemistry tasks, e.g., binding affinity prediction. To this end, we collaborate with domain experts to release the first Supramolecular Benchmark, called SupraBench, to evaluate LLMs in chemistry reasoning. Specifically, we design four fundamental tasks, i.e., binding affinity prediction, top-binder selection, solvent identification, and host-guest description, plus an auxiliary vision-based task for molecular identification. We also release SupraPMC, a curated 16M-token corpus of Supramolecular chemistry articles distilled from Europe PMC, to support the adaptation to the supramolecular domain. We benchmark a broad range of open and proprietary LLMs and find that LLMs leave substantial headroom across all tasks. Domain adaptation pretraining over SupraPMC transfers cleanly to in-distribution regression but trades off against strict letter-format output. Moreover, the difficulty profile differs sharply across task families, revealing distinct failure modes that indicate specific gaps in current supramolecular chemistry reasoning. Our source codes and benchmark datasets are available at https://github.com/Tianyi-Billy-Ma/SupraBench.

13.
arXiv (math.PR) 2026-06-12

Storage and Transport Capacity Design for a Self-Reliable Two-Node Stochastic Resource System

arXiv:2606.12707v1 Announce Type: cross Abstract: We study a two-node stochastic resource system operating over a finite horizon. Each node experiences uncertain supply and demand and is equipped with finite storage. The objective is to ensure that resource levels remain within prescribed limits with high probability. To this end, we formulate a chance-constrained capacity-design problem in which resources can be exchanged through a capacity-limited transport link. We characterize the minimum storage required at each node, derive the optimal transport policy, and quantify the trade-off between storage and transport capacities. Our results show the existence of a critical transport-capacity threshold that enables full risk pooling between the nodes. Moreover, this threshold decreases with the operating horizon, implying that full-pooling performance can be achieved with progressively smaller transport capacity over longer horizons.

14.
bioRxiv (Bioinfo) 2026-06-13

PertDiffBench: Benchmarking Diffusion Models for Single-Cell Perturbation Response Prediction

Diffusion models are increasingly used to predict transcriptional responses to perturbations, but whether they improve on simpler generative and representation-based baselines remains unclear. Existing evaluations often do not separate the effects of model architecture, input representation, biological context and metric choice, making it difficult to determine where diffusion-based methods are useful. Here we introduce PertDiffBench, a standardized benchmark for diffusion-based transcriptomic perturbation prediction across single-cell and bulk RNA-seq datasets. PertDiffBench evaluates diffusion-based models across three complementary evaluation settings: standard prediction in known single-cell contexts and bulk perturbation conditions, generalization to unseen cell types, species, drugs and intermediate time points, and stress tests of feature dimensionality, input representation, noise type and gene ordering. Across these settings, diffusion models did not show a consistent advantage. scGen remained a strong baseline in common prediction tasks, whereas scDiffusion was the most competitive diffusion-based method in several generalization settings. Temporal imputation showed a different pattern, with a simple DDPM operating directly in expression space outperforming more specialized models. Stress tests showed that performance was model dependent and sensitive to feature dimensionality, encoder choice, noise type and gene ordering. Pretrained encoders did not consistently improve performance, with the classical scVI representation slightly exceeding STATE in seen-condition and unseen-cell-type settings. These results indicate that diffusion-model performance in perturbation response prediction depends strongly on task design and representation choice. PertDiffBench provides a practical framework for evaluating these models under biologically varied and stress-tested conditions.

15.
arXiv (CS.AI) 2026-06-19

Hard or Just Unreached? Diagnosing the Sampling Blind Spot in Math-Reasoning Difficulty Estimation

arXiv:2606.19636v1 Announce Type: cross Abstract: Math and science reasoning benchmarks rely on pass@k, the fraction of sampled chains that reach gold, as the canonical per-example difficulty signal. The same signal drives RL with verifiable rewards, math data curation, synthetic curricula, and verifier training. We show this proxy has a persistent blind spot on its hardest stratum: on the eight free-form math cells we test (GSM8K and MATH across four open-weight models), 10.3-22.9% of the examples that no sampling seed solves in six tries are instead solved at matched compute by a six-chain deterministic regime. These are greedy decoding plus five cheap residual-stream perturbations applied via activation grafting, while greedy alone solves at most 6% on these math cells. Recovery scales with the additional budget, across perturbations whose mechanistic distinctness we verify across all twelve cells (cross-kind fix-set Jaccard

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

Beyond Scalar Rewards by Internalizing Reasoning into Score Distributions

Reward models are central to text-to-image post-training, but visual preference is subjective and better represented as a distribution over rubric scores than as a deterministic scalar. Existing scalar, score-token, and pairwise reward models over-compress uncertainty and fine-grained score differences, while reasoning-based generative rewards provide stronger judgments but are costly to deploy and difficult to use as direct optimization signals. We propose Z-Reward, a teacher-student reward modeling framework that decouples reasoning-heavy judgment from efficient reward deployment. The teacher is a large VLM that uses reasoning to infer rubric-aligned score distributions, and is trained with Group-wise Direct Score Optimization (GDSO), which combines policy-gradient rewards from distribution expectations with direct pointwise and pairwise supervision on score distributions and score gaps. The student is trained with Reasoning-Internalized Score Distillation (RISD), which transfers the teacher's reasoning-conditioned score distribution into a compact VLM without requiring explicit reasoning chains at inference time. On our internally annotated evaluation set, the 27B GDSO teacher reaches 89.6% human preference accuracy, outperforming SFT, RewardDance, and GRPO, while the 9B RISD student reaches 88.6%, outperforming the OPD baseline and closely matching the larger teacher. We further show that Z-Reward can serve as a differentiable reward signal for text-to-image optimization, yielding a 41.3% net human-preference improvement over the SFT baseline.

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

AI4SLT: Empirical Processes in Lean 4 for Formal Statistical Learning Theory

We present the first comprehensive Lean 4 formalization of statistical learning theory (SLT) grounded in empirical process theory. Our en-to-end formal infrastructure implement the missing contents in latest Lean library, including a complete development of Gaussian Lipschitz concentration, Dudley's entropy integral theorem for sub-Gaussian processes, and an application to least-squares (sparse) regression with a sharp rate. The project was carried out using a human-AI collaborative workflow, in which humans design proof strategies and AI agents execute tactical proof construction, leading to the human-verified Lean 4 toolbox for SLT. Beyond implementation, the formalization process exposes and resolves implicit assumptions and missing details in standard SLT textbooks, enforcing a granular, line-by-line understanding of the theory. This work establishes a reusable formal foundation and opens the door for future developments in machine learning theory. The code is provided in https://github.com/YuanheZ/lean-stat-learning-theory.

18.
arXiv (CS.LG) 2026-06-16

AREAL-DTA: Dynamic Tree Attention for Efficient Reinforcement Learning of Large Language Models

arXiv:2602.00482v2 Announce Type: replace Abstract: Reinforcement learning (RL)-based post-training for large language models (LLMs) is computationally expensive, as it generates many rollout sequences that frequently share long token prefixes. Existing RL frameworks usually process these sequences independently during policy training, i.e., repeatedly recomputing identical prefixes in both the forward and backward passes of policy gradient computation, leading to substantial inefficiencies in computation resources and memory usage. Although prefix sharing naturally induces a tree structure over rollouts, packed tree-mask approaches scale poorly in RL settings. In this paper, we introduce AReaL-DTA, which efficiently exploits prefix sharing in RL training. AReaL-DTA employs a depth-first search (DFS)-based execution strategy that dynamically traverses the rollout prefix tree during both forward and backward computation, materializing only a single root-to-leaf path at a time. To further improve scalability, AReaL-DTA incorporates a load-balanced distributed batching mechanism that dynamically constructs and processes prefix trees across multiple GPUs. On $\tau^2$-bench, AReaL-DTA improves training throughput by up to $8.31\times$ over dense training and up to $1.70\times$ over sparse training. Our code is available at https://github.com/areal-project/AReaL/tree/feat/dta.

19.
arXiv (CS.AI) 2026-06-16

Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoning

arXiv:2606.15576v1 Announce Type: cross Abstract: Reinforcement learning from verifiable rewards assigns a single scalar to each rollout, leaving token-level credit assignment underspecified in long reasoning traces. On-policy self-distillation addresses this by letting the same model act as a teacher conditioned on privileged information, producing a dense per-token signal. But the common choice of a ground-truth answer is only an endpoint cue: on terse-answer tasks, the teacher falls silent at the intermediate positions where path-level guidance matters most. We propose Hindsight Self-Distillation (HSD), which conditions the teacher on a successful peer rollout drawn from the current training group. Such a peer is an exact sample from the success-conditioned policy, requiring no additional sampled rollouts. By providing a full successful continuation rather than only the final answer, the resulting credit signal concentrates at the divergence position between a failed rollout and a successful peer. Across Qwen3-8B and Qwen3-32B on math and code benchmarks, HSD obtains the best result against GRPO variants and on-policy distillation baselines, with the largest gains on terse-answer tasks such as AIME.

20.
arXiv (quant-ph) 2026-06-15

Modeling light-matter coupled systems with neural quantum states

arXiv:2606.14352v1 Announce Type: cross Abstract: Recent advances in cold atom manipulation enable the study of many-body systems where short-range interactions between neighboring atoms coexist with long-range interactions mediated by photons. Such a combination of interactions makes a theoretical approach challenging beyond mean-field methods. In this work, we develop a neural quantum state based approach to study these systems numerically. We introduce a neural-network architecture capable of handling hybrid Hilbert spaces with large local bosonic dimensions in strongly interacting spin-photon systems. We benchmark this approach on a model of a two-dimensional lattice of Rydberg atoms coupled to a photon mode. The superradiant ground states found in the large spin-photon coupling regime allow us to demonstrate the efficiency of the method in the presence of high photon occupation. Furthermore, the ability to capture spin-spin and spin-photon correlations leads us to observe quantitative deviations in the ground state phase boundaries with respect to mean-field theory. The method extends to other systems with a similar hybrid Hilbert space structure, such as spin-phonon systems, and provides a scalable framework for investigating their ground state properties.

21.
arXiv (CS.AI) 2026-06-17

Towards Leveraging AutoML for Sustainable Deep Learning: A Multi-Objective HPO Approach on Deep Shift Neural Networks

arXiv:2404.01965v3 Announce Type: replace-cross Abstract: Deep Learning (DL) has advanced various fields by extracting complex patterns from large datasets. However, the computational demands of DL models pose environmental and resource challenges. Deep shift neural networks (DSNNs) offer a solution by leveraging shift operations to reduce computational complexity at inference. Following the insights from standard DNNs, we are interested in leveraging the full potential of DSNNs by means of AutoML techniques. We study the impact of hyperparameter optimization (HPO) to maximize DSNN performance while minimizing resource consumption. Since this combines multi-objective (MO) optimization with accuracy and energy consumption as potentially complementary objectives, we propose to combine state-of-the-art multi-fidelity (MF) HPO with multi-objective optimization. Experimental results demonstrate the effectiveness of our approach, resulting in models with over 80\% in accuracy and low computational cost. Overall, our method accelerates efficient model development while enabling sustainable AI applications.

22.
arXiv (CS.CL) 2026-06-11

LLMpedia: A Transparent Framework to Materialize an LLM's Encyclopedic Knowledge at Scale

Benchmarks like MMLU suggest flagship language models approach factuality saturation above 90\%. LLMpedia shows this picture is incomplete. We materialize ${\sim}$1.3M encyclopedia articles entirely from parametric memory across three model families, then audit every claim against Wikipedia and curated web evidence. For \texttt{gpt-5-mini}, the verifiable true rate is 68.4\% on Wikipedia-covered subjects - more than 21\,pp below MMLU - and the gap is driven by unverifiability (30.5\%), not refutation (1.2\%). Beyond Wikipedia, frontier articles audited against curated web evidence reach 57.6\%; Wikipedia covers only 56.7\% of model-surfaced subjects, and three model families overlap in just 7.3\% of subject choices. In a retrieval-trap benchmark inspired by prior analysis of Grokipedia, LLMpedia is more factual at roughly half the textual similarity to Wikipedia. Every prompt, article, and verdict is released. Data, code, interface: https://llmpedia.net.

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

Variance Reduction for Non-Log-Concave Sampling with Applications to Inverse Problems

arXiv:2606.16257v1 Announce Type: cross Abstract: Sampling from high-dimensional, non-log-concave distributions with unnormalized densities is a fundamental challenge in machine learning, particularly when the exact gradient of the potential is unavailable and must be approximated via stochastic gradients that exhibit high variance under a fixed budget of gradient computations per iteration. Although variance reduction techniques such as SGD with momentum, STORM, and PAGE have demonstrated improved convergence properties in non-convex optimization, their implications for sampling from non-log-concave distributions remain largely unexplored. In this work, we develop the first unified analysis of these estimators for sampling from non-log-concave distributions. We establish improved non-asymptotic convergence rates in $\varepsilon$-relative Fisher information and, under a Poincaré inequality assumption, in squared total variation distance, and further prove weak convergence to the target distribution. We extend our analysis to solving inverse problems with score-based generative priors. We empirically validate our theory and demonstrate that, under a fixed gradient computations per iteration, variance-reduction techniques consistently improve sample quality in two standard imaging applications.

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

Hierarchical symmetry selects log-Poisson cascades: classification, uniqueness, and stability

arXiv:2604.01632v2 Announce Type: replace Abstract: Within i.i.d. multiplicative cascades, a single axiom – the hierarchical symmetry, a linear contraction on incremental scaling exponents – is shown to be necessary and sufficient for the cascade multiplier to be log-Poisson. We prove: (1) a characterization theorem determining the log-Poisson law with explicit parameters, within the class of all multipliers with finite lattice moments; (2) a classification theorem locating the log-Poisson class inside the log-infinitely-divisible family and identifying the mechanism by which every rival sub-family fails the symmetry; (3) a stability theorem with sharp constants – $(1+\beta)^{1/2}$ when the limiting increment is known, $\sqrt{2}$ when it is fitted – and (4) an unconditional propagation theorem transferring the bound to the multiplier distribution at the sharp rate $\Theta(\sqrt{\varepsilon})$, with a matching lower bound. Beyond independence, the classification extends exactly at the level of asymptotic statistics (limiting cumulant generating function, large deviations, multifractal spectrum) and provably not at the level of laws: an explicit stationary ergodic Markov multiplier satisfies the symmetry exactly with a non-log-Poisson marginal, while exchangeable multipliers collapse to the i.i.d. log-Poisson cascade and finite-state Markov multipliers cannot satisfy the symmetry at all. In the continuous category of exactly scale-invariant log-infinitely-divisible multifractal random measures, no finite moment window of structure-function exponents identifies the cascade class, whereas at the level of the scale-invariance generator the symmetry selects exactly the Barral-Mandelbrot compound Poisson cascade, with scale-ratio-free stability constants. The proofs reduce to second-moment identities on [0,1] via the change of variables $u = e^{kx}$, boundedness of the multiplier, and multiplicative couplings.

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

AP-GRPO: Anchor-Gated Phonetic Alignment with Policy Optimization for Pathological Speech Reconstruction

arXiv:2606.15540v1 Announce Type: cross Abstract: Pathological speech from patients with neurodegenerative and neuromotor disorders is often acoustically distorted and linguistically fragmented, making pathological speech reconstruction necessary to recover intended textual content from distorted and incomplete speech recordings. Crucially, such recordings are rarely uniformly degraded: some words or short phrases remain reliable and can serve as audible anchors for reconstructing the corrupted surrounding content. We introduce Anchor-gated Phonetic Group Relative Policy Optimization (AP-GRPO), a GRPO framework with phonetic reward that aligns speech language models (SLMs) through audible-anchor preservation and inter-anchor phonetic compatibility to the original speech signal. AP-GRPO consists of: (i) an anchor-gated reward that matches reliable audible anchors in clear regions; and (ii) an inter-anchor phonetic alignment reward that evaluates whether recovered contents are phonetically supported by the corresponding corrupted inter-anchor speech span. Across four disease conditions, AP-GRPO improves faithful speech reconstruction, and the learned anchor constraint automatically adapts to each condition and thus reveals interpretable disease-specific profiles: conditions with severe articulatory degradation require stronger anchor enforcement, whereas milder impairment or linguistically impaired conditions rely more on phonetic alignment for inter-anchor recovery.