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01.
arXiv (math.PR) 2026-06-11

Capital Asset Pricing Model with Size Factor and Normalizing by Volatility Index

arXiv:2411.19444v5 Announce Type: replace-cross Abstract: The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on average. For some size-based stock portfolios, dividing their returns by the Volatility Index makes them closer to independent and normal. In this article, we combine these ideas to create a new discrete-time model, which includes volatility, relative size, and CAPM. We fit this model using real-world data, prove the long-term stability, and connect this research to Stochastic Portfolio Theory. We fill important gaps in our previous article on CAPM with the size factor.

02.
arXiv (CS.CV) 2026-06-12

From Seeing to Experiencing: Scaling Navigation Foundation Models with Reinforcement Learning

Navigation foundation models trained on massive web-scale data enable agents to generalize across diverse environments and embodiments. However, these models, which are trained solely on offline data, often lack the capacity to reason about the consequences of their actions or adapt through counterfactual understanding. They thus face significant limitations in real-world urban navigation, where interactive and safe behaviors, such as avoiding obstacles and moving pedestrians, are critical. To tackle these challenges, we introduce the Seeing-to-Experiencing (S2E) learning framework to scale the capability of navigation foundation models with reinforcement learning. S2E combines the strengths of pretraining on offline videos and post-training through reinforcement learning. It maintains the model's generalizability acquired from large-scale real-world videos while enhancing its interactivity through reinforcement learning in simulation environments. Specifically, we introduce two innovations: (1) an Anchor-Guided Distribution Matching strategy for offline pretraining, which stabilizes learning and models diverse motion patterns through anchor-based supervision; and (2) a Residual-Attention Module for reinforcement learning, which obtains reactive behaviors from simulation environments without erasing the model's pretrained knowledge. Moreover, we establish a comprehensive end-to-end evaluation benchmark, NavBench-GS, built on photorealistic 3D Gaussian Splatting reconstructions of real-world scenes that incorporate physical interactions. It can systematically assess the generalizability and safety of navigation foundation models.

03.
arXiv (CS.AI) 2026-06-11

Blind Dexterous Grasping via Real2Sim2Real Tactile Policy Learning

arXiv:2606.11767v1 Announce Type: cross Abstract: Blind grasping with a dexterous hand is a crucial manipulation capability. Nevertheless, learning such tactile-only policies for real robots remains challenging due to the tactile sim-to-real gap and the limited expressiveness of sparse tactile signals. To bridge this gap, we propose a framework for tactile-only blind grasping that is deployable on a physical multi-fingered robotic hand. Our approach combines three key components. First, we introduce a Real2Sim tactile calibration pipeline that constructs a contact-calibrated digital-twin simulator capable of reproducing real tactile signals. Second, we improve the expressiveness of sparse tactile observations using a layout-aware tactile encoder, which incorporates sensor-geometry priors through self-supervised pretraining. Third, to improve generalization to unseen objects, we train object-specific reinforcement-learning experts in the calibrated simulator and aggregate their successful grasp trajectories into a tactile-conditioned Diffusion Policy. We evaluate our method on a physical LEAP Hand equipped with distributed tactile sensing across 10 seen and 10 unseen objects. The deployed policy achieves a 27\% real-world grasp success rate across all 20 objects, without real-world grasping demonstrations or visual input. Simulation ablations show that layout-aware tactile pretraining improves grasping performance, while sensing-level evaluations confirm that Real2Sim calibration increases the consistency of tactile contact events between simulation and hardware. Together, these results suggest that contact-event calibration, geometry-aware tactile representation learning, and diffusion-based policy aggregation provide an effective path toward tactile-only blind grasping on real dexterous robotic hands. Project page:Dex-Blind-Grasp.github.io.

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

Calibration Drift Under Reasoning: How Chain-of-Thought Budgets Induce Overconfidence in Large Language Models

The ability of large language models (LLMs) to express calibrated uncertainty is important for safe deployment. Chain-of-thought (CoT) reasoning is widely used to improve accuracy and reliability, but its effect on calibration is not fully understood. We show that this picture is incomplete: in some settings, increasing the reasoning budget beyond a task-specific threshold can cause models to become systematically overconfident, assigning high confidence to incorrect answers. We call this phenomenon Calibration Drift Under Reasoning (CDUR) and study it both theoretically and empirically. We define reasoning budget B and analyze conditions under which Expected Calibration Error ECE(B) follows a non-monotonic pattern: it first decreases as reasoning corrects errors, then increases as longer reasoning produces internally consistent but incorrect explanations. We propose a Hypothesis Lock-In model based on autoregressive generation to explain this behavior. We evaluate Llama-3.1-8B and Llama-3.3-70B on 47 reasoning-trap questions across four reasoning budgets and three seeds (1,368 API calls; 574 valid responses). The 8B model shows non-monotonic calibration behavior, while results for the 70B model are limited to baseline evaluation and are inconclusive for budget-dependent effects. We introduce CABStop, a calibration-aware stopping rule that halts reasoning when confidence diverges from an auxiliary accuracy estimate. These results suggest that increasing reasoning depth does not always improve reliability and should be monitored carefully.

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

LLM-as-Judge in Education: A Curriculum-Grounded Marking Pipeline

arXiv:2606.17507v1 Announce Type: new Abstract: Generative AI and large language models (LLMs) are increasingly applied to question generation and automated assessment. However, deploying LLMs in preparation for high-stakes exams requires more than prompt engineering; it demands software pipelines that systematically ground model outputs in authorised curriculum artefacts and marking guidelines issued by education authorities. This paper presents a curriculum-grounded, configurable LLM-as-Judge pipeline for question-level marking, co-developed with an industrial partner, to support exam preparation for university admission. The pipeline identifies the relevant topics, subtopics, and cognitive demand of a question, and assembles verifiable and authorised context to support LLM judgement. Curriculum intent is operationalised through concrete syllabus artefacts, including prescribed verbs and outcomes, performance band descriptors, glossary definitions, and marking-guideline principles. A staged LLM workflow is employed to first generate question-specific rubrics, capturing structured expectations of performance, and then derive and evaluate marking criteria used to allocate marks to student responses. This design improves consistency, transparency, and alignment with official marking practices. Preliminary evaluation shows that the proposed LLM-as-Judge pipeline delivers marking outcomes comparable to human tutors, while yielding justifications that are more traceable to authorised curriculum artefacts and marking standards. The pipeline has also been integrated into an online study platform, where early deployment data provide initial insights into operational usage and manual overrides.

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

RippleBench: Capturing Ripple Effects Using Existing Knowledge Repositories

arXiv:2512.04144v2 Announce Type: replace Abstract: Targeted interventions on language models, such as unlearning or model editing, aim to modify specific information, but their effects often propagate to related, unintended areas (e.g., removing virology content may degrade performance on allergies); these side-effects are commonly referred to as the ripple effect. We introduce RippleBench-Maker, an automatic pipeline that retrieves semantic neighbors of any source concept from a knowledge repository and generates multiple-choice questions at varying semantic distances. We instantiate this framework using WikiRAG, an open-source RAG system over English Wikipedia, to construct RippleBench-WMDP-Bio (584 seed topics, 352,961 questions), and evaluate eight unlearning methods on Llama3-8B-Instruct. All eight exhibit accuracy drops that are largest near the unlearned target and decay with semantic distance, each with a distinct propagation profile. We replicate these findings across Mistral-7B, Zephyr-7B, and Yi-34B; cross-model delta curves are nearly identical, suggesting ripple effects are a property of the unlearning method rather than the base model. We validate all major pipeline stages using a four-experiment Mechanical Turk study (5,200+ responses, 61 workers). We release all code, data, and infrastructure.

07.
arXiv (quant-ph) 2026-06-19

Applications of quantum annealing to magnetic dipole hyperfine structure constants: First results beyond energies for atoms

arXiv:2606.20166v1 Announce Type: new Abstract: We report the first results of the magnetic dipole hyperfine structure (HFS) constants of neutral $\mathrm{Li}$, Li-like $\mathrm{Be}$, neutral $\mathrm{Na}$, and Na-like $\mathrm{Mg}$ using a modified version of the Quantum Annealer Eigensolver (QAE) algorithm on D-Wave's quantum hardware. The results are benchmarked against relativistic configuration interaction with multiconfiguration Dirac Hartree-Fock (MCDHF) calculations using the General-purpose Relativistic Atomic Structure Package (GRASP), and simulated annealing. In our modified QAE, a zooming-and-sigma-annealing approach with a floating-point encoding scheme is adopted to estimate the ground-state eigenvalue and eigenvector of the relativistic Dirac-Coulomb Hamiltonian matrices ($H_{\mathrm{DC}}$) constructed from 11 or fewer configuration state functions (CSFs). For calculations with extended correlation orbital sets, we applied a CSF truncation scheme, retaining only CSFs (up to 12) that make significant contributions to the ground-state wavefunction. Our modified QAE precision is kept limited to three decimal places (up to 10 qubits). Hardware demonstrations on the D-Wave quantum processing unit (QPU) yielded results that were completely consistent with GRASP (at the chosen precision) in determining the magnetic dipole HFS constants, with accuracy varying across systems and $H_{\mathrm{DC}}$ matrix dimensions.

08.
bioRxiv (Bioinfo) 2026-06-17

Beyond phylogeny: Genome-wide DNA sequence patterns suggest DNA physical properties associated with thermal adaptation in extremophile microbes

Authors:

Temperature is a fundamental constraint on biological systems, yet how it is reflected in genome sequence organization remains unclear. Here, we show that genome-wide distributions of short DNA sequences contain a robust signal of thermal adaptation that is largely independent of phylogeny. Using Structural Topic Modelling (STM), a machine-learning approach for identifying groups of co-occurring sequence motifs, we analyze canonical 6-mer and 9-mer frequency profiles of bacterial and archaeal genome proxies (randomly sampled genomic regions) and identify motif families systematically associated with thermophiles and psychrophiles. In bacterial thermophiles, the identified motif families are dominated by highly specific, overrepresented and co-occurring C- and G-stacked hexamers, and a distinct family of CG-periodic hexamers recurring across multiple temperature comparisons. In contrast, bacterial psychrophile-associated motifs are dominated by low-complexity A-, T-, and AT-run hexamers. Thermophilic archaea generally exhibit a distinct CTAG-centred hexamer family, suggesting that different domains may adapt to similar environmental constraints through different sequence-level solutions. However, this domain-level contrast is not absolute: in a targeted analysis of two thermophilic bacterium–archaeon pairs, we find unusually similar frequencies of all the STM-identified thermophile-associated hexamer families, suggesting that shared high-temperature environments can, in specific cases, partially override phylogenetic divergence. Notably, the identified motif families constitute only a small and highly selective subset of the vast space of possible G+C-rich or A+T-rich sequences. This indicates that thermal adaptation is associated with specific sequence architectures rather than broad shifts in nucleotide composition. Accordingly, the observed signal cannot be explained by overall base composition alone, but instead arises from structured combinations and positional arrangements of nucleotides within short sequence contexts. Related motif families are recovered at both k=6 and k=9, indicating that the signal reflects systematic shifts in genome-wide sequence organization rather than isolated sequence motifs. These patterns are consistent with known sequence-dependent DNA physical properties documented in biochemical and biophysical studies, including differences in base-stacking interactions and conformational flexibility. Together, our results suggest that genome-wide sequence organization reflects sequence-dependent DNA physical properties associated with thermal adaptation, revealing a previously underappreciated physical layer of genomic information beyond phylogenetic history.

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

Extending Item Response Theory for Efficient and Meaningful Multilingual Evaluation

Multilingual benchmarks are central to evaluating large language models (LLMs) across languages, but they suffer from three issues: exhaustive evaluation scales linearly with the number of languages, automatic translation introduces errors that are easily missed at scale, and some items conflate general and culture-specific knowledge. We address all three with a unified statistical framework, Multilingual-IRT, which extends Item Response Theory with per-language difficulty deviations, split discriminability separating content from language effects, and per-language ability residuals. Fitting Multilingual-IRT on 25 LLMs across 29 languages of MMLU-Pro-X, we show that its fitted parameters support three practical applications: predicting unobserved (item, LLM, language) instances with 11-16% lower binary cross-entropy than the strongest accuracy-based baseline, surfacing candidate translation errors distributed across all 28 non-English languages, whereas accuracy-based baselines concentrate detections in a few languages, and recovering culture-specific items that accuracy-based baselines miss.

10.
medRxiv (Medicine) 2026-06-11

Population-scale detection of methylation outliers from long-read genome sequencing

Background: Aberrant DNA methylation can mediate the functional effects of rare genetic variation and contribute to imprinting disorders, repeat expansion diseases, and other pathogenic regulatory mechanisms. Long-read sequencing technologies now enable genome-wide detection of CpG methylation alongside genetic variation from a single assay. However, methods for systematic identification and interpretation of methylation outliers from long-read sequencing data remain limited. Methods: We developed METAFORA, a computational workflow for detecting methylation outlier regions from PacBio and Oxford Nanopore long-read sequencing data. METAFORA constructs population-level methylation references, segments the genome into correlated CpG blocks, infers technical and biological sources of variation through hidden factor estimation, models uncertainty due to variable depth sequencing, and computes covariate-adjusted methylation outlier scores for individual samples. We applied METAFORA across large long-read sequencing cohorts and integrated methylation outliers with multi-omic data. METAFORA is implemented as a snakemake workflow available at https://github.com/tjense25/METAFORA. Results: METAFORA identified methylation outlier regions associated with rare structural variants, tandem repeat expansions, and imprinting abnormalities. We found outlier regions were enriched for molecular outliers across transcriptomic and chromatin accessibility datasets, supporting their functional relevance in gene regulation. In a representative case, METAFORA identified an imprinting defect affecting the GNAS locus associated with an STX16 deletion. Conclusions: METAFORA enables scalable detection and interpretation of methylation outliers from long-read sequencing data and provides a framework for integrating epigenetic outliers with genomic and multi-omic analyses. These approaches may improve interpretation of rare regulatory variation and support discovery of clinically relevant epigenetic abnormalities in genomic medicine.

11.
Nature Medicine 2026-06-11

Clinical Profile and Genomic Characterization of the 2026 Bundibugyo Virus Index Case in Uganda

Bundibugyo virus disease (BVD) remains a high-consequence threat in Eastern and Central Africa, where cross-border mobility, nonspecific early symptoms, and delayed recognition can obscure transmission. In this case report, we describe Uganda’s 2026 BVD index case: a male patient who traveled from the Democratic Republic of the Congo to Uganda and was admitted to a private hospital in Kampala on 11 May 2026 after more than two weeks of vomiting and diarrhea, with epigastric pain, weakness, and hiccups. He deteriorated rapidly, developing acute kidney injury, pulmonary edema, hepatic dysfunction, hypoxemia, delirium, atrial flutter, possible disseminated intravascular coagulation, and multiorgan failure, and died on 14 May. A posthumous EDTA whole-blood specimen tested at the Central Emergency Response and Surveillance Laboratory was positive for orthoebolavirus RNA and confirmed as Bundibugyo virus (BDBV) by RT-qPCR. Sequencing achieved 99% genome coverage at ≥100× depth. The 2026 BDBV genome formed a distinct lineage approximately equidistant from the 2007–2008 Butalya and 2012 Isiro variants, differing by 216–227 nucleotides (~1.2% sequence divergence). Here, we demonstrate the value of fatality surveillance, private-sector surveillance, diagnostic optimization through national specimen referral, and rapid molecular-genomic diagnostics for early detection, transmission chain interruption, and public health response coordination.

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

Sentinel: Decoding Context Utilization via Attention Probing for Efficient LLM Context Compression

Retrieval-augmented generation (RAG) often suffers from long and noisy retrieved contexts. Existing context compression methods typically rely on heuristic relevance estimation or supervised compression models rather than on how LLMs utilize retrieved context during inference. We propose Sentinel, a lightweight sentence-level compression framework that decodes inference-time contextual utilization behaviors from head-wise attention patterns of frozen LLMs. To ground supervision in retrieval-dependent answering behavior, Sentinel trains a lightweight probe using QA examples where the model succeeds only when retrieved context is available. Sentinel performs compression using only a single non-autoregressive forward pass without dedicated compression training or autoregressive scoring. Empirically, we find that effective contextual utilization signals remain accessible even in compact proxy models. On LongBench, Sentinel with a 0.5B proxy model achieves up to 5$\times$ compression while attaining question-answering performance competitive with compression methods built on 7B-scale models. Despite being trained only on English QA data, Sentinel also generalizes effectively to Chinese and out-of-domain settings.

13.
arXiv (CS.LG) 2026-06-12

A Unified Latent Space Disentanglement VAE Framework with Robust Disentanglement Effectiveness Evaluation

arXiv:2603.11242v2 Announce Type: replace-cross Abstract: Evaluating and interpreting latent representations, such as variational autoencoders (VAEs), remains a significant challenge for diverse data types, especially when ground-truth generative factors are unknown. To address this, we unify several state-of-the-art disentangled VAE approaches for latent space disentanglement into one framework – bfVAE. To assess the effectiveness of a disentangled VAE model and enhance latent space interpretability, we propose Feature Variance Heterogeneity via Latent Traversal (FVH-LT) and Dirty Block Sparse Regression in Latent Space (DBSR-LS). To ensure robust interpretability of learned latent space, we develop a greedy alignment strategy (GAS) that mitigates label switching and aligns latent dimensions across runs to set the foundation of result aggregation. We also introduce a convenient scalar latent space separation index (LSSI) based on the GAS-aligned outputs of FVH-LT and DBSR-LS to summarize the overall latent structural separation without knowledge of the ground-truth generative factors. We compare bfVAE to five VAE models and validate the effectiveness FVH-LT, DBSR-LS, and LSSI in on seven tabular and image datasets. Under our examined experimental settings, bfVAE provides a more flexible disentanglement framework achieves more favorable overall trade-off between disentanglement and reconstruction than the benchmark VAE models; FVH-LT and DBSR-LS reliably uncover semantically meaningful and domain-relevant latent structures and generally yield consistent results; and LSSI makes an effective quantitative summary of latent structural separation.

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

Stabilizing Bandits using Regularization: Precise Regret and A Quantitative Central Limit Theorem

arXiv:2603.10184v2 Announce Type: replace-cross Abstract: Statistical inference with bandit data presents fundamental challenges owing to adaptive sampling, which violates the independence assumptions underlying classical asymptotic theory. Recent work has identified stability~\citep{laiwei82} as a sufficient condition for valid inference under adaptivity. This paper first provides a refined stability condition, stated in terms of the iterates of an online algorithm, and shows that a large class of regularized stochastic-mirror-descent-style algorithms satisfy it. This refined condition allows us to strengthen the asymptotic results of~\citet{laiwei82} in several ways. First, we derive a non-asymptotic Berry–Esseen bound for the empirical reward estimates under adaptive sampling. Second, we derive matching non-asymptotic upper and lower bounds on the regret of the proposed algorithm, yielding a precise characterization of its regret. Third, we show that these regularized algorithms preserve asymptotic normality and valid inference under a prescribed level of adversarial corruption. Finally, we show that regularization is necessary rather than incidental: Lai–Wei stability is incompatible with the optimal $O(\sqrt{T})$ regret rate – the rate attained by unregularized algorithms such as EXP3 – so that a controlled, polylogarithmic inflation in regret is the price of valid inference.

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

Metis: A Generalizable and Efficient World-Action Model for Autonomous Driving and Urban Navigation

World action models~(WAMs) have shown great promise for autonomous driving and urban navigation. Built upon Vision-Language-Action models or video generation models, existing approaches suffer key limitations: (1) High inference latency due to future observation prediction at test time, and (2) tightly coupled video and action modeling leading to representational mismatch and degraded generalization. To address both issues, we propose Metis, an end-to-end WAM framework that decouples video generation and action prediction. Specifically, Metis employs a Mixture-of-Transformers architecture with dedicated experts for video generation and action prediction, preserving the intrinsic distributional properties of each task. To enhance efficiency, we introduce an asymmetric attention mask that enables joint training of both experts while allowing the action model to bypass explicit video generation during inference. This design ensures training-inference consistency and significantly reduces computational costs without compromising planning performance. Extensive experiments demonstrate state-of-the-art performance on the NAVSIM navhard and navtest benchmarks and the CityWalker navigation benchmark, validating both the generalizability and efficiency across diverse tasks. Real-robot deployments further confirm the practical feasibility of our approach.

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

PaLMR: Towards Faithful Visual Reasoning via Multimodal Process Alignment

Reinforcement learning has recently improved the reasoning ability of Large Language Models and Multimodal LLMs, yet prevailing reward designs emphasise final-answer correctness and consequently tolerate process hallucinations–cases where models reach the right answer while misperceiving visual evidence. We address this process-level misalignment with PaLMR, a framework that aligns not only outcomes but also the reasoning process itself. PaLMR comprises two complementary components: a perception-aligned data layer that constructs process-aware reasoning data with structured pseudo-ground-truths and verifiable visual facts, and a process-aligned optimisation layer that constructs a hierarchical reward fusion scheme with a process-aware scoring function to encourage visually faithful chains-of-thought and improve training stability. Experiments on Qwen2.5-VL-7B show that our approach substantially reduces reasoning hallucinations and improves visual reasoning fidelity, achieving state-of-the-art results on HallusionBench while maintaining strong performance on MMMU, MathVista, and MathVerse. These findings indicate that PaLMR offers a principled and practical route to process-aligned multimodal reasoning, advancing the reliability and interpretability of MLLMs.

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

EQPO: Equitable Group Relative Policy Optimization for Clinical Reasoning

arXiv:2510.19893v2 Announce Type: replace Abstract: Medical AI systems demonstrated impressive diagnostic performance, yet they routinely show uneven accuracy across demographic groups, disadvantaging underrepresented populations. Although multimodal reasoning foundation models have pushed clinical diagnosis forward, reinforcement learning-based post-training tends to absorb and magnify the biases present in majority-dominated training corpora. We propose Equitable Group Relative Policy Optimization (EQPO), a hierarchical reinforcement learning method that encourages balanced learning across heterogeneous clinical populations by adaptively reweighting samples according to subgroup representation, task difficulty, and data source. As demographic annotations are frequently missing in real-world clinical data, EQPO additionally applies unsupervised clustering to recover latent subpopulations when they are unavailable. On 7 diagnostic benchmarks covering 5 modalities (X-ray, CT, dermoscopy, mammography, ultrasound), EQPO reduces F1 standard deviation by 43.9% and the maximum cross-group F1 gap by 42.7% on QoQ-Med3-8B over vanilla GRPO, and narrows predictive parity gaps by 27.2% on MedGemma-4B over bias-mitigated RL baselines while raising F1 by 12.5% even without any demographic labels. Examining the training trajectory shows that EQPO steadily improves fairness over the course of optimization, in contrast to baseline methods whose fairness degrades as training proceeds, and the discovered implicit groups remain stable and align with masked demographic attributes. We further release EquiMedGemma-4B and EquiQoQ-Med3-8B, equitability-aware clinical VLLMs that attain state-of-the-art accuracy with markedly smaller demographic gaps.

20.
arXiv (CS.AI) 2026-06-15

Learning Coordinated Preference for Multi-Objective Multi-Agent Reinforcement Learning

arXiv:2606.14693v1 Announce Type: cross Abstract: Cooperative multi-objective multi-agent reinforcement learning (MOMARL) models team decision making under multiple, potentially conflicting objectives. In this setting, conflicts arise not only across objectives but also across agents with different observations, roles, and contributions. We propose Preference Coordinated Multi-agent Policy Optimization (PCMA), which learns coordinated agent-specific preferences to enable complementary trade-offs among agents. Theoretically, we formulate cooperative MOMARL as a team-optimal game and show that, under suitable conditions, preference diversity can induce team improvement through a first-order improvement decomposition. Experiments on multiple cooperative MOMA environments and a practical traffic-control scenario show that PCMA improves both performance and trade-off coordination.

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

Odds Law: The Decomposition Algebra On How Intelligence Organizes Itself to Solve Difficult Problems Reliably

Authors:

arXiv:2606.15712v1 Announce Type: cross Abstract: We ask a structural question: given unreliable elementary problem-solvers, what organizations of them solve hard problems reliably, and what are the limits? We develop a $decomposition~algebra$: elementary solvers are morphisms in a stochastic category, and four combinators (sequential composition, parallel ensembling, verification gating, and recursive reduction) generate the space of compound solvers. We equip this algebra with two homomorphisms, a $reliability$ valuation into the ordered monoid $([0,1],\le)$ and a $cost$ valuation into a commutative semiring, and we derive the composition laws that govern how reliability flows through structure. Our central results are (i) a $verification~odds~law$ (the result that names this report), showing that a verification gate multiplies the odds of correctness by the verifier's likelihood ratio $\Lambda$, so that $k$ conditionally independent gates yield geometric amplification; (ii) a $reliability~amplification~theorem$, giving target reliability $1-\delta$ at $O(\log 1/\delta)$ verification depth whenever $\Lambda>1$; and (iii) a $threshold~dichotomy$: above the critical parameters reliability can be driven arbitrarily close to one at logarithmic cost, while at or below them no amplification is possible. We then show that $self-organization$ is the least fixed point of a monotone improvement operator on the complete lattice of strategies, and that this fixed point equalizes marginal log-odds gain per unit cost. Finally, we prove matching limits: an information ceiling bounds per-gate amplification by a divergence quantity; shared error causes create a strictly positive voting floor, so diversity is $necessary$ for unbounded amplification. Reliability, in short, is neither free nor magical: it is bought with independent information, arranged by composition, and bounded by the verifier.

22.
arXiv (CS.AI) 2026-06-12

ARMOR-MAD: Adaptive Routing for Heterogeneous Multi-Agent Debate in Large Language Model Reasoning

arXiv:2606.13197v1 Announce Type: new Abstract: Multi-agent debate (MAD) can improve large language model reasoning, but fixed debate pipelines often waste computation and can amplify correlated errors among similar agents. We propose ARMOR-MAD, a training-free heterogeneous MAD framework that treats debate as conditional computation. ARMOR-MAD combines three components: Pre-debate Agreement Routing (PAR) decides whether independently generated Round-0 answers require debate; Early Agreement Stopping Evaluator (EASE) stops debate after convergence; and Semantic Outlier Detection (SOD) down-weights abnormal final answers during aggregation. Across MATH Level 5, GSM8K, MMLU, and MMLU-Pro, ARMOR-MAD consistently improves over fixed-round heterogeneous debate with the same model pool, reaching 65.5\%, 96.5\%, 90.0\%, and 81.5\% accuracy, respectively. The results suggest that genuine model heterogeneity and agreement-based control are both important for making MAD more accurate and efficient.

23.
arXiv (math.PR) 2026-06-11

Approximation Properties of Evolutionary Dynamics in Continuous-Time Finite State Space Games

Authors:

arXiv:2606.11193v1 Announce Type: cross Abstract: This thesis studies the convergence of finite-population stochastic evolutionary dynamics to their deterministic mean-field limit in continuous-time finite state space games. We first develop refined ergodic theorems for Markov chains with a single positive-recurrent class, guaranteeing the existence of a unique invariant distribution and almost-sure convergence of time averages. Next, we prove that the mean-field model, described by a system of Lipschitz-continuous ordinary differential equations, admits a unique solution that depends continuously on its initial condition and that constitutes the almost-sure limit for the empirical distributions with fixed policy. Furthermore, we show that every Mixed Stationary Nash Equilibrium of the mean-field game is approximated by a Nash equilibrium of the corresponding $N$-player game within an error $\epsilon$ for sufficiently large $N$. We finally demonstrate, by Kurtz's theorem, that the empirical state-policy distribution converges in probability to the mean-field trajectory. Numerical simulations conducted in MATLAB confirm the theoretical $\mathcal{O}(N^{-1/2})$ convergence rate in both models across a range of population sizes.

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

Modeling Day-Long ECG Signals to Predict Heart Failure Risk with Explainable AI

arXiv:2601.00014v2 Announce Type: replace-cross Abstract: Heart failure (HF) affects 11.8% of adults aged 65 and older, reducing quality of life and longevity. Preventing HF can reduce morbidity and mortality. We hypothesized that artificial intelligence (AI) applied to 24-hour single-lead electrocardiogram (ECG) data could predict the risk of HF within five years. To research this, the Technion-Leumit Holter ECG (TLHE) dataset, including 69,663 recordings from 47,729 patients, collected over 20 years was used. Our deep learning model, DeepHHF, trained on 24-hour ECG recordings, achieved an area under the receiver operating characteristic curve of 0.80 that outperformed a model using 30-second segments and a clinical score. High-risk individuals identified by DeepHHF had a two-fold chance of hospitalization or death incidents. Explainability analysis showed DeepHHF focused on arrhythmias and heart abnormalities. This study highlights the feasibility of deep learning to model 24-hour continuous ECG data, capturing paroxysmal events essential for reliable risk prediction. Artificial intelligence applied to single-lead Holter ECG is non-invasive, inexpensive, and widely accessible, making it a promising tool for HF risk prediction.

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

Sharp analysis of linear ensemble sampling

arXiv:2602.08026v2 Announce Type: replace Abstract: We analyse linear ensemble sampling (ES) with standard Gaussian perturbations in stochastic linear bandits. We show that for ensemble size $m=\Theta(d\log n)$, ES attains $\tilde O(d^{3/2}\sqrt n)$ high-probability regret, closing the gap to the Thompson sampling benchmark while keeping computation comparable. The proof brings a new perspective on randomized exploration in linear bandits by reducing the analysis to a time-uniform exceedance problem for $m$ independent Brownian motions. This continuous-time lens appears particularly natural here: it yields an exact representation of the relevant discrete-time processes, and we do not know another route to a sharp ES bound.