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01.
arXiv (CS.LG) 2026-06-15

Towards Efficient Large Language Reasoning Models via Extreme-Ratio Chain-of-Thought Compression

arXiv:2602.08324v5 Announce Type: replace Abstract: Chain-of-Thought (CoT) reasoning successfully enhances the reasoning capabilities of Large Language Models (LLMs), yet it incurs substantial computational overhead for inference. Existing CoT compression methods often suffer from a critical loss of logical fidelity at high compression ratios, resulting in significant performance degradation. To achieve high-fidelity, fast reasoning, we propose a novel EXTreme-RAtio Chain-of-Thought Compression framework, termed Extra-CoT, which aggressively reduces the token budget while preserving answer accuracy. To generate reliable, high-fidelity supervision, we first train a dedicated semantically-preserved compressor on mathematical CoT data with fine-grained annotations. An LLM is then fine-tuned on these compressed pairs via a mixed-ratio supervised fine-tuning (SFT), teaching it to follow a spectrum of compression budgets and providing a stable initialization for reinforcement learning (RL). We further propose Constrained and Hierarchical Ratio Policy Optimization (CHRPO) to explicitly incentivize question-solving ability under lower budgets by a hierarchical reward. Experiments on three mathematical reasoning benchmarks show the superiority of Extra-CoT. For example, on MATH-500 using Qwen3-1.7B, Extra-CoT achieves over 73\% token reduction with an accuracy improvement of 0.6\%, significantly outperforming state-of-the-art (SOTA) methods. Our source codes have been released at https://github.com/Mwie1024/Extra-CoT.

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

Cascaded Sparse Autoencoders Learn Multi-Level Visual Concepts in Multimodal LLMs

Multimodal Large Language Models (MLLMs) have demonstrated strong performance on vision-language tasks, yet their internal visual representations remain difficult to interpret. Sparse Autoencoders (SAEs) provide a scalable way to decompose dense model activations into sparse, interpretable features. However, existing SAE architectures primarily recover flat feature dictionaries and are less suited for explicit multi-level concept organization. In this paper, we introduce cascaded sparse autoencoders (CSAEs) for learning hierarchical visual concepts in MLLMs. Rather than nesting or stacking SAE sparse activation codes, CSAEs train a second-level SAE directly on the decoder weights of the first-level SAE, treating learned low-level feature directions as inputs for higher-level abstraction. This design enables CSAEs to learn "concepts of concepts" while avoiding drawbacks from the shared-prefix coupling of nesting, Matryoshka-style hierarchies and the bottlenecks of naively stacked SAEs. Experiments across Qwen3-VL, Gemma-3, and LLaVA on multiple visual datasets show that CSAEs improve interpretability in terms of hierarchical concept coherence over state-of-the-art SAE baselines. Results on concept steering further demonstrate that the learned concept groups support effective group-level interventions in MLLM outputs.

03.
arXiv (CS.CV) 2026-06-25

Did Models Learn Sufficiently? Attribution-Guided Training via Subset-Selected Counterfactual Augmentation

In current visual model training, models often rely on only limited sufficient causes for their predictions, which makes them sensitive to distribution shifts or the absence of key features. Attribution methods can accurately identify a model's critical regions. However, masking these areas to create counterfactuals often causes the model to misclassify the target, while humans can still easily recognize it. This divergence highlights that the model's learned dependencies may not be sufficiently causal. To address this issue, we propose Subset-Selected Counterfactual Augmentation (SS-CA), which integrates counterfactual explanations directly into the training process for targeted intervention. Building on the subset-selection-based LIMA attribution method, we develop Counterfactual LIMA to identify minimal spatial region sets whose removal can selectively alter model predictions. Leveraging these attributions, we introduce a data augmentation strategy that replaces the identified regions with natural background, and we train the model jointly on both augmented and original samples to mitigate incomplete causal learning. Extensive experiments across multiple ImageNet variants show that SS-CA improves generalization on in-distribution (ID) test data and achieves superior performance on out-of-distribution (OOD) benchmarks such as ImageNet-R and ImageNet-S. Under perturbations including noise, models trained with SS-CA also exhibit enhanced generalization, demonstrating that our approach effectively uses interpretability insights to correct model deficiencies and improve both performance and robustness.

04.
arXiv (quant-ph) 2026-06-11

Probing Quantum States over Spacetime Through Interferometry

arXiv:2507.19258v3 Announce Type: replace Abstract: Establishing a notion of the quantum state that applies consistently across space and time could be a crucial step toward formulating a relativistic quantum theory. We give an operational meaning to multipartite quantum states over arbitrary regions in spacetime through a causally agnostic measurement, a measurement scheme that can be consistently implemented independently of the causal relation between the regions. We prove that such measurements can always be implemented with interferometry, also known as the scattering circuit technique, wherein the conventional density operator, the recently developed quantum state over time (QSOT), and the process matrix formalisms smoothly merge. This framework allows for a systematic study of mixed states in the temporal setting, which turn out to be crucial for modeling quantum non-Markovianity. Based on this, we demonstrate that two different ensembles of quantum dynamics can be represented by the same QSOT, indicating that they cannot be distinguished through interferometry. Moreover, our formalism reveals a new type of spatiotemporal correlation between two quantum dynamics that originates from synchronized propagation in time under time-reversal symmetry. We show that quantum systems with such correlation can be utilized as a reference frame to distinguish certain dynamics indistinguishable under time-reversal symmetry.

05.
arXiv (CS.CL) 2026-06-19

Prompt, Plan, Extract: Zero-Shot Agentic LLMs Workflows for Lung Pathology Extraction from Clinical Narratives

Information extraction from pathology reports is essential for cancer staging, tumor registry population. Yet key data remains embedded in narrative reports, making manual extraction labor-intensive and error-prone. Traditional supervised Natural Language Processing pipelines address this through fully supervised Named Entity Recognition and Relation Extraction, but require expensive manual annotation and suffer cascading failures when upstream entities are missed. In this study, we developed a zero-shot, agentic workflow, and evaluated five open-source generative Large Language Models (LLMs) to populate 13 College of American Pathologists synoptic fields from lung resection pathology reports. We compared them against a state-of-the-art supervised GatorTron NER-RE baseline using a novel, registry-aligned evaluation framework. The baseline achieved Micro-F1of 0.960, while the best zero-shot model (GPT-OSS-20B) achieved Micro-F1 of 0.893 (recall: 0.949), accurately extracting complex relations like Pathologic Stage without task-specific training. These results suggest that open-source, zero-shot agentic LLMs are a low-cost solution for extracting lung pathology information.

06.
bioRxiv (Bioinfo) 2026-06-22

From hotspot dependence to distributed robustness in resistance-aware lead optimization

Drug resistance remains a recurrent failure mode in targeted anticancer and antiviral therapy, and resistance evidence often enters only after compound selection. ResistAgent is an evidence-constrained framework that converts mutational liabilities into design-time objectives through site- and combo-aware resistance mapping, deterministic mechanism diagnosis and robust counter-design. In EGFR-Erlotinib and HIV-RT-Rilpivirine, the framework separated residue-level liabilities from observed HIV combination liabilities and linked prioritized mutations to anchor loss, pocket rearrangement, electrostatic shifts and contact redistribution. Same-budget paired searches showed that robust objectives changed lower-tail mutant-panel behavior and interaction-dependence profiles while prioritizing robustness over average-affinity behavior. Under predefined liability panels, selected robust-best trajectories shifted support away from mutable hotspot contacts toward more distributed interaction networks. Supplementary physical summaries and ranking-first benchmarks support the scope of this resistance-aware design strategy while preserving clear boundaries for prospective validation.

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

Pre-Training for Simulation-Based Science: A Study on Jet Foundation Model Training Objectives

arXiv:2606.14870v1 Announce Type: cross Abstract: Foundation models (FMs) trained on large datasets and fine-tuned on downstream tasks have emerged as a powerful paradigm in AI for science. Industrial FMs are typically trained using self-supervision with masking due to the lack of labels. In many scientific domains, accurate simulations are plentiful and facilitate large, labeled datasets. This opens up new possibilities for pre-training. We present a systematic comparison of pre-training methods using the OmniLearned High Energy Physics FM framework. We test supervised classification, flow-matching generation, and self-supervised masked particle modeling. All models are pre-trained on the JetClass dataset and fine-tuned on two representative downstream tasks, top jet classification and JetNet conditional generation. Among other observations, for classification tasks, we find that pure classifier pre-training is optimal when downstream labels and model capacity are plentiful, but combining it with self-supervised masked particle modeling (MPM) is uniquely powerful in the low-finetuning label regime. Flow matching-based generative pre-training seems to provide little benefit for downstream classification, and interestingly, for downstream generation, we find that flow matching must be in the pre-training objective to see a significant finetuning advantage, hinting at the orthogonality of classification and generation tasks. That is, for a model to transfer to both generative and classification downstream tasks, it must be pre-trained on both. This study provides a template for controlled scaling analysis of pre-training objectives for foundation models in simulation-based sciences.

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

Forged Calamity: Benchmark for Cross-Domain Synthetic Disaster Detection in the Age of Diffusion

The rapid advancement of text-to-image diffusion models has enabled the creation of highly photorealistic synthetic images that closely resemble real photographs, making it increasingly difficult to distinguish authentic content from AI-generated fabrications. This poses challenges for cybersecurity, digital forensics, and disaster response, where fake imagery of floods, fires, or earthquakes can spread misinformation or disrupt emergency operations. To address this, we introduce Forged Calamity, a benchmark dataset for synthetic disaster detection containing 30,000 images, including 6,000 real and 24,000 synthetic samples generated by four diffusion models. Comprehensive experiments across fine-tuned and zero-shot settings reveal consistent weaknesses in current forensic approaches. Fine-tuned detectors perform well in-distribution but lose up to 50\% accuracy on unseen generators or disaster types, showing overfitting to model-specific artifacts. Zero-shot generalized detectors also struggle to maintain stable accuracy, with only limited resilience in a few representation-robust models. These findings highlight persistent generalization gaps and the urgent need for domain- and model-agnostic detection methods to ensure visual authenticity in the diffusion era.

09.
Nature (Science) 2026-06-18

Daily briefing: The proteins that protect us from deadly mutations

Authors:

Proteins that ‘buffer’ the effects of mutations could help to treat diseases such as cancers. Plus, goats can follow human voices and the battle over a key ocean observatory project in the United States. Proteins that ‘buffer’ the effects of mutations could help to treat diseases such as cancers. Plus, goats can follow human voices and the battle over a key ocean observatory project in the United States.

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

Latent Thought Flow: Efficient Latent Reasoning in Large Language Models

arXiv:2606.16222v1 Announce Type: new Abstract: Large Language Models (LLMs) increasingly rely on intermediate reasoning, yet explicit Chain-of-Thought (CoT) suffers from a linguistic space bottleneck: each thought must be decoded into tokens, causing high inference overhead. Latent reasoning moves deliberation into continuous space, but existing methods mostly learn deterministic or reward-maximizing paths, lacking a principled way to allocate probability across trajectories with different correctness and costs. We propose Latent Thought Flow (LTF), which models reasoning as variable-length continuous trajectories and trains a sampler to match a reward-induced posterior over answer quality and computation cost. We instantiate this with a continuous GFlowNet using stochastic latent transitions. To handle sparse answer supervision, we introduce an Entropy-Weighted Subtrajectory Balance objective for intermediate rewards and a reference-prior regularizer to anchor exploration. Experiments under finetuning and transfer learning settings show that LTF outperforms explicit CoT and latent reasoning baselines, improving accuracy by 9.5% while reducing reasoning length by 27.2% on average compared with strong latent reasoning baselines.

11.
PLOS Medicine 2026-06-23

Prevalence and epidemiological patterns of <i>Neisseria gonorrhoeae</i> infection in sub-Saharan Africa, 1964–2025: Systematic review, meta-analyses, and meta-regressions

Authors:

by Aisha Osman, Hina Akram, Bayan Alemrayat, Sumaya Al-Maraghi, Manale Harfouche, Laith J. Abu-Raddad Background Neisseria gonorrhoeae (NG) infection is a global health concern because of its morbidity and increasing antimicrobial resistance. Sub-Saharan Africa is believed to carry a disproportionately high burden of NG infection, but the epidemiology of NG infection in this region has not been comprehensively synthesized. This study systematically reviewed and analyzed NG prevalence in sub-Saharan Africa to characterize prevalence patterns and identify populations at risk. Methods and findings A systematic review was conducted and reported following PRISMA guidelines. Embase, PubMed, Scopus, and Web of Science were searched from inception to June 4, 2025. Eligible studies reported NG prevalence in sub-Saharan Africa. Random-effects meta-analyses generated pooled prevalence estimates, and random-effects meta-regression analyses identified associations and sources of heterogeneity.Nine hundred fifty publications contributed 1,604 prevalence measures spanning 1964–2025. In the general population, pooled urogenital prevalence was 3.2% (95% confidence interval (CI): 2.9–3.5), with substantial between-study heterogeneity and a wide prediction interval, indicating considerable variation in prevalence across settings. Prevalence was high in key populations: among female sex workers, 11.5% (95% CI: 9.9–13.2) for urogenital and 2.0% (95% CI: 0.4–4.5) for anorectal infection; and among men who have sex with men, 2.8% (95% CI: 2.4–3.3) for urogenital, 8.3% (95% CI: 5.8–11.0) for anorectal, and 5.7% (95% CI: 3.6–8.3) for oropharyngeal infection. Symptomatic men exhibited high urogenital prevalence (51.5%; 95% CI: 47.5–55.5), and symptomatic women showed 9.0% (95% CI: 7.7–10.4). Among women with adverse pregnancy or birth outcomes, urogenital prevalence was 8.6% (95% CI: 5.3–12.6). Meta-regression analyses explained over half of the variability in prevalence, showing a long-term decline of 1% per year, a clear population type gradient, subregional differences, and decreasing prevalence with increasing age, but no variation by sex. These findings may be affected by variability in data availability across countries, anatomical sites, and population groups, as well as heterogeneity across included studies. Conclusions NG prevalence remains markedly high in this region but has declined over time. These findings highlight the need for strengthened surveillance, expanded prevention and diagnostic strategies, and continued monitoring of gonococcal antimicrobial resistance to support effective control efforts in sub-Saharan Africa.

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

Seeing Below the Limit of Detection: A Censored-Poisson Bayesian Latent-Growth Change-Point Detector (the Span Detector) for Serial ctDNA in HR+/HER2- Metastatic Breast Cancer

arXiv:2606.11876v1 Announce Type: cross Abstract: Circulating-tumour DNA (ctDNA) carries evidence of drug resistance months before imaging shows it, but the earliest evidence lives below the assay's limit of detection (LoD): a nascent subclone is detected only intermittently, producing a flickering sequence of faint detects and non-detects. Commercial liquid biopsies treat each draw as an independent snapshot and a non-detect as nothing. We argue a non-detect is a left-censored observation, and the pattern of non-detects and faint detects over time carries actionable evidence of growth before any single value is trustworthy. We introduce Span, a censored-Poisson Bayesian latent-growth change-point detector that models the binary detection process, accumulates a sequential generalised-likelihood-ratio statistic for an upward change-point in the per-variant detection rate, and raises a competing-risks alarm with calibrated false-alarm control. Span has no learned weights, so there is nothing to overfit. On a synthetic cohort of HR+/HER2- metastatic breast cancer on first-line CDK4/6-inhibitor plus endocrine therapy, at a matched 10% false-alarm rate, Span roughly doubles the fraction of impending progressions caught three months ahead (indolent regime: 25% vs 11% for the snapshot), with a falsifiable dose-response: large for indolent emergence, vanishing for fast emergence. A value-trajectory baseline performs identically to the snapshot, isolating the gain to the censored detection model. The survival backbone matches a Cox baseline on real breast-cancer data (GBSG-2, n=686; C-index 0.67 vs 0.68), and on a real longitudinal cohort with clean biomarkers (PBC2, n=312) the same pipeline correctly declines to win, a falsifiable boundary test confirming the mechanism is regime-specific. All ctDNA trajectories are synthetic.

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

Learning from the Self-future: On-policy Self-distillation for dLLMs

On-policy self-distillation (OPSD) has proven effective for post-training large language models (LLMs), yet its application to diffusion LLMs (dLLMs) remains unexplored. Existing OPSD methods are inherently autoregressive-centric. They inject privileged information via left-to-right prefix conditioning with token-level divergence supervision, a design that fundamentally conflicts with the arbitraryorder generation of dLLMs. We introduce d-OPSD, the first OPSD framework tailored for dLLMs. Our approach makes two core contributions. First, we reframe self-teacher construction by using self-generated answers as suffix conditioning, enabling the student model to learn from "self future-experience" rather than privileged prefixes. Second, we shift supervision from token-level to step-level, aligning training with the iterative denoising process of dLLMs. Experiments across four reasoning benchmarks show that d-OPSD consistently outperforms RLVR and SFT baselines with superior sample efficiency, requiring only around 10% of the optimization steps by RLVR and opening a promising pathway for dLLM posttraining. The code is available at https://github.com/xingzhejun/d-OPSD.

14.
arXiv (CS.AI) 2026-06-16

Red-Teaming Agent Execution Contexts: Open-World Security Evaluation on OpenClaw

arXiv:2605.11047v2 Announce Type: replace-cross Abstract: Agentic language-model systems increasingly rely on mutable execution contexts, including files, memory, tools, skills, and auxiliary artifacts, creating security risks beyond explicit user prompts. This paper presents DeepTrap, an automated framework for discovering contextual vulnerabilities in OpenClaw. DeepTrap formulates adversarial context manipulation as a black-box trajectory-level optimization problem that balances risk realization, benign-task preservation, and stealth. It combines risk-conditioned evaluation, multi-objective trajectory scoring, reward-guided beam search, and reflection-based deep probing to identify high-value compromised contexts. We construct a 42-case benchmark spanning six vulnerability classes and seven operational scenarios, and evaluate nine target models using attack and utility grading scores. Results show that contextual compromise can induce substantial unsafe behavior while preserving user-facing task completion, demonstrating that final-response evaluation is insufficient. The findings highlight the need for execution-centric security evaluation of agentic AI systems. Our code is released at: https://github.com/ZJUICSR/DeepTrap

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

The ACUTE Protocol: Operationalizing Language Model Activations for Better Calibration, Utility, and Trust

As language models improve and become increasingly deployed to solve a variety of tasks, trustworthiness becomes essential. Calibration is a good proxy for trust: well-calibrated confidence estimates help inform the risk versus reward tradeoff when trusting a specific model output. Unfortunately, even as models improve, they remain poorly calibrated, often biasing towards overconfidence. Additionally, calibration can be gamed: a policy that always predicts the base rate is perfectly calibrated, but completely uninformative. To resolve this, we develop a new metric, expected utility renormalized by the oracle (EURO), that balances calibration and informativeness. We also propose a general-purpose activation-based confidence, utility, and trust estimation protocol (ACUTE) to appropriately adjudicate uncertainty. The ACUTE protocol provides flexible, sample-efficient, and compute-efficient confidence estimators for 3 tasks including multiple choice question answering, tool-calling, and scientific document summarization across 6 models from 4 model families. ACUTE outperforms strong baselines on EURO, while maintaining low calibration error. Taken together, our work shows that equipping LLMs with the ACUTE protocol can improve calibration, utility, and trustworthiness in numerous settings.

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

Knowledge Reutilization in Meta-Reinforcement Learning

arXiv:2606.18132v1 Announce Type: new Abstract: Meta-reinforcement learning enables fast adaptation by extracting shared structure from related tasks, but existing end-to-end methods often couple task inference with embodiment-specific control. This coupling can obscure non-parametric task semantics, reduce sample efficiency, and limit cross-agent reuse. We propose a meta-knowledge reutilization framework that learns task-level knowledge on a dynamics-simplified agent and transfers it to heterogeneous agents. The framework uses a Bayesian non-parametric prior to organize latent task modes and a high-level policy to generate task-level magnitude guidance. To bridge reusable task knowledge with different embodiments, we introduce a semantic-magnitude interface and a lightweight temporal adaptor, which convert frozen meta-knowledge into temporally aligned subgoals for embodiment-specific low-level controllers. Experiments on multiple locomotion agents show that our framework reduces final-step tracking error by 94.75% – 99.79% compared with recent state-of-the-art baselines and achieves comparable deployment performance with about 23.8% of their interaction data.

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

Finite-Time Queue Peak Laws in Stochastic Networks: Logarithmic Scaling After Geometric Thresholds

arXiv:2606.18218v1 Announce Type: cross Abstract: We study finite-horizon queue peaks in generalized switches, a standard stochastic-network model in which many queues share constrained service resources. Arrivals may be dependent, time-varying, and adapted to the past; the standing load condition is uniform interior slack, meaning the conditional mean arrival vector stays in a fixed contraction of the capacity region. We show that this slack reshapes the finite-time peak law for drift-minimizing scheduling policies such as MaxWeight. The square-root envelope that is sharp without slack persists only up to a geometry-dependent threshold; beyond that threshold, the running maximum grows only logarithmically with the horizon, both with high probability and in expectation. The mechanism is self-normalization: in the current queue direction, the projected fluctuation scale is normalized by the stabilizing drift scale. This removes capacity geometry from the logarithmic coefficient, while geometry remains in the threshold. Matching lower bounds show that both the logarithmic term and a geometric threshold are unavoidable. When finite-time state-space collapse is available, the threshold can be sharpened using local bottleneck geometry. For generalized input-queued switches, we obtain finite-time peak bounds with tight logarithmic coefficients. Simulations illustrate the two-phase envelope, local geometric refinements, and variance-sensitive improvements predicted by the theory.

18.
arXiv (CS.AI) 2026-06-11

SPEA2$^+$: Improved Density Estimation in SPEA2 with Provable Runtime Guarantees

arXiv:2606.12382v1 Announce Type: cross Abstract: The Strength Pareto Evolutionary Algorithm 2 (SPEA2) is a popular and prominent evolutionary algorithm for solving multi-objective optimisation problems. Despite its popularity, theoretical analyses of SPEA2 have only appeared recently. Moreover, these analyses focus exclusively on how SPEA2 handles non-dominated solutions and disregard the algorithmic components responsible for handling dominated solutions. We conduct a first runtime analysis of SPEA2 for which these components are analysed. We prove that, unlike other prominent algorithms, including NSGA-II, NSGA-III and SMS-EMOA under the same setting of constant population size and duplicate elimination, SPEA2 is unable to cover the Pareto front of the OneTrapZeroTrap benchmark efficiently. Our results indicate that using k-th nearest-neighbour distance in the fitness assignment provides an insufficient signal to maintain diversity among dominated individuals. To address this issue, we propose an improved variant, SPEA2$^+$, that considers all pairwise distances. The new algorithm achieves the same performance guarantees as the other prominent algorithms on OneTrapZeroTrap, while matching the performance of the original SPEA2 on simpler problems. Experimental results complement our theoretical findings.

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

Decision-Aware Memory Cards: Counterfactual-Inspired Context Selection and Compression for Tool-Using LLM Agents

arXiv:2606.08151v2 Announce Type: replace Abstract: Modern large language model (LLM) agents do not simply need longer contexts; they need decision-relevant evidence at the moment of action. We study decision-aware context selection: ranking retrieved files, tests, traces, rules, and memories by their expected effect on an agent's next action rather than by semantic similarity alone. We present the Counterfactual-Inspired Context Layer (CICL), which builds an instance context graph, estimates decision-oriented utility for candidate units, and compresses selected evidence into typed memory cards. The same schema can be instantiated with hosted LLM judges, local surrogates, or lightweight rankers, making the selection protocol auditable across model choices. On 50 SWE-bench Verified file-retrieval instances, Qwen3.6-Plus reranking of BM25 top-50 candidates improves hit@1 from 0.58 to 0.78 and MRR@10 from 0.634 to 0.790, with all 2,500 judgments parseable. Controlled diagnostics show that CICL identifies action-critical evidence: removing the top-utility semantic unit reduces F1 from 0.245 to 0.000. In selected-then-compressed mode, memory cards save 44.93 tokens per query while preserving selected evidence. CICL provides a practical layer for measuring, ranking, and compressing decision-critical context for tool-using agents. Code is available at https://github.com/stephen-guan-researcher/CICL.

20.
arXiv (math.PR) 2026-06-16

Small moments of the sensitivity of polynomial threshold functions

arXiv:2606.16004v1 Announce Type: new Abstract: In the first version of Chang, Slote, Volberg, and Zhang's paper [BSA_of_PTF], the authors modify a nice recursive approach due to Kane in [Correct_exponent_for_AS] where he bounded the average sensitivity of polynomial threshold functions. In [BSA_of_PTF] Kane's argument was adopted to estimate the boolean surface area of polynomial threshold function. The bridge is a combinatorial averaging lemma considering all balanced partitions. The lemma serves as a substitute for an additive property of average sensitivity. With the lemma, one can apply a Kane-type algorithm to derive a recurrence. Solving the recurrence then gives an upper bound of $e^{C_d \sqrt{\log n}}$ for the boolean surface area. In the second version of the same paper, the authors derive a polylog upper bound for BSA of PTFs. The difference is that they use a tail estimate for the sensitivity function. With the help of a polynomial restriction lemma in [poly_restriction] they sharpen the upper bound. It is noteworthy that when applying the polynomial restriction, each coordinate is put into each part independently with equal probability. As a result, a partition does not necessarily have equal-size blocks. In other words, it may not be balanced. In this note, we first investigate the effect of different partitioning. Second, we use the recursive method in the first version to derive a polylog upper bound for $\mathbb E[s(x)^{\eta}]$ where $\eta < 1/2$. It is interesting to note the phase transition that happens at $\eta=1/2$ in both versions of the proof (but in a completely different form). Section [PhaseTr-s] treats that.

21.
arXiv (CS.CL) 2026-06-18

Depth-Width tradeoffs in Algorithmic Reasoning of Graph Tasks with Transformers

Transformers have revolutionized the field of machine learning. In particular, they can be used to solve complex algorithmic problems, including graph-based tasks. In such algorithmic tasks a key question is what is the minimal size of a transformer that can implement the task. Recent work has begun to explore this problem for graph-based tasks, showing that for sub-linear embedding dimension (i.e., model width) logarithmic depth suffices. However, an open question, which we address here, is what happens if width is allowed to grow linearly, while depth is kept fixed. Here we analyze this setting, and provide the surprising result that with linear width, constant depth suffices for solving a host of graph-based problems. This suggests that a moderate increase in width can allow much shallower models, which are advantageous in terms of inference and train time. For other problems, we show that quadratic width is required. Our results demonstrate the complex and intriguing landscape of transformer implementations of graph-based algorithms. We empirically investigate these trade-offs between the relative powers of depth and width and find tasks where wider models have the same accuracy as deep models, while having much faster train and inference time due to parallelizable hardware.

22.
medRxiv (Medicine) 2026-06-15

Prevalence and Clinical Impact of Pathogenic Variants in Cardiomyopathy Genes Among Individuals with Cardiac Conduction Disorders

Importance: Cardiac conduction disorders have traditionally been regarded as a secondary manifestation of underlying structural heart diseases. However, isolated conduction disorders may precede the onset of heart failure (HF) suggesting shared mechanisms. Objective: To evaluate the prevalence and clinical significance of pathogenic/likely pathogenic (P/LP) rare variants in cardiomyopathy genes among individuals with conduction disorders. Design, Setting, and Participants: Biobank analysis of 192,834 participants with whole genome sequence data from Vanderbilt's BioVU and 353,092 participants from the All of Us Research Program (AoU). Participants with primary conduction disorder (left bundle branch block [LBBB], right bundle branch block [RBBB], high-grade atrioventricular block [AVB]) were identified after excluding secondary causes. Exposures: P/LP variants in cardiomyopathy genes. Main Outcomes and Measures: Primary outcome was P/LP carrier status by age and HF status. Secondary outcomes included incident HF and composite ventricular arrhythmias/sudden cardiac death/mortality (VA/SCD/mortality). Results: Among 16,959 participants with conduction disorders in BioVU and 13,442 in AoU, 432 (2.6%) and 206 (1.5%) were P/LP carriers, respectively. Conduction disorder was independently associated with carrier status (BioVU p

23.
medRxiv (Medicine) 2026-06-24

The role of Mediterranean diet adherence, smoking and their interactions in epigenetic age acceleration: A cross-sectional analysis of the Airwave cohort.

Background: Epigenetic clocks are markers of biological aging that may vary in their sensitivity to environmental stressors and lifestyle modifiers. To evaluate the utility of these biomarkers as sensors of the human exposome, we investigated how they respond to two powerful and opposing exposures: smoking, a source of oxidative stress, and the antioxidant-rich Mediterranean diet. Objectives: We assessed the sensitivity of eleven epigenetic clocks to diet and smoking and evaluated whether Mediterranean diet adherence modifies associations between smoking and epigenetic aging. Methods: We analysed 928 participants (mean age 41 years, 59% male) from the Airwave Health Monitoring Study. Linear regression models assessed associations between Mediterranean Diet Score (MDS) and epigenetic age acceleration (EAA), alongside smoking status and blood cotinine. Interaction terms between smoking status and MDS were included to detect dietary attenuation of smoking-related EAA. Models were adjusted for demographic, socioeconomic, lifestyle, and psychological covariates. Results: Higher MDS was associated with lower EAA for GrimAge ({beta} = -0.07 SD; 95% CI: -0.13, -0.01) and Bernabeu ({beta} = -0.08 SD; 95% CI: -0.14, -0.02) after false discovery rate correction. Smoking was strongly associated with increased EAA, particularly for GrimAge, Bernabeu, and DunedinPACE. Among current smokers, effect sizes were greater in those with lower dietary adherence (e.g. GrimAge: 1.79 SD, 95% CI: 1.54, 2.04) compared with those with higher adherence (1.35 SD, 95% CI: 1.01, 1.68; P_interaction < 0.001). Similar attenuation patterns were observed for Bernabeu. Higher intake of fruits, vegetables, and whole grains contributed most to the attenuation of smoking-related EAA. Conclusions: Our findings indicate that certain epigenetic clocks effectively capture the tension between harmful and protective exposures within the exposome. Rather than suggesting that diet neutralises the risks of tobacco, these results demonstrate that specific clocks are sensitive enough to monitor how lifestyle factors modify molecular responses to environmental toxins. This highlights the value of second-generation clocks in quantifying biological resilience.

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

Compressed Quantum Operators and Roots of Hermite Polynomials

arXiv:2606.24792v1 Announce Type: new Abstract: The fundamental position and momentum operators of quantum mechanics are unbounded, but finite rank compressions of the operators can be considered to obtain partial information on the operators and their properties. Motivated by problems in photonic quantum computing, we bring together results from quantum theory and the theory of orthogonal polynomials to show that a natural finite rank compression of the position and momentum operator representation on Fock space Hilbert space has eigenvalues given by roots of the classical Hermite polynomials. We discuss the corresponding compressed displacement operators and potential applications in approximate quantum error correction.

25.
arXiv (CS.AI) 2026-06-12

ReCal: Reward Calibration for RL-based LLM Routing

arXiv:2606.12479v1 Announce Type: cross Abstract: Large language model (LLM) routing has emerged as an effective paradigm for leveraging the complementary strengths of multiple LLMs through dynamic model and reasoning-strategy selection. Recent reinforcement learning (RL)-based routing methods further improve routing quality by optimizing routing policies from interaction feedback. However, they still struggle to provide informative and comparable learning signals under heterogeneous tasks with varying difficulty. In practice, multiple objectives (e.g., correctness, format behavior) are aggregated into a single scalar reward, leading to ambiguous credit assignment and conflicting optimization signals. Moreover, reward signals exhibit significant variability across instances, where some instances produce higher or more variable rewards, introducing optimization bias that favors trivial samples over informative ones. To address these issues, we propose ReCal, a \underline{Re}ward \underline{Cal}ibration framework for RL-based LLM routing. We first introduce a hierarchical reward decomposition mechanism with component-wise advantage estimation. We further propose a distribution-aware optimization strategy that calibrates optimization variability through variance-aware reweighting and per-dataset normalization. Experiments on seven datasets demonstrate that ReCal consistently improves routing performance, and training stability over baselines. Code is available at https://anonymous.4open.science/r/ReCal.