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01.
arXiv (CS.AI) 2026-06-12

Competition and Diversity in Generative AI

arXiv:2412.08610v3 Announce Type: replace-cross Abstract: Recent evidence, both in the lab and in the wild, suggests that the use of generative artificial intelligence reduces the diversity of content produced. The use of the same or similar AI models appears to lead to more homogeneous behavior. Our work begins with the observation that there is a force pushing in the opposite direction: competition. When producers compete with one another (e.g., for customers or attention), they are incentivized to create novel or unique content. We explore the impact competition has on both content diversity and overall social welfare. Through a formal game-theoretic model, we show that competitive markets select for diverse AI models, mitigating monoculture. We further show that a generative AI model that performs well in isolation (i.e., according to a benchmark) may fail to provide value in a competitive market. Our results highlight the importance of evaluating generative AI models across the breadth of their output distributions, particularly when they will be deployed in competitive environments. We validate our results empirically by using language models to play Scattergories, a word game in which players are rewarded for answers that are both correct and unique. Overall, our results suggest that homogenization due to generative AI is unlikely to persist in competitive markets, and instead, competition in downstream markets may drive diversification in AI model development.

02.
arXiv (CS.AI) 2026-06-24

HOLMES: Evaluating Higher-Order Logical Reasoning in LLMs

arXiv:2606.23238v2 Announce Type: replace Abstract: Logical reasoning is essential for reliable AI, yet existing benchmarks are largely first-order-logic-centric, focusing on object-level deduction over fixed predicates. This misses many realistic scenarios where models must reason over rules, predicates, functions, constraints, and decision procedures themselves. We introduce HOLMES (Higher-Order Logic Meets real-world Explainable Symbolic reasoning), the first real-world benchmark for higher-order symbolic reasoning in LLMs, containing 1379 instances. Built on higher-order logic, HOLMES pairs natural-language problems with HOL formalizations, ground-truth answers, verifiable reasoning traces, and fine-grained controllable reasoning factors across law and finance. Experiments show that current LLMs still struggle on HOLMES, with an average accuracy of only 50.64% and the best model reaching 59.54%. Our analyses further reveal that high final-answer accuracy can mask shortcut reasoning in conflict-resolution settings, while performance drops sharply under scope-conditioned and compositional reasoning. These findings identify higher-order symbolic reasoning as a key bottleneck for building reliable and verifiable LLMs. The project code and dataset are publicly available at https://github.com/wuyucheng2002/HOLMES.

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

Point-Identification of a Robust Predictor Under Latent Shift with Imperfect Proxies

arXiv:2603.15158v2 Announce Type: replace Abstract: Addressing the domain adaptation problem becomes more challenging when distribution shifts across domains stem from latent confounders that affect both covariates and outcomes. Existing proxy-based approaches that address latent shift rely on a strong completeness assumption to uniquely determine (point-identify) a robust predictor. Completeness requires that proxies have sufficient information about variations in latent confounders. For imperfect proxies the mapping from confounders to the space of proxy distributions is non-injective, and multiple latent confounder values can generate the same proxy distribution. This breaks the completeness assumption and observed data are consistent with multiple potential predictors (set-identified). To address this, we introduce latent equivalent classes (LECs). LECs are defined as groups of latent confounders that induce the same conditional proxy distribution. We show that point-identification for the robust predictor remains achievable as long as multiple domains differ sufficiently in how they mix proxy-induced LECs to form the robust predictor. This domain diversity condition is formalized as a cross-domain rank condition on the mixture weights, which is substantially weaker assumption than completeness. We introduce the Proximal Quasi-Bayesian Active learning (PQAL) framework, which actively queries a small, targeted set of diverse domains that satisfy this rank condition. PQAL can recover the point-identified predictor, demonstrates robustness to varying degrees of shift and outperforms previous methods on synthetic data and semi-synthetic dSprites, IHDP, ACS Folktables datasets.

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

A nonparametric two-sample test using a parametric integral probability metric

arXiv:2606.16941v1 Announce Type: cross Abstract: Detecting distributional differences between two independent samples is a fundamental problem in statistics and machine learning. Nonparametric two-sample testing provides a principled framework for determining whether two samples are drawn from the same underlying distribution, without assuming any specific parametric form for the distribution. In this study, we propose a new two-sample test statistic based on a newly introduced integral probability metric (IPM), using a specially designed parametric discriminator class with a single node of a neural network. We show that the resulting test statistic, called PReLU-IPM, is nonparametric and establish theoretical guarantees for the associated two-sample testing procedure, PReLU-TST, including its consistency and asymptotical equivalence to nonparametric IPM-based tests under regularity conditions. By analyzing multiple simulated and real benchmark datasets, we demonstrate that PReLU-TST achieves higher power across a range of alternatives or performs comparably to its competitors, for finite samples.

05.
arXiv (CS.CV) 2026-06-24

Counting Trees from Satellite Imagery with Noisy Supervision

Counting individual trees is a fundamental task for environmental monitoring, yet remains largely unexplored with satellite imagery. At these resolutions, isolated trees may still be identifiable, but crown boundaries become ambiguous in dense forests, making the notion of an individual tree inherently ill-defined. Moreover, large-scale manual annotations of individual trees are prohibitively expensive. While scalable supervision can be derived from airborne LiDAR, the resulting annotations are noisy and difficult to exploit effectively. We address these challenges by formulating tree counting as a spatial density matching problem supervised through Unbalanced Optimal Transport. This formulation naturally accommodates both precise localization of isolate trees and robust density estimation in dense forests. We further introduce a self-correction mechanism that leverages transport residuals to progressively refine noisy supervision during training. We evaluate our approach on TinyTrees, a new benchmark spanning three continents and three satellite sensors, comprising over 215 million tree annotations (including 773K manually verified instances) across 23,000 sq.km. Our method consistently outperforms detection-based, regression-based, and transport-based distribution-matching baselines, demonstrating the effectiveness of unbalanced transport and reliability-aware supervision for large-scale tree counting from satellite imagery. Code, data and models are available at https://github.com/dgominski/treematch.

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

Probing Dec-POMDP Reasoning in Cooperative MARL

arXiv:2602.20804v2 Announce Type: replace Abstract: Cooperative multi-agent reinforcement learning (MARL) is typically framed as a decentralised partially observable Markov decision process (Dec-POMDP), a setting whose hardness stems from two key challenges: partial observability and decentralised coordination. Genuinely solving such tasks requires Dec-POMDP reasoning, where agents use history to infer hidden states and coordinate based on local information. Yet it remains unclear whether popular benchmarks actually demand this reasoning or permit success via simpler strategies. We introduce a diagnostic suite combining statistically grounded performance comparisons and information-theoretic probes to audit the behavioural complexity of baseline policies (IPPO and MAPPO) across 37 scenarios spanning MPE, SMAX, Overcooked, Hanabi, and MaBrax. Our diagnostics reveal that success on these benchmarks rarely requires genuine Dec-POMDP reasoning. Reactive policies match the performance of memory-based agents in over half the scenarios, and emergent coordination frequently relies on brittle, synchronous action coupling rather than robust temporal influence. These findings suggest that some widely used benchmarks may not adequately test core Dec-POMDP assumptions under current training paradigms, potentially leading to over-optimistic assessments of progress. We release our diagnostic tooling to support more rigorous environment design and evaluation in cooperative MARL.

07.
medRxiv (Medicine) 2026-06-24

External Validation and Calibration Assessment of Explainable Machine Learning Models for GVHD Prediction After Allogeneic HSCT

Background Graft versus host disease (GVHD) remains a major determinant of morbidity and mortality following allogeneic hematopoietic stem cell transplantation (allo HSCT). Existing GVHD prediction models demonstrate modest discrimination and limited generalizability, and calibration drift across external populations is rarely characterized despite its essential role in the clinical interpretability of predicted probabilities. Objectives To develop and externally validate an explainable machine learning framework for predicting acute and chronic GVHD and associated overall survival in patients with acute myeloid leukemia (AML), acute lymphoblastic leukemia (ALL), and myelodysplastic syndromes (MDS) undergoing allo HSCT, and to systematically characterize calibration across heterogeneous external validation cohorts to inform deployment requirements. Study Design The model was developed on three publicly available registry-derived datasets (N = 2,509) and externally validated across six independent cohorts (N = 14,788) comprising adult and pediatric allo HSCT recipients, including a regional Middle Eastern cohort (UAE and Jordan). A standardized preprocessing pipeline harmonized heterogeneous datasets. Gradient boosting models (CatBoost) were used for binary GVHD prediction; exploratory overall survival analysis used a Cox proportional hazards model with predicted acute GVHD risk as a covariate. Discrimination (AUROC with bootstrap 95% CI), calibration (logistic recalibration intercept and slope with analytical 95% CI), and feature importance (SHapley Additive exPlanations, SHAP) were assessed in training out-of-fold and all external cohorts. Results In internal validation, AUROC was 0.63 (95% CI 0.61-0.65) for acute GVHD and 0.72 (95% CI 0.70-0.74) for chronic GVHD. External validation demonstrated AUROC ranges of 0.51-0.57 (acute) and 0.54-0.64 (chronic), with consistent performance across disease subgroups despite substantial heterogeneity in transplant practices and feature availability. In exploratory survival analysis, the acute-GVHD-informed Cox model achieved a training-cohort C-index of 0.679 (95% CI 0.658-0.697); external C-indices ranged from 0.47-0.53. Calibration analysis identified systematic external risk overestimation (negative calibration intercept in 10 of 11 evaluable external cohort-target combinations) with heterogeneous slope drift requiring cohort-specific recalibration. Key predictors included recipient age, graft source, conditioning intensity, GVHD prophylaxis, and HLA match ratio. Conclusions An explainable, externally validated GVHD prediction framework was developed using heterogeneous registry-derived datasets, with systematic characterization of calibration drift across multiple external cohorts, an analysis rarely reported in prior GVHD prediction literature. Predictive performance was modest for acute GVHD and moderate for chronic GVHD, constrained by missing immunobiological variables and incomplete HLA characterization. Per-cohort recalibration is required before clinical deployment, with prospective validation and benchmarking against established GVHD risk scores identified as priority next steps.

08.
Nature (Science) 2026-06-10

Whole-genome duplication shaped cell-type evolution in the vertebrate brain

作者:

The complex brains of vertebrates have more cell types than those of their closest relatives. Whole-genome duplications (WGDs) occurred during early vertebrate evolution1, but it is unclear whether the duplicated genes (ohnologues) facilitated cell-type evolution. Here using brain single-cell transcriptomes from five chordates—human2, mouse3, lizard4, lamprey5 and amphioxus—we report that many cell-type families with conserved core transcription factors in vertebrates do not show one-to-one homology with amphioxus. Moreover, ohnologues, particularly those from the first WGD, were more important than small-scale duplication paralogues for vertebrate cell-type evolution. To explore whether ohnologues are mechanistically important for this process, we predicted ancestral cell-type states and compared them to amphioxus and experimentally investigated macroglia. The findings indicate that ohnologues had a role in early vertebrate cell-type diversification. Moreover, by examining paralogue expression across cell types and species, we show that expression changes were mainly driven by dosage selection and subfunctionalization. We also link ohnologues to cellular diversity at different anatomical and cell-type scales. Our findings demonstrate the importance of WGDs for the evolution of early vertebrate brain complexity and highlight that the resultant ohnologues continued to capacitate cell-type evolution long after they were formed. Analyses of brain single-cell transcriptomes from human, mouse, lizard, lamprey and amphioxus reveal that duplicated genes (ohnologues) played a pivotal part in early vertebrate cell-type diversification.

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

Categorical Prior Lock-in: Why In-Context Learning Fails for Structured Data

arXiv:2606.11961v1 Announce Type: cross Abstract: Large language models (LLMs) are increasingly used as conditional generators for structured data, relying on in-context learning (ICL) to adapt to new distributions without parameter updates. We investigate the limits of ICL for structured generation under distribution mismatch, using high-cardinality tabular data as a controlled test case, and identify a structural failure mode we term categorical prior lock-in: the inability of ICL to update the model's prior over token distributions inherited from pre-training. Across two 7B-parameter open-weight models, ICL improves numerical fidelity with additional examples but exhibits a sharp ceiling on categorical distributions, failing to reproduce rare classes entirely. Parameter-efficient fine-tuning (LoRA) overcomes these limitations but introduces measurable memorization risk and, in some cases, destabilizes structured output generation, highlighting a fundamental trade-off between adaptability and privacy.

10.
arXiv (CS.LG) 2026-06-11

Persistent Homology as a Theory of Emergent Structure

作者:

arXiv:2507.03065v2 Announce Type: replace Abstract: Why do some macroscopic structures remain identifiable even though their microscopic constituents continually change? Vortices persist while fluid parcels turn over, neural memories persist while spikes and synapses fluctuate, and institutions persist while individuals enter and leave. We propose a scale-relative answer: an emergent property is a persistent nontrivial homology class $[z]\in H_p=\ker\partial_p/\im\partial_{p+1}$, a macro-feature that is closed but not exact across a filtration of descriptions. This identification turns emergence into a measurement problem. Persistent bars detect stable macro-features, and we introduce a contractive-similarity (CS) graph operator to supply scaffold spectral gaps that predict robustness. Hodge decomposition separates harmonic macro-scaffold from exact and co-exact micro-flow; and functorial condensation explains when one level's emergent class becomes a unit for the next. The resulting scaffold-flow framework expresses six familiar signatures of emergence (i.e., inevitability, coherence, irreducibility, complementarity, robustness, and hierarchy) within one mathematical language. It also yields falsifiable predictions across atmospheric, neural, and social systems: genuine emergent structures should persist across filtrations, remain spectrally stable, respond disproportionately to harmonic interventions, and require timescale separation for hierarchical autonomy.

11.
arXiv (math.PR) 2026-06-17

Critical spectral behavior and large deviations for geometric $\alpha$-stable processes

arXiv:2606.17501v1 Announce Type: new Abstract: In this paper, we study the Schrödinger-type operator associated with geometric stable processes on $\mathbb{R}^{d}$, especially the differentiability of spectral function. Let $\mathcal{H}$ be the generator of the geometric stable process and $\mu$ a smooth measure on $\mathbb{R}^{d}$. Then the spectral function $C(\theta)$ is defined as $C(\theta) = -\inf \sigma(-\mathcal{H} - \theta \mu)$, where $\sigma(\mathcal{A})$ denotes the spectrum of $\mathcal{A}$ and $\theta$ is a real parameter. Since the geometric stable process exhibits severe local singularities in its Lévy measure, its transition semigroup lacks ultracontractivity, which invalidates classical methods for proving the differentiability. To overcome this obstacle, we use the compact embedding of the extended Dirichlet space into $L^2(\mu)$. As a primary application of this differentiability, we establish a large deviation principle for a positive continuous additive functional associated with the smooth measure $\mu$.

12.
arXiv (CS.LG) 2026-06-24

Stochastic Expectation Maximization for Robust State-Space Radio Interferometric Imaging

arXiv:2606.23944v1 Announce Type: cross Abstract: State–space models provide a flexible framework for analyzing dynamical systems, yet they often rely on Gaussian assumptions that fail to capture heavy-tailed or outlier-prone measurement noise. We propose a robust estimation scheme for linear state–space models subject to compound-Gaussian noise, as encountered for instance in radio interferometry affected by radio-frequency interference (RFI). The method relies on a Stochastic Approximation Expectation–Maximization (SAEM) algorithm in which the standard E-step is replaced by Monte Carlo sampling of the latent states and noise texture through closed-form Gibbs updates, enabling tractable inference despite the heavy-tailed likelihood. Numerical experiments show that the proposed method significantly improves reconstruction fidelity and robustness to RFI, outperforming a Gaussian EM algorithm and even an oracle RTS smoother. These results highlight the benefits of heavy-tailed state–space modeling and SAEM-based inference in interference-dominated imaging scenarios.

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

NoContactNoWorries: Estimating Contact through Vision and Proprioception for In-Hand Dexterous Manipulation

arXiv:2606.24450v1 Announce Type: cross Abstract: Perceiving physical contact is fundamental to dexterous manipulation. While robots often rely on dedicated hardware tactile sensors, humans exhibit a remarkable ability to infer contact by integrating visual information with an innate sense of their body's pose and movement. Inspired by this embodied perceptual skill, we investigate whether a robot can learn to infer contact from vision, an approach that also offers a scalable alternative to tactile hardware specifically for binary contact estimation, which faces practical challenges in cost, fragility, and integration. We present NoContactNoWorries, a transformer-based multimodal framework that fuses RGB-D vision with the robot's proprioception to infer binary contact states as a pseudo-tactile signal for hand-object interactions. We validate by training a single contact prediction model on multiple objects and show that the inferred contact signal supports downstream reinforcement learning agents for in-hand object reorientation, generalizing to novel objects. Experiments in both simulation and on a real-world robot validate our approach, highlighting the feasibility of inferring contact from vision and proprioception. Project Page: https://soham2560.github.io/no-contact-no-worries/

14.
arXiv (CS.AI) 2026-06-17

From Democracies to Autocracies: How AI Systems Enable Authoritarianism by Design

arXiv:2606.17286v1 Announce Type: cross Abstract: AI-enabled authoritarianism is not confined to autocracies. In this paper, we provide greater transparency by investigating and mapping the lifecycles of six AI systems deployed in different political regimes, ranging from the US to China. By drawing on an extensive range of sources (academic publications, investigative research reports, third-party evaluations, media interviews, government procurement notices), we conduct a systematic, qualitative comparison across systems to identify the critical technical and operational features that enable authoritarianism within their respective political contexts. We find that enabling features include the centralization and co-optation of administrative data for law enforcement and political punishment, regulatory gaps that fail to deter misuse, weak user compliance that nullifies human oversight mechanisms, and the encoding of protected group traits that identify members of vulnerable populations. We find that these features are present across systems deployed in autocratic and democratic regimes, albeit in varying configurations. We also find that both centralized and fragmented AI systems can contribute to authoritarianism by exploiting governance gaps: centralized systems directed by executive authorities, particularly within security and military institutions, are often not subjected to formal oversight mechanisms, while fragmented systems diffuse accountability between stakeholders, paving the way for entrenchment. These findings reveal that AI-enabled authoritarianism is distributed, resulting from design and operational choices made by developers, administrators, and users alike. We conclude with recommendations for developers and policymakers to mitigate these risks.

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

CisTransCell: Single-Cell Perturbation Prediction via Gene Function, Regulatory Control, and Cellular Context

arXiv:2606.13713v1 Announce Type: cross Abstract: Predicting cellular transcriptional responses to genetic perturbations is a central problem in single-cell biology, especially in the zero-shot setting where the perturbed gene or gene combination is unseen during training. A major difficulty is that perturbation effects are not determined by expression state alone: they depend on how the perturbed gene product influences other genes and proteins, how those downstream factors act on cis-regulatory elements, and which regulatory programs are active in the current cell state. To better capture this biological complexity, we propose CisTransCell, a cell-conditioned multi-modal framework for single-cell perturbation prediction that augments each gene with two complementary priors: a regulatory-sequence prior that captures how the gene is controlled, and a coding-sequence prior that captures what the gene product does. By integrating these priors with cellular expression state, CisTransCell models perturbation response as a cascade from gene function to regulatory control to downstream transcriptional change. Experiments on benchmark single-cell perturbation datasets show that CisTransCell achieves strong performance in zero-shot perturbation prediction.

16.
arXiv (CS.CL) 2026-06-15

Reward-SQL: Boosting Text-to-SQL via Stepwise Execution-Aware Reasoning and Process-Supervised Rewards

Recent advances in large language models (LLMs) trained with reinforcement learning (RL) have improved Text-to-SQL performance. However, RL-based approaches still struggle with complex queries due to two key limitations: insufficient stepwise execution-aware reasoning grounded in database feedback, and the lack of process-level rewards for guiding reasoning optimization. To address these issues, we propose CoCTE, a divide-and-conquer and execution-aware reasoning framework that progressively composes SQL queries through intermediate view validation and structured Common Table Expressions (CTEs), improving both accuracy and interpretability. To realize a CoCTE reasoning process, we develop Reward-SQL, a unified approach with three stages: (1) model initialization, which equips LLMs with structured CoCTE reasoning capabilities; (2) process reward design, which delivers fine-grained, execution-aware supervision; and (3) process-supervised RL and inference, which integrates process rewards into training and guides the inference stage by process rewards. This paper addresses the core challenges in Reward-SQL and makes the following contributions. We introduce a process reward model (PRM) that combines execution-aware trajectory scoring with entropy-based step weighting, providing dense and interpretable supervision across reasoning steps. We integrate PRM into both RL training and inference stages, stabilizing optimization and improving trajectory exploration with process-level signals. Experiments show that Reward-SQL significantly outperforms baselines with comparable model sizes, and exhibits strong cross-domain generalization.

17.
arXiv (CS.AI) 2026-06-12

Decoding Insect Song: A Multitask Semisupervised Orthoptera Bioacoustic Classifier

arXiv:2606.13236v1 Announce Type: cross Abstract: Passive acoustic monitoring holds great promise for ecological inference, yet existing automated tools are typically narrowly trained and non-transferable. We address these limitations with PULSE, a semi-supervised, multi-task framework for Orthoptera bioacoustics, combining weakly-supervised species classification, self-supervised learning on unlabelled field audio, and knowledge distillation from a general-purpose bioacoustic model. Our domain-adapted specialist model outperforms a state-of-the-art general model across all metrics (macro F1: 0.21 vs. 0.07; AUC: 0.74 vs. 0.45; AP: 0.32 vs. 0.19), with active learning further raising F1 to 0.34 and AUC to 0.84. Beyond classification, the learned embeddings encode ecologically meaningful structure, exposed through an interactive visualisation tool for ecological discovery.

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

Anatomy of Post-Training: Using Interpretability to Characterize Data and Shape the Learning Signal

arXiv:2606.12360v1 Announce Type: new Abstract: Language-model post-training is the main stage at which model behavior is shaped, yet it still largely involves optimization of scalar rewards that summarize diverse desiderata. This abstraction gives practitioners little visibility into what their data actually teaches models, allowing spurious correlations to be learned by a model and inducing undesirable behaviors such as over-stylization and sycophancy. To address this problem, we ask: can we inspect a preference dataset before optimization and decide, at the level of concepts, which behaviors a model should be allowed to learn? Motivated by this, we introduce a data-centric post-training pipeline that uses interpretability protocols to develop statistical hypotheses for the latent concepts separating preferred from dispreferred generations, making them explicit for fine-grained user feedback. Building on this view, we unify several interpretability-based training protocols as ways of shaping rewards via feature or data interventions. Empirically, we show that our pipeline diagnoses undesirable signals in existing preference data, mitigates off-target learning, and can also help amplify or shape desired properties such as safeguards and model personality. More broadly, our results suggest that interpretability can turn post-training from optimizing opaque proxy rewards into a process of auditing and sculpting the learning signal itself.

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

Physics-conforming Latent Twins

arXiv:2606.15053v1 Announce Type: new Abstract: Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems. For time-dependent problems, however, accurate interpolation of training trajectories is not sufficient: reliable surrogates should also respect the conservation laws, invariants, admissibility conditions, and dissipative structures that give those trajectories physical meaning. We introduce Physics-conforming Latent Twins, a framework for learning latent surrogate solution operators whose dynamics satisfy selected physical principles by design. The method builds on the Latent Twin formulation by jointly learning an encoder, a decoder, and a latent flow map between arbitrary time-indexed states, while constraining the latent dynamics to preserve or dissipate prescribed structural quantities. We develop a constraint-transfer viewpoint that connects physical structure in the original state space with compatible constraints in latent space, and prove structure-preservation bounds showing how latent enforcement improves control of physical defects after decoding. We also derive algebraic conditions for latent flow maps that preserve linear and quadratic invariants or enforce dissipative inequalities. Numerical experiments on representative ODE and PDE benchmarks demonstrate improved constraint satisfaction, structural fidelity, and qualitative long-time behavior while maintaining accurate surrogate prediction.

20.
arXiv (math.PR) 2026-06-18

Evolution of Conditional Entropy for Diffusion Dynamics on Graphs

arXiv:2510.19441v2 Announce Type: replace-cross Abstract: The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these processes and the diversity of the modeled systems. While results about their steady state are well-known, very few exact results about their finite-time evolution exist. Here, we introduce the conditional entropy of heat diffusion in graphs, and outline a mathematical framework that contextualizes diffusion and conditional entropy within the theories of continuous-time Markov chains and information theory. In particular, we highlight that this entropic measure satisfies an information-theoretical version of the second law of thermodynamics, thereby providing a parallelism between diffusion dynamics on networks and their physical counterparts. Furthermore, we obtain explicit results for its evolution on complete, path, and circulant graphs, as well as a mean-field approximation for Erdös-Rényi graphs. We also obtain asymptotic results for general networks and provide bounds for the evolution of conditional entropy. Finally, we experimentally demonstrate several properties of conditional entropy for diffusion over random graphs, such as the Watts-Strogatz model.

21.
arXiv (math.PR) 2026-06-12

Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability

arXiv:2606.08683v2 Announce Type: replace Abstract: We determine the Fourier dimension of dyadic Mandelbrot cascades under the minimal Kahane-Peyriere integrability condition. The interval theorem is proved in a vector-valued dyadic cascade model in which sibling weights may have arbitrary dependence. For every balanced energy-admissible vector law, almost surely on non-extinction, dim_F(mu)=dim_E(mu)=dim_2(mu)=D_E(X). In the canonical scalar case, under W>=0, E W=1, E[W log_2^+ W]

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

When Should Agent Trust Be Conditional? Characterizing and Attacking Skill-Conditional Reputation in Agent Swarms

arXiv:2606.14200v1 Announce Type: new Abstract: Open platforms increasingly route tasks among heterogeneous LLM agents–differing in base model, scaffold, and tool stack–whose competence varies sharply by skill: an agent excellent at one skill may be useless at another. The standard reputation approach summarizes each agent by a single global trust score, but that scalar is the wrong object here, because routing every task to the globally most-trusted agent leaves the value of specialization unclaimed. We study skill-conditional trust R(i | k)–the trust to place in agent i for a task requiring skill k, rather than one score per agent–and pose three falsifiable questions: when is conditioning worth it, how much cross-skill evidence should be borrowed, and whether that borrowing is safe. A controlled phase-diagram analysis answers the first two: conditional trust wins only in a specific regime–high agent heterogeneity, sparse per-skill evidence, and correlated skills–and the coupling strength beta that buys this data efficiency is dual-use, because the same cross-skill borrowing is also a laundering channel. On a public benchmark of 14 genuinely heterogeneous AppWorld agents, real pools land inside the beneficial regime–a small but genuine gain, with the per-skill best agent genuinely changing across skills. We then show that an attacker with cheap evidence in one skill and none in a target skill hijacks the conditional router, driving routing regret from 0 to 0.94 on a pool our zero-cost Conditional Information Value Test (CIVT) rates GREEN–while the ungated trust verdict it contaminates reads -0.06 instead of the honest +0.19. A zero-evidence gate bounds the attack but does not eliminate it; we characterize the residual cost under an explicit budget. We do not claim Sybil-resistance–we quantify the trade-off.

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

Unifying Acoustic Features and Text with Multimodal LLMs for Neurodegenerative Screening

arXiv:2606.14788v1 Announce Type: cross Abstract: Voice-based screening offers a scalable and non-invasive way to assess neurodegenerative diseases such as Alzheimer's disease (AD) and Parkinson's disease (PD), but their staging remains challenging due to the difficulty of integrating heterogeneous data. This paper presents NeurMLLM, an efficient multimodal generative framework for neurodegenerative disease staging. NeurMLLM first encodes the spectrograms and Mel-frequency cepstral coefficients of audio data with vision transformers and projects their representations into the embedding space of a large language model (LLM), where they are concatenated with transcript and demographic instruction tokens as a single unified sequence. The LLM is then instruction-tuned via Low-Rank Adaptation using task prompts to autoregressively predict a constrained label token, enabling a generative classification. By evaluating on the Bridge2AI-Voice dataset for fine-grained staging of AD and PD, we observe that NeurMLLM achieves strong performance, consistently outperforming classical machine learning methods and existing LLM-based approaches. The results show the high potential of multimodal LLMs in neurodegenerative disease staging, improving staging accuracy and supporting accessible deployment.

24.
arXiv (CS.CL) 2026-06-12

Operads for compositional reasoning in LLMs

Question decomposition, i.e. breaking a complex query into simpler sub-queries whose answers are composed to produce a final answer, is a widely used strategy for improving LLM reasoning, yet it currently lacks a rigorous mathematical foundation. In this paper, we propose operads, mathematical structures that model many-in, one-out operations and compositions thereof, as a natural framework for describing question decomposition. We define the questions operad $Q$, in which operations correspond to question templates and composition corresponds to substitution of sub-answers, and show how QA models can be interpreted as algebras over $Q$. Beyond reframing existing practice, this operadic perspective points toward new methods, in particular a notion of operadic consistency, which measures whether a QA model's answers agree across the partial collapses of a question decomposition tree. Empirical evaluation of operadic consistency is reported in our companion paper (Bottman, Liu, and Richardson, 2026), which finds it strongly correlated with accuracy across twelve LLMs and four multi-hop QA datasets and outperforming standard temperature-based self-consistency baselines. We argue that operads are the natural mathematical home for question decomposition, and that invariants such as operadic consistency open new directions for analyzing and improving the reliability of multi-step reasoning.

25.
arXiv (CS.AI) 2026-06-11

Rule Taxonomy and Evolution in AI IDEs: A Mining and Survey Study

arXiv:2606.12231v1 Announce Type: cross Abstract: The adoption of AI-powered Integrated Development Environments (AI IDEs) has introduced "Rules" as a novel software artifact, allowing developers to persistently inject project-specific constraints and architectural guidelines into the context of Large Language Models (LLMs). Despite their role in aligning AI behavior with developer intent, the taxonomy, evolution, and practical impact of these rules remain largely unexplored. To bridge this gap, we conducted a mixed-methods empirical study on AI IDE rules. By mining 83 open-source projects and extracting 7,310 rules, we established a comprehensive taxonomy comprising 5 primary and 25 secondary categories. We then triangulated these artifacts with survey responses from 99 practitioners. Our analysis identified a contrast between developer priorities and actual configurations: while practitioners rate architectural constraints as highly important, rule files in repositories primarily consist of low-level workflow and code formatting constraints. Furthermore, our analysis of 1,540 rule evolution events revealed that rules are updated frequently. Repository data further indicate that rule evolution is primarily driven by constructive context expansions (29.17%) and enrichments (26.59%). In contrast, surveyed developers reported modifying rules primarily to correct AI errors (77.78%), typically by adding new negative constraints rather than editing existing ones. Finally, an artifact compliance assessment of 160 rule evolution events revealed that updating rules significantly improves the adherence of software artifacts, with the average artifact compliance rate increasing by 22.99% (from 49.14% to 72.13%) following an update. Our study provides empirical insights that can help developers optimize prompting strategies and guide tool builders in designing automated conflict-detection and context-management mechanisms for AI IDEs.