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01.
arXiv (CS.CL) 2026-06-18

Human-AI Coevolution Dynamics: A Formal Theory of Social Intelligence Emergence Through Long-Term Interaction

Current conversational AI systems have made significant progress in language generation, personalization, and long-context interaction. However, most existing methods model social behavior through isolated components such as emotion modeling, memory retrieval, or persona conditioning, lacking a unified framework to explain the emergence of stable social relationships and social intelligence in long-term human-AI interaction.To address this, we propose the Human-AI Coevolution Dynamics Framework (HACD-H), a formal model of human-AI interaction as a self-organizing social cognitive system. HACD-H integrates emotional adaptation, relational organization, social memory, and personality consistency into a unified dynamical framework and introduces principles including multi-timescale social cognition, relational attractors, trust basins, developmental phase transitions, and social cognitive energy dynamics.We construct a conversational dataset with approximately 14,700 interaction turns and develop a theory-driven empirical evaluation framework. Results reveal a hierarchy of temporal persistence in social cognition, stable relational attractors, phase-transition-like developmental patterns, and a structured social cognitive energy landscape. Social intelligence shows a significant negative correlation with social cognitive energy (r = -0.391, p < 0.001), and interaction trajectories exhibit progressive energy reduction over time.These findings suggest that social intelligence emerges from long-term social cognitive coevolution rather than isolated conversational capabilities. HACD-H provides a unified theoretical foundation for modeling adaptive human-AI social interaction and developing socially intelligent AI systems.

03.
Nature Medicine 2026-06-12

General-purpose large language models outperform specialized clinical AI tools on medical benchmarks

Specialized clinical artificial intelligence (AI) tools are entering medical practice despite scarce independent evaluation. We quantitatively evaluate two clinical AI tools, OpenEvidence and UpToDate Expert AI, built on large language models (LLMs) against three frontier LLMs: GPT-5.2, Gemini 3.1 Pro and Claude Opus 4.6. Our evaluation has three stages: (1) 500 MedQA questions testing medical knowledge, (2) 500 HealthBench items measuring alignment with clinicians and (3) the real clinical queries (RCQ) benchmark, built from 100 de-identified queries from physicians to a general-purpose language model in a live clinical environment. For the RCQ benchmark, 12 US clinicians performed randomized, blinded review of model outputs, producing 1,800 model–question annotations. Frontier LLMs outperformed clinical AI tools in all three evaluations. Clinical AI tools performed comparably to auto-enabled Google Search AI Overview on the RCQ. These findings highlight the need for independent, real-world evaluation of AI tools before they enter clinical settings. In an independent evaluation, frontier large language models outperformed specialized clinical artificial intelligence tools on medical knowledge, clinician alignment and real-world clinical queries.

04.
medRxiv (Medicine) 2026-06-15

Non-invasive intracranial pressure waveform reconstruction with deep learning

Purpose: Continuous intracranial pressure (ICP) monitoring requires invasive instrumentation, reaching only a narrow subset of critically ill patients. We tested whether deep learning models trained on routinely acquired extracranial signals can reconstruct continuous ICP waveforms at clinically relevant accuracy in an independent external cohort. Methods: In adults admitted to the ICU at a single quaternary health system, five deep learning architectures were trained on high-frequency arterial blood pressure (ABP), photoplethysmography (PPG), and electrocardiography (ECG) waveforms, using invasive (intraparenchymal) ICP as ground truth. Two fusion strategies (early and late) and three training objectives (waveform-morphology, baseline robust regression, and weighted robust regression) were evaluated. Models were externally validated on the held-out MIMIC-III Waveform Database. Performance was assessed by mean absolute error (MAE) and waveform similarity by Pearson correlation (r). Results: We analyzed data from 158 critically ill adults (~5,322 hours) across two quaternary health systems (Johns Hopkins Hospital, Baltimore; Beth Israel Deaconess Medical Center, Boston). Validation MAE ranged from 4.276 mmHg [95% CI 4.269, 4.283] (gated recurrent, late fusion) to 4.946 mmHg [95% CI 4.938, 4.956] (attention-based, early fusion), with Pearson r ranging from 0.599 [95% CI 0.599, 0.600] to 0.722 [95% CI 0.722, 0.723]. The multiscale encoder-decoder model demonstrated the most favorable MAE-correlation tradeoff. Conclusion: This is the first demonstration that continuous ICP waveform reconstruction from bedside signals generalizes across institutions at clinically relevant accuracy, establishing a foundation for non-invasive ICP monitoring and motivating validation across broader populations and ICP ranges.

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

DeepSWIP: Quotient-WMC Counterfactuals for Neural Probabilistic Logic Programs

arXiv:2606.20526v1 Announce Type: new Abstract: Neurosymbolic systems such as DeepProbLog combine neural perception with probabilistic logic, but standard inference is associational. Counterfactual reasoning additionally requires a causal semantics for interventions and evidence. We introduce DeepSWIP, a single-world counterfactual semantics for DeepProbLog programs. Using neural materialization, we reduce fixed-context neural predicates to ordinary ProbLog choices, apply Single World Intervention Programs (SWIPs), and compute counterfactuals by weighted model counting (WMC) over a single transformed program. Under finite grounding and unique-supported-model assumptions, DeepSWIP is exact relative to the learned materialized FCM. The standard quotient-WMC form of ProbLog conditionals identifies active neural probabilities and explains intervention cleaning, calibration sensitivity, and rare-evidence instability. Experiments on MPI3D confirm the transformation against a DeepTwin construction against 12,000 queries, as predicted and a 2.14$\times$ inference speedup from avoiding the Twin's endogenous duplication. A SUMO HOV experiment shows that neural calibration degradation biases plug-in estimates, while a correctly scoped randomized-policy AIPW estimator removes most first-order bias for population mean and ATE estimands. Code is at https://github.com/saibib/deep_SWIP.

06.
bioRxiv (Bioinfo) 2026-06-11

Machine Learning-Guided Discovery of Bacterial-Selective Membrane-Active Compounds Reveals Mechanistic Bias in Antibiotic Training Datasets

The rise of antibiotic resistance necessitates the discovery of antibacterial compounds with novel mechanisms of action (MoAs). Recent machine learning approaches have shown promise in antibacterial compound discovery, but often identify derivatives of known antibiotic classes rather than mechanistically novel compounds. Previous approaches applied Tanimoto similarity filters at the end of screening pipelines, but this method has substantial drawbacks: Tanimoto similarity can be misleading in chemical space, and post-hoc filtering does not influence what activity models learn to prioritize. Here, we present a machine learning pipeline that addresses chemical novelty upfront by employing an XGBoost-based MoA classifier to explicitly prioritize compounds predicted to have mechanisms distinct from known antibiotic classes, combined with graph neural networks for antibacterial activity and toxicity prediction. Applied to the Zinc20 database, our approach successfully identified non-toxic antibacterial compounds structurally distinct from known antibiotics. Notably, the majority of these hits exhibited membrane-targeting activity with selectivity for bacterial cells over mammalian cells, suggesting potential for next-generation membrane-active antibiotics. However, we did not identify compounds with novel protein targets. Systematic analysis revealed that this limitation stems from mechanistic bias in training data rather than model architecture. Specifically, our activity model learned to preferentially score compounds similar to specific groups in the training data, thus overrepresenting certain MoA classes including membrane-active compounds. Even substantial model architecture and training data enhancements did not overcome this constraint. Our findings demonstrate that the primary bottleneck for discovering mechanistically novel antibiotics is the scarcity of diverse, mechanistically-annotated training data. This work provides both a methodological framework for mechanism-aware screening and critical insights into data requirements for genuinely novel antibiotic discovery.

07.
arXiv (CS.CV) 2026-06-15

Fast Autoregressive Video Diffusion and World Models with Temporal Cache Compression and Sparse Attention

Autoregressive video diffusion models enable streaming generation, opening the door to long-form synthesis, video world models, and interactive neural game engines. However, their core attention layers become a major bottleneck at inference time: as generation progresses, the KV cache grows, causing both increasing latency and escalating GPU memory, which in turn restricts usable temporal context and harms long-range consistency. In this work, we study redundancy in autoregressive video diffusion and identify three persistent sources: near-duplicate cached keys across frames, slowly evolving (largely semantic) queries/keys that make many attention computations redundant, and cross-attention over long prompts where only a small subset of tokens matters per frame. Building on these observations, we propose a unified, training-free attention framework (FAST-AR) for FAST-AutoRegressive diffusion, consisting of three components: TempCache compresses the KV cache via temporal correspondence to bound cache growth; AnnCA accelerates cross-attention by selecting frame-relevant prompt tokens using fast approximate nearest neighbor (ANN) matching; and AnnSA sparsifies self-attention by restricting each query to semantically matched keys, also using a lightweight ANN. Together, these modules reduce attention, compute, and memory and are compatible with existing autoregressive diffusion backbones and world models. Experiments demonstrate up to x5 - x10 end-to-end speedups while preserving near-identical visual quality and, crucially, maintaining stable throughput and nearly constant peak GPU memory usage over long rollouts, where prior methods progressively slow down and suffer from increasing memory usage.

08.
arXiv (CS.CV) 2026-06-16

Facial Affect Analysis for Service-Oriented Systems: Advances, Challenges, and Future Visions

Facial Affect Analysis (FAA) is evolving from a stand-alone recognition task into a reusable perception capability for Service-Oriented Software Ecosystems (SoSE). This paper preserves the FAA methodological core while reframing recent advances through systems-engineering requirements for composable and dependable services. We review representative progress in static and dynamic expression analysis, action-unit and micro-expression modeling, and modern CNN, Transformer, graph, and hybrid architectures, then interpret these advances by their operational fit in edge, cloud, and hybrid service pipelines. The synthesis emphasizes SoSE concerns that determine deployability: service contracts for uncertainty-aware outputs, latency and availability envelopes, lifecycle monitoring and recalibration, governance-aware integration, and interoperability across independently evolving components. Our analysis shows that benchmark gains alone are insufficient for SoSE readiness; robustness under shift, intervention stability, fairness, privacy posture, and runtime guarantees are equally critical. We conclude with a roadmap for treating FAA as an operational service component with explicit interfaces, measurable quality attributes, and accountable lifecycle management.

09.
arXiv (CS.CL) 2026-06-18

PragReST: Self-Reinforcing Counterfactual Reasoning for Pragmatic Language Understanding

Natural language understanding often depends on meanings that are implied rather than explicitly stated, requiring pragmatic reasoning. Despite strong performance on math and logical reasoning, large language models (LLMs) still struggle with making pragmatic inferences, often choosing literal interpretations. To improve LLM pragmatic reasoning, we introduce PragReST, a self-supervised framework that constructs pragmatic QA data, generates counterfactual reasoning traces, and trains models to internalize them through supervised fine-tuning and reinforcement learning, without human-labeled training data or distillation from a stronger teacher. Across four pragmatic benchmarks (PragMega, Ludwig, MetoQA, and AltPrag), PragReST improves over backbone models, task-specific pragmatic tuning baselines, and non-counterfactual variants of the same pipeline. On accuracy-based benchmarks, PragReST improves over the instruct backbone by 5.37 and 5.50% (absolute) for Qwen3-8B and Qwen3-14B, respectively. Our error analysis and ablations underscore the importance of counterfactual reasoning: PragReST primarily reduces errors caused by failures to contrast observed utterances with plausible alternatives, and removing counterfactual reasoning substantially reduces performance. Moreover, our training preserves out-of-domain performance on general-knowledge and mathematical reasoning benchmarks.

10.
arXiv (CS.AI) 2026-06-15

From Prompts to Responses: Dual-Sided Data Leakage and Defense in Split Large Language Models

arXiv:2606.14210v1 Announce Type: cross Abstract: Large language models (LLMs) are increasingly deployed in privacy-sensitive domains, where users must balance the risk of data exposure through external APIs against the high computational cost of local deployment. Split learning has therefore emerged as a promising paradigm for LLM fine-tuning and inference under limited local resources. However, it introduces new privacy risks. Prior work primarily studies leakage of private input prompts, typically via inversion attacks on intermediate representations, while the potential for sensitive information leakage through generative response outputs remains largely unexplored. In this work, we unveil novel vulnerabilities of Split-LLM by presenting Patched Model Inversion with Dual-Sided Initialization (PIDI), a two-stage attack that simultaneously targets both private input prompts and output responses in Split-LLM settings. It combines dual-sided initialization with a patched inversion strategy to tackle long sequences, substantially outperforming prior inversion methods. To counter threats from both sides, we further propose the Adapter-based DualGuard with Mutual Information Defense (ADMI), which integrates an adapter-based local warmup strategy and mutual information regularization to provide a strong empirical privacy protection with minimal impact on task performance. Extensive experiments across diverse tasks and models demonstrate that ADMI effectively defends against PIDI and other state-of-the-art inversion attacks. Our code is publicly available at https://github.com/FLAIR-THU/VFLAIR-LLM.

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

Something from Nothing: Data Augmentation for Robust Severity Level Estimation of Dysarthric Speech

arXiv:2603.15988v3 Announce Type: replace-cross Abstract: Dysarthric speech quality assessment (DSQA) is critical for clinical diagnostics and inclusive speech technologies. However, subjective evaluation is costly and difficult to scale, and the scarcity of labeled data limits robust objective modeling. To address this, we propose a three-stage framework that leverages unlabeled dysarthric speech and large-scale typical speech datasets to scale training. A teacher model first generates pseudo-labels for unlabeled samples, followed by weakly supervised pretraining using a label-aware contrastive learning strategy that exposes the model to diverse speakers and acoustic conditions. The pretrained model is then fine-tuned for the downstream DSQA task. Experiments on five unseen datasets spanning multiple etiologies and languages demonstrate the robustness of our approach. Our Whisper-based baseline significantly outperforms SOTA DSQA predictors such as SpICE, and the full framework achieves an average SRCC of 0.761 across unseen test datasets.

12.
medRxiv (Medicine) 2026-06-15

Unveiling the Awareness of Private Health Insurance Coverage among Healthcare Professionals in Freetown, Sierra Leone: Insights Extracted from Their Perspectives.

Our study is an assessment of the knowledge, personal coverage, and related determinants of private health insurance as revealed by healthcare professionals in Freetown, the urban capital of Sierra Leone. This study stands as a precursor for Low- and Middle-Income Countries (LMICs), like Sierra Leone, seeking to establish Universal Health Coverage (UHC) to provide healthcare access and coverage through publicly arranged risk pooling, designed to help protect against unmanageable medical costs. In parallel, such countries face significant challenges with achieving sustainable universal coverage due to limited public resources, inefficient allocation systems, uneasy reliance on out-of-pocket payments, and large struggling populations. Our research sheds particular light on how healthcare professionals view their own participation with private healthcare options. A cross-sectional, analytical study was conducted, openly recruiting individuals from various facilities in Freetown. Using the Yamane Formula, a sample size of 109 participants was calculated. STATA 14.0 was used for data analysis. Our findings revealed that 96 (88.9%) participants did not have private health insurance, while 12 (11.1%) did have private coverage. However, 105 (97.2%) reported other modes of health insurance, with only 3 (2.8%) uninsured. Notably, 97.2% expressed willingness to join a private health insurance scheme. Our study found no statistically significant associations between selected indicators (demographic or socioeconomic fac tors) and current insurance coverage among study participants. These results highlight a low prevalence and understanding of private health insurance among healthcare professionals in a representative urban center in Sub-Saharan Africa (SSA), while acknowledging high willingness to enroll. The lack of any significant determinants suggests other unexamined factors, such as cost, accessibility, or awareness, capable of influencing the adoption and implementation of a universal health program.

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

Perceptual compensation for tonal context in self-supervised speech models

This study examines the extent to which the wav2vec2.0 architecture exhibits evidence of compensation for phonological context. We conducted a pseudo-replication of a perceptional compensation experiment on Mandarin Chinese tones, and compared the embedding similarities and probing classifier outputs between a purely self-supervised pre-trained model and a model fine-tuned for Mandarin ASR. No evidence of compensation was found in the embedding similarities of the purely pre-trained model. Probing classifiers showed some evidence of compensation in addition to the expected layer-wise improvements in categorization, but failed to replicate human performance on isolated test syllables. Our findings contrast with previous reports of sensitivity to phonological structure emerging through pre-training alone, and suggest that supervised objectives may be necessary to encourage the abstraction of at least some types of phonological regularities.

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

Human-like autonomy emerges from self-play and a pinch of human data

arXiv:2606.19370v1 Announce Type: cross Abstract: Self-play reinforcement learning has recently emerged as a way to train driving policies without any human data. It uses cheap, large-scale simulations to substitute expensive, large-scale human driving demonstrations. A key limitation of this approach is that policies trained through pure self-play can learn effective but alien driving conventions incompatible with people. Previous works attempt to mitigate such behavioral misalignments through extensive reward engineering and domain randomization, which are brittle and labor-intensive. Instead of completely discarding human demonstrations, our method treats them as a regularization objective on top of a minimal safe goal-reaching reward. Like the spice in a good stew, we find that a little human data goes a long way: our method uses only 30 minutes of human demonstrations, 2500x fewer than comparable imitation learning approaches. Resulting policies coordinate with held-out human trajectories and complete training in 15 hours on a single consumer-grade GPU. Videos and full source code are available at https://spiced-self-play.com/.

15.
Nature (Science) 2026-06-09

People are turning to AI chatbots to plug gaps in health information

A systematic assessment of health-related queries to a chatbot powered by artificial intelligence highlights shortfalls in health-care provision and the responsibilities of AI companies. A systematic assessment of health-related queries to a chatbot powered by artificial intelligence highlights shortfalls in health-care provision and the responsibilities of AI companies.

16.
PLOS Medicine 2026-05-20

Associations between hematologic dynamics during pregnancy and obstetric complications: A retrospective observational study

by Veronica Tozzo, Rachel Petherbridge, Kaitlyn James, Sarah Hsu, Deepti Pant, Chloe Michalopoulos, Brody H. Foy, Tanayott Thaweethai, Christopher Mow, Jacqueline Maya, Carolina Batlle Camero, Lydia Shook, Kathryn J. Gray, Logan Mauney, John M. Higgins, Camille E. Powe Background Pregnancy alters hematologic state as measured by complete blood count (CBC), but the longitudinal changes in CBC indices that define healthy pregnancies are not well established. In a large cohort based at an academic health system in the United States, we aimed to define reference intervals and typical longitudinal changes in CBC indices during pregnancy. We then tested for associations between extreme CBC values for gestational age or extreme longitudinal changes in CBC indices and obstetric complications. Methods and findings We studied nine CBC indices in individuals with singleton pregnancies who delivered after 30 weeks’ gestation and presented for prenatal care prior to 20 weeks. The electronic health record (EHR)-based Maternal Health Cohort (Massachusetts General Hospital; 1998–2016) formed our discovery cohort of 45,992 pregnancies, 18% of which had relevant complications. We developed a validation cohort of 48,868, 27% with complications from EHR data in the Mass General Brigham healthcare system from 2016 to 2024. In pregnancies without complications in the discovery cohort, we derived gestational-age-specific reference intervals (2.5th–97.5th percentile) and established typical intra-pregnancy longitudinal changes. In the validation cohort, we then tested CBC values outside of the 26–29 weeks’ gestation reference interval and CBC rare changes (uncommon changes in magnitude and direction) between 7–14 and 26–29 weeks’ gestation for association with a composite outcome (hypertensive disorders of pregnancy, small for gestational age birthweight, preterm birth) and its individual components using generalized estimating equations. Derived reference intervals differed from those in the literature for mean red cell volume, mean red cell hemoglobin, red cell count, and mean red cell hemoglobin concentration; reference intervals for other indices were similar to those previously published. In validation, hematocrit, hemoglobin, and red cell count values above their gestational-age specific reference intervals were associated with increased risk of the composite obstetric outcome: odds ratios (ORs) of 1.4 (95% CI [1.2, 1.5] p 

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

APCyc: Property-Informed Design of Cyclic Peptides via Automated Cyclization

arXiv:2606.12991v1 Announce Type: new Abstract: Cyclic peptides represent a promising class of therapeutic compounds in modern drug discovery, often offering improved stability and binding affinity. However, the de novo design of cyclic peptides remains challenging because methods must identify pocket-adaptive cyclization patterns and linkage sites while simultaneously controlling drug-relevant properties. This challenge is particularly pronounced for recent generative models trained predominantly on linear peptide data, which may fail to capture cyclization-specific constraints. To address the limitation, we introduce APCyc, a target-aware de novo cyclic peptide generation framework that explicitly models cyclization and jointly optimizes multiple essential physicochemical properties. By using an expanded residue vocabulary and explicitly encoding cyclization-site and linkage-type information, APCyc learns cyclization-aware representations and leverages Bayesian posterior guidance to steer sampling toward cyclic peptides satisfying multiple property objectives. Experimental results demonstrate that our model learns target-dependent cyclization preferences, and enables effective and controllable multi-property optimization for cyclic peptide design. The source code of this paper is available at https://github.com/HKUSTGZ-ML4Health-Lab/APCyc.

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

Formalize Once, Edit the Rest: Efficient Lean-Based Answer Selection for Math Reasoning

With large language models (LLMs) increasingly applied to mathematical reasoning, formal proof assistants such as Lean can be leveraged to verify reasoning outputs with machine-checkable rigor, enabling use cases such as answer selection in test-time scaling with K sampled candidate answers. However, employing Lean requires that LLM outputs, originally in natural language, first be formalized. Existing Lean-based answer-selection work uses an autoformalization model to generate a formal statement in Lean for each candidate answer independently, incurring a significant computational cost. We propose BASE, a base-and-edit pipeline that formalizes a single base candidate per problem and derives the remaining K-1 statements by editing the answer expression in place. To facilitate this, we train a rewriter model LEANSCRIBE to localize the answer in the base formalization and generate a reusable edit function for the other K-1 candidates. BASE simultaneously improves selection accuracy and reduces formalization cost - a Pareto improvement that holds on all 12 (dataset, solver) configurations across four benchmarks and three solvers, cutting autoformalizer calls by about 5x at K=8, with the reduction expected to become larger as K grows. Code is available at https://github.com/ucr-rai/base-and-edit.

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

Towards CONUS-Wide ML-Augmented Conceptually-Interpretable Modeling of Catchment-Scale Precipitation-Storage-Runoff Dynamics

arXiv:2510.02605v2 Announce Type: replace Abstract: While many modern studies are dedicated to ML-based large-sample hydrologic modeling, these efforts have not necessarily translated into predictive improvements that are grounded in enhanced physical-conceptual understanding. Here, we report on a CONUS-wide large-sample study (spanning diverse hydro-geo-climatic conditions) using ML-augmented physically-interpretable catchment-scale models of varying complexity based in the Mass-Conserving Perceptron (MCP). Results were evaluated using attribute masks such as snow regime, forest cover, and climate zone. Our results indicate the importance of selecting model architectures of appropriate model complexity based on how process dominance varies with hydrological regime. Benchmark comparisons show that physically-interpretable mass-conserving MCP-based models can achieve performance comparable to data-based models based in the Long Short-Term Memory network (LSTM) architecture. Overall, this study highlights the potential of a theory-informed, physically grounded approach to large-sample hydrology, with emphasis on mechanistic understanding and the development of parsimonious and interpretable model architectures, thereby laying the foundation for future models of everywhere that architecturally encode information about spatially- and temporally-varying process dominance.

20.
arXiv (CS.CL) 2026-06-12

Detect, Remask, Repair: Diffusion Editing for Faithful Summarization of Evolving Contexts

Summaries of real-world events can become outdated as contexts evolve and new information arrives. A common response is to generate a new summary from the updated context, but full regeneration discards the previous draft, can obscure what changed, and may be unnecessary when only a few claims are unsupported. We study localized faithfulness repair: updating outdated spans in an existing summary while preserving supported content. We propose DETECT-REMASK-REPAIR, a diffusion-based framework that identifies, remasks, and repairs outdated regions with masked diffusion language models. To evaluate evolving-context summarization, we introduce StreamSum, a benchmark of synthetic event timelines. Experiments on DialogSum and StreamSum show that localized diffusion repair provides a controllable alternative to full rewriting: faithfulness-steered repair improves early drafts, one-step repair reduces repair cost to under half a second, with the framework enabling faithfulness-speed-preservation tradeoffs across datasets. We also find that the framework can provide a post-hoc correction step that improves faithfulness for autoregressive systems.

21.
arXiv (math.PR) 2026-06-15

Universality for Products of Random Matrices with i.i.d. Entries and the Fuss–Catalan Number

arXiv:2606.14450v1 Announce Type: cross Abstract: Let \((w_{ij})_{i,j\ge1}\) be a single infinite array of independent identically distributed real- or complex-valued entries of mean zero, variance \(\sigma^2\), and finite fourth moment. Set \(W_n=(w_{ij})_{1\le i,j\le n}\) and \(X_n=n^{-1/2}W_n\). For every fixed \(k\ge1\), we identify the almost sure limiting operator norm of several fixed products built from this family. Define the \(k\)-th freeness coefficient by \[ \gamma_k:=\sqrt{\frac{(k+1)^{k+1}}{k^k}}. \] Then we prove \[ \|X_n^k\|\to\sigma^k\gamma_k \qquad almost surely. \] The same limit holds for products sampled with replacement from any fixed finite pool of independent copies of \(X_n\); in particular, it holds for the product of \(k\) independent copies. Thus, the freeness coefficient captures the non-commuting characteristic between large random matrices %powers and independent or fixed-pool sampled products under the finite fourth moment assumption. The improvement of the classical Bai–Yin-type power estimate from the scale \(\sigma^k(k{+}1)\) to \(\sigma^k \sqrt{k{+}1}\) is a direct corollary of our result. The main technical challenge is to prove the upper bound using a high-moment expansion of %the upper bound is proved by a high-moment expansion of \(\E\Tr((X_n^kX_n^{*k})^m)\). The leading zero-defect trace words are tree-like and are counted by the Fuss–Catalan number \[ F_{k,m}= \frac1{km+1}\binom{(k+1)m}{m}. \] The combinatorial tool helps to devise a defect-sensitive global enumeration: if \(L=km\) and \[ r=(L+1-v)+(L-q), \] then the number of admissible word classes with defect \(r\) is at most \(F_{k,m}(Cm)^{Dr}\). This polynomial-in-\(m\) loss, with degree proportional to the defect, is summable in the logarithmic moment range.

22.
arXiv (CS.LG) 2026-06-19

Insulin4RL: Real-Time Insulin Management in the Intensive Care Unit for Offline Reinforcement Learning

arXiv:2606.19481v1 Announce Type: new Abstract: Offline reinforcement learning (ORL) offers the potential to improve the quality of clinical decision-making using historical electronic health record (EHR) data. Current training and evaluative practices in this field rely heavily on EHR datasets that have been temporally discretised into fixed, regular time intervals. Discretisation creates fictional representations of complex clinical scenarios and compromises the generalisability of retrospective model evaluations. In this paper, we introduce Insulin4RL, a healthcare ORL dataset featuring naturally irregular inputs and actions from real clinical trajectories. Derived from MIMIC-IV, Insulin4RL comprises over 375,000 labelled decisions across 12,209 patients requiring insulin infusion titration in the Intensive Care Unit. The dataset can thus be used for research into ORL model performance under realistic clinical sampling assumptions. We provide a description of the dataset's structure and characteristics, baseline performance metrics using model-free offline reinforcement learning, and a standardised evaluation protocol using fitted Q-evaluation. We conclude with suggested areas for future research that could be addressed using this resource.

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

Phase Transitions in Attention: A Bayesian Theory of Copy Head Emergence

arXiv:2606.12058v1 Announce Type: cross Abstract: Attention is the key mechanism underlying in-context learning in transformers, and attention patterns have been observed empirically to emerge abruptly during training. We present a Bayesian theory of feature learning in attention; we then focus on how the copy subcircuit in the first layer of an induction head is learned by analyzing a single-layer softmax attention network trained on a copy task. We derive a closed-form posterior over the attention matrix and reduce it to a low-dimensional order parameter space. This reduction reveals a phase transition in the amount of training data, which we verify using both Bayesian sampling and standard training with Adam. We contrast our results with linear attention and find that softmax attention exhibits a first-order phase transition while in linear attention an initial second-order phase transition is followed by a smooth, continuous evolution toward the structured attention pattern (crossover). Our work provides a first-principles theoretical account of the abrupt emergence of the copy subcircuit, reminiscent of the one observed in training large language models.

24.
arXiv (CS.LG) 2026-06-18

Regular Fourier Features for Nonstationary Gaussian Processes

arXiv:2602.23006v2 Announce Type: replace-cross Abstract: Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation and treating the spectral density as a probability distribution suitable for Monte Carlo approximation. Although this probabilistic interpretation is valid for stationary processes, it is overly restrictive for the nonstationary case, where spectral densities are generally not probability measures. We propose regular Fourier features for harmonizable processes to avoid this limitation. Our method discretizes the spectral representation directly, preserving the correlation structure among spectral weights without requiring probability assumptions. Under a finite-spectral-support assumption, this yields an efficient low-rank approximation that is consistent and positive semi-definite by construction. When the spectral density is unknown, the framework extends naturally to kernel learning from data. We demonstrate the method on locally stationary and harmonizable mixture kernels, the latter with a complex-valued spectral density, and apply the kernel-learning extension to real and synthetic data.

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

Evolutionary Bilevel Reward Shaping for Generalization in Reinforcement Learning

arXiv:2606.16236v1 Announce Type: new Abstract: Reinforcement learning (RL) often suffers from performance degradation when deployed in environments that differ from those encountered during training. Existing techniques such as domain randomization (DR) mitigate this, but require access to diverse training environments and full trajectory observability, assumptions that fail in privacy-preserving or restricted scenarios where only scalar performance metrics are available. We propose Generalization via Evolutionary Reward Shaping (GERS), a bilevel optimization approach to improve generalization on unseen test environments using only scalar feedback from validation environments. At the lower level, an RL agent guided via a reward function shaped by the upper level learns a policy on a limited set of training environments with accessible trajectory data; at the upper level, CMA-ES optimizes the reward shaping parameters to maximize the cumulative unshaped reward on separate validation environments for which trajectory access is unavailable. Results on continuous control tasks indicate that GERS outperforms the standard RL baseline on unseen test environments. GERS performance is comparable to DR, despite DR treating the combined set of training and validation environments of GERS as a single training set that requires trajectory access, whereas GERS cannot access validation trajectories. These results confirm that GERS effectively enhances generalization under restricted data access constraints.