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01.
arXiv (CS.CL) 2026-06-11

Agentic Environment Engineering for Large Language Models: A Survey of Environment Modeling, Synthesis, Evaluation, and Application

Environments serve as interactive systems for large language model (LLM) based agents across diverse scenarios and play a crucial role in driving the continual evolution of model capabilities. Despite this importance, existing work lacks a systematic categorization and deep analysis. This paper systematically studies current researches on agentic environments from the perspective of the environment engineering lifecycle, covering their modeling, synthesis, evaluation and application. Specifically, the paper first introduces representative environments from the perspectives of eight attributes and eight domains, providing detailed analyses of their development paths and highlighting their core capabilities. Second, for automated environment synthesis, two paradigms are introduced, such as symbolic synthesis and neural synthesis. This paper also shows different environment evaluation methods in each paradigm. Thirdly, the corresponding environment applications from the perspective of agent-environment co-evolution are discussed. In specific, the paper characterizes the primary pathways for agent evolution in dynamic environments from four complementary perspectives: memory-centric experience evolution, orchestration-centric workflow evolution, trajectory-centric offline evolution, and exploration-centric online evolution. And three paradigms of environment evolution are identified, namely neural-driven, difficulty-driven, and scaling-driven approaches. At last, several promising future directions are discussed, including Environment-as-a-Service, Multi-agent Environments, and Neural-Symbolic Environments.

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

RefGC-SR$^2$: Reference-guided Generated Content Super-Resolution and Refinement

Reference-guided generation (e.g., object compositing, customization) has progressed rapidly, yet current pipelines share a fundamental limitation: the object-centric high-resolution reference image (HRRI) provided by users is downsampled to a fixed low-resolution (LR) before being fed into the model, so the fine-grained details are discarded before the output is even produced. In addition, the generation step then introduces its own artifacts (e.g., identity distortion) on top of this loss. Existing reference-guided generated content refinement (RefGCR) methods can correct some of these artifacts but still operate in the LR domain; reference-guided super-resolution (RefSR) methods recover resolution but assume natural-image degradations and ignore the artifact distribution of generative pipelines. To address both gaps in a single formulation, we introduce a new task: reference-guided generated content super-resolution-refinement (RefGC-SR$^2$), where the original HRRI is reused at the post-processing stage to recover lost details, refine generative artifacts, and upscale the output simultaneously. We construct the first real-world triplet data generation pipeline for this RefGC-SR$^2$ task, training a diptych-conditioned generator to synthesize paired low-quality anchors that public pretrained models cannot provide. We further present a frequency-aware diffusion transformer model for RefGC-SR$^2$ that selectively injects fine details from the HRRI while removing generative artifacts. Extensive experiments demonstrate that our RefGC-SR$^2$ model successfully (i) refines the object identity faithfully with respect to the reference, and (ii) recovers high-resolution details, so that the final result is significantly higher quality and practically more usable compared to existing RefGCR and RefSR baselines.

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

Verifiable Environments Are LEGO Bricks: Recursive Composition for Reasoning Generalization

Reinforcement Learning (RL) with verifiable environments has emerged as a powerful approach for enhancing the reasoning capabilities of Large Language Models (LLMs). While prior research demonstrates that scaling environment quantity improves RL performance, existing manual or individual construction methods suffer from linear scaling limits, thereby hindering scalable reasoning generalization. This paper introduces RACES (Recursive Automated Composition for Environment Scaling), a framework that conceptualizes verifiable environments as composable building blocks that can be recursively assembled. The key insight is that when the codomain (output type) of one environment matches the domain (input type) of another, they can be automatically fused into a new verifiable environment, enabling recursive composition. RACES is implemented with 300 individual environments and defines a set of composition operators (\textsc{SEQUENTIAL}, \textsc{PARALLEL}, \textsc{SORT}, and \textsc{SELECT}) that induce diverse reasoning patterns. Extensive experiments show that RL training on these composite environments consistently enhances reasoning generalization. Specifically, RACES improves DeepSeek-R1-Distill-Qwen-14B by an average of 3.1 points (from 48.2 to 51.3) and boosts Qwen3-14B performance from 58.8 to 61.1 on six benchmarks, which are unseen during the construction of training environments. Moreover, RACES achieves performance comparable to training on 300 individual environments using only 50 base environments, demonstrating significant efficiency in environment utilization.

05.
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.

06.
medRxiv (Medicine) 2026-06-10

Towards the Virtual Amyotrophic Lateral Sclerosis Patient: Inferring Cortical Excitability through Whole-Brain Dynamical Modeling

Amyotrophic lateral sclerosis (ALS) is increasingly recognized as a multisystem neurodegenerative disorder in which motor-neuron degeneration is accompanied by widespread alterations in cortical dynamics. Among its most reproducible neurophysiological signatures is cortical hyperexcitability, yet how this local excitability imbalance shapes distributed whole-brain activity remains poorly understood. Here, we combined source-reconstructed resting-state MEG data, tractography-informed whole-brain modeling, and simulation-based inference to investigate whether ALS-related alterations in large-scale brain dynamics can be mechanistically explained by changes in cortical excitability. First, we characterized empirical brain dynamics using complementary features spanning regional activity amplitude and variability, functional connectivity, and avalanche-based metrics. These analyses revealed significant alterations in ALS patients relative to healthy controls, as well as associations with clinical impairment and disease staging. To mechanistically interpret these changes, we employed a reduced Wong-Wang whole-brain model in which local recurrent excitation modulates emergent large-scale neural dynamics. Simulations showed that increasing excitability systematically reproduced the empirical dynamical signatures observed in ALS. We then applied a simulation-based inference framework to estimate latent excitability parameters directly from empirical observations. Whole-brain model inversion revealed increased excitability in ALS patients compared with controls. The recovered excitability parameter was associated with disease staging, supporting its clinical relevance as a model-derived descriptor of ALS progression. Finally, by extending the model to estimate frontal and non-frontal excitability separately, we found that ALS-related alterations were predominantly associated with increased frontal excitability, whereas non-frontal regions appeared comparatively less affected. The recovered parameters related to disease staging. Together, these findings provide a mechanistic framework linking altered large-scale brain dynamics in ALS to selective cortical hyperexcitability, explaining how local excitability changes can give rise to global network reorganization. More broadly, they show how computational model inversion can recover latent multiscale pathophysiological processes from empirical neural recordings, offering a non-perturbative alternative to complex experimental paradigms typically required to causally probe local-to-global mechanisms.

07.
arXiv (CS.CV) 2026-06-18

Mem-World: Memory-Augmented Action-Conditioned World Models for Persistent Robot Manipulation

Action-conditioned world models have emerged as a promising paradigm for robot learning, offering a scalable alternative to costly real-world experimentation by generating action-consistent video rollouts. However, persistent world modeling remains challenging in manipulation: frequent end-effector occlusions and rapid wrist-camera motion make the current observation insufficient for predicting future views, causing models to forget or hallucinate scene details seen in earlier frames. Existing memory retrieval strategies often fail to identify informative history in dynamic manipulation scenarios. To address this limitation, we propose Mem-World, a memory-augmented multi-view action-conditioned world model. At its core, we present W-VMem, a 4D wrist-view-centered surfel-indexed memory that anchors historical observations to temporally evolving surface elements. By explicitly modeling when and where scene elements are observed, W-VMem enables geometry-aware retrieval of relevant history frames conditioned on future actions. During generation, relevant history frames are selected via surfel-based rendering and scoring, providing informative and non-redundant context for prediction. Extensive experiments show that Mem-World generates persistent rollouts in complex manipulation scenarios, enables more reliable policy evaluation than Ctrl-World, improving the Pearson correlation with real-world performance by 14.5\%, and supports effective policy improvement through synthetic data generation, increasing success rates from 58\% to 72\% on long-horizon tasks.

08.
arXiv (CS.LG) 2026-06-15

Provably Safe, Yet Scalable Reinforcement Learning

arXiv:2606.14536v1 Announce Type: new Abstract: Safe reinforcement learning (RL) aims to learn policies that optimize rewards while satisfying constraints. Predominant approaches rely on soft-constrained policy optimization, which has achieved empirical success but does not provide formal safety guarantees for the learned policy. In contrast, methods with strict guarantees typically rely on explicit certificate functions, whose construction requires the direct synthesis and verification of control-invariant sets, a process that scales poorly with state dimension and often yields overly conservative behavior. In this paper, we present the Provably Safe, yet Scalable RL (PS2-RL) framework, a novel two-phase architecture for learning provably safe policies in a scalable manner, designed to overcome the key bottlenecks of prior methods. Rather than explicitly computing invariant sets, PS2-RL leverages a learned backup policy to forward-integrate the system dynamics, generating an implicit control-invariant set online. In the first phase, the backup policy is trained with our proposed safe-arrival value function, which characterizes the optimal backup policy for invariant-set construction. In the second phase, an RL policy is trained end-to-end through a differentiable projection layer that strictly enforces the safety guarantees induced by the learned backup policy. By maximizing the volume of the implicit control-invariant set in the first phase, the resulting PS2 policy from the second phase is performant and scalable, while maintaining provable safety. Crucially, PS2-RL imposes no restrictions on the underlying RL algorithm and can be plugged into any existing training pipeline. We establish theoretical guarantees for the proposed framework and evaluate it on robotic control tasks with state dimensions up to 10, a regime in which prior provably safe RL methods struggle or become impractical.

09.
bioRxiv (Bioinfo) 2026-06-11

DivQuant: Estimation of Species Richness and Entropy from Small Samples

Estimating diversity properties of discrete distributions from a small observed sample is a fundamental problem in algorithmic statistics that has applications in many fields, in particular bioinformatics, but also in ecology or linguistics. The two most common diversity measures are the number of distinct elements in a multiset, also referred to as species richness in ecology or alpha diversity in microbial analysis, and the Shannon entropy, also referred to as evenness. Estimating these properties from a small sample is particularly challenging for distributions with many rare elements. Thus, many estimators have been proposed in the past that, in practice, work well for different types of distributions. We present DivQuant, an optimization-based, extrapolating richness and entropy estimator with three contributions. First, we formulate the upsampling problem as a convex quadratic program with a Neyman {chi}2 objective. Unlike the linear program of its predecessor RichnEst, DivQuant admits confidence intervals via {chi}2 test inversion that are empirically well-calibrated. Second, we replace RichnEst's fixed-threshold fingerprint truncation with the rare/abundant fingerprint split of Valiant and Valiant, which strongly reduces problem size and preserves enough degrees of freedom for the confidence-interval program to remain valid and feasible. Third, we plug the optimal population fingerprint returned by the program into Shannon's entropy formula to obtain an entropy estimate. DivQuant attains close-to-nominal 95% confidence intervals in essentially all tested regimes, including six simulated distribution families, Tara Oceans microbiome data, and 10X Genomics scRNA-seq data, while competing state-of-the-art methods (RichnEst, iNext, PreSeq) miss the true richness in up to 80% of instances, well above the nominal 5%. In addition, DivQuant outperforms classical asymptotic entropy estimators (Miller-Madow, CAE) and the extrapolating iNext estimator. Running times remain competitive, with DivQuant typically completing in seconds. DivQuant is available as a command-line tool at https://gitlab.com/rahmannlab/divquant.

10.
arXiv (CS.CV) 2026-06-12

Multi-Label Test-Time Adaptation with Bayesian Conditional Priors

Multi-label recognition with frozen Vision-Language Models (VLMs) is brittle under distribution shift: standard zero-shot inference scores labels independently, ignoring co-occurrence structure and producing incoherent label sets where dominant concepts suppress weaker but compatible labels. We introduce Bayesian Conditional Priors (BCP) Estimation, a gradient-free test-time adaptation method that injects label dependency without tuning the backbone. BCP views zero-shot logits as a proxy for marginal posteriors under a fixed image-text likelihood and attributes shift-induced errors mainly to a mismatched label prior. For each test image, it selects a high-confidence anchor label and applies an anchor-conditioned Bayesian refinement. This update is closed-form in logit space and admits a pointwise mutual information (PMI) interpretation, explicitly promoting compatible labels and suppressing incompatible ones. BCP operates without target annotations by estimating anchor-conditioned priors online from the unlabeled test stream via lightweight second-order co-occurrence statistics, adding negligible overhead beyond a single forward pass. Across standard multi-label benchmarks and multiple CLIP backbones, BCP consistently outperforms strong TTA baselines, e.g., improving RN50 average mAP from 57.31 to 69.22 and ViT-B/16 from 62.61 to 71.79.

11.
arXiv (math.PR) 2026-06-19

Asymptotic properties for fully coupled delayed forward-backward stochastic differential equations

arXiv:2606.19925v1 Announce Type: new Abstract: We investigate the asymptotic behavior of solutions to a class of fully coupled forward-backward stochastic differential equations with time-delayed generators. Such systems arise naturally in stochastic models with memory effects and constitute a significant extension of the classical fully coupled FBSDE framework. The presence of delay introduces additional analytical difficulties due to the dependence of the coefficients on the past trajectories of the solution processes and the resulting non-Markovian structure. Under suitable assumptions on the coefficients, we study the asymptotic properties of a perturbed delayed FBSDE driven by a small noise parameter. We first establish the convergence in distribution of the associated solution processes as the perturbation parameter tends to zero. We then prove almost sure convergence towards the solution of the corresponding deterministic limiting system. As a consequence of these asymptotic results, we derive a large deviation principle for the solution processes. Our results extend the asymptotic analysis of Cruzeiro, Gomes and Zhang (2014) from the classical fully coupled FBSDE setting to the delayed framework, and complement existing works on weakly coupled delayed forward-backward systems. They provide, to the best of our knowledge, the first large deviation principle for fully coupled forward-backward stochastic differential equations with delayed generators.

12.
arXiv (CS.AI) 2026-06-19

JustDiag!: A Diagnostic Justification Engine for Accountable Root Cause Analysis

arXiv:2606.19407v1 Announce Type: cross Abstract: Large language models can produce fluent root cause analyses, but fluent final answers alone are insufficient evidence for accountability in high-stakes operations. In real incident response, engineers need to know what evidence supported a diagnosis, which alternatives were considered, where contradictions remained, and whether the system resolved the case or preserved uncertainty. We address this gap with JustDiag, a diagnostic justification engine for RCA that maintains an explicit process state over evidence, findings, competing hypotheses, conflicts, and next checks. We evaluated the system on 66 real-world incidents using a two-layer protocol that separately scores final-answer quality and process quality. Relative to a matched control without diagnostic justification, JustDiag achieved stronger outcome and process scores, while accepting slightly lower terminal completion due to more calibrated non-closure. These results suggest that accountable RCA requires explicit diagnostic justification artifacts and process-aware evaluation, not only fluent final answers.

13.
arXiv (math.PR) 2026-06-11

Multiple Poisson-Dirichlet diffusions on generalized Kingman simplices

arXiv:2602.20266v2 Announce Type: replace Abstract: We construct a new class of infinite-dimensional diffusions with values in a generalized Kingman simplex with finitely many marks. The model describes the temporal evolution of the relative frequencies of infinitely many types that are labeled by a finite number $H$ of marks, but unlabeled within each mark. We first establish a blockwise skew-product representation for a finite-type Wright-Fisher diffusion, extending the aggregation-renormalization self-similarity property of Dirichlet laws. The decomposition separates an $H$-dimensional Wright-Fisher diffusion governing the evolving random mark masses, from $H$ Wright-Fisher diffusions, each run on its own random clock, which describe the evolution of the relative frequencies within each mark. After ranking the within-mark frequencies in decreasing order, we identify the distributional limit as the number of types per mark tends to infinity and we derive an explicit form of its infinitesimal generator on a suitable domain. The limiting diffusion admits the multiple Poisson-Dirichlet distribution as a stationary distribution; it recovers the infinitely-many-neutral-alleles diffusion when all types share the same mark and yields a diffusion on the Thoma simplex when there are two marks.

14.
medRxiv (Medicine) 2026-06-16

High-Risk Anti-Seizure Medication Use in Childbearing-Age People with Epilepsy in a Taenia solium Endemic Region

Background: People of childbearing potential with epilepsy in regions endemic for Taenia solium, where neurocysticercosis (NCC) is highly prevalent, represent a vulnerable population due to the elevated burden of epilepsy and resource limitations. Clinical practice in these settings remains poorly characterized. This study characterized anti-seizure medication (ASM) prescribing patterns by medication risk profiles among people of childbearing potential with epilepsy in Northern Peru, a region highly endemic for T. solium. Methods: Participants were drawn from a prospective, population-based epilepsy cohort in Tumbes, Peru (2006 to 2020). The analytic population included females with epilepsy aged 15 to 49 years. The primary outcome was pregnancy-associated ASM risk of congenital malformations and adverse neurodevelopmental outcomes. ASMs were classified as ''Established Low Risk'' (lamotrigine, levetiracetam), ''Possible Risk/Inadequate Data'' (carbamazepine, phenobarbital, phenytoin), and ''Established High Risk'' (valproic acid). Prescription patterns were examined in relation to demographic and clinical characteristics. Results: Among 1,975 individuals with epilepsy, 685 were people of childbearing potential. Approximately 34.9% met criteria for probable or definite NCC. Most ASM prescriptions were in the ''Possible Risk/Inadequate Data'' category (87.0%), and 12.8% received ''Established High Risk'' medications. In multivariable analysis, high-risk prescribing was associated with prior ASM use and polytherapy. Discussion: People of childbearing potential with epilepsy were predominantly treated with carbamazepine, phenytoin, phenobarbital, and valproate, reflecting local ASM availability. Despite evidence supporting lamotrigine and levetiracetam in pregnancy, prescribing patterns reflect local formulary constraints. These findings highlight a gap between guideline recommendations and real-world prescribing in resource-limited settings, underscoring the need for context-specific treatment strategies.

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

Contrast-Informed Augmentation and Domain-Adversarial Training for Adult-to-Neonatal MR Reconstruction Generalization

Purpose: To investigate whether contrast-informed data augmentation and domain-adversarial training improve the adult-to-neonatal generalization of the E2E-VarNet. Methods: Three training regimes were investigated: (1) adult-only training with unaugmented adult data, (2) mixed training with paired unaugmented and neonatal-informed augmented adult data, and (3) mixed training with a domain-adversarial objective. Models were trained on retrospectively undersampled multi-coil adult T2-weighted brain MR data and evaluated on neonatal and adult test data at acceleration factors $R=4$ and $R=8$ using quantitative metrics and qualitative evaluation. Feature analyses assessed whether domain-adversarial training altered the latent representations of unaugmented adult, augmented adult, and neonatal test samples. Results: Mixed training (Mixed) and mixed domain-adversarial training (Mixed-DAT) outperformed unaugmented adult-only training (Unaug-Only) when evaluated on neonatal data. At R=4, Mixed-DAT achieved the best performance (SSIM = 0.924 +/- 0.027, PSNR = 33.98 +/- 1.15 dB). At R=8, Mixed-DAT performed best when measured using SSIM (0.848 +/- 0.031 vs. 0.766 +/- 0.037 for Unaug-Only and 0.814 +/- 0.035 for Mixed) and Mixed performed best when measured using PSNR (29.56 +/- 0.83 dB vs. 26.26 +/- 0.78 dB for Unaug-Only and 29.43 +/- 0.83 dB for Mixed-DAT). Qualitative assessment of t-SNE plots suggested that Mixed-DAT increased the overlap among the latent representations of the unaugmented adult, augmented adult, and neonatal test data. Conclusion: Contrast-informed augmentation and domain-adversarial training improved adult-to-neonatal generalization of deep learning-based MR reconstruction. These findings suggest that contrast-informed data augmentation combined with adversarial training may improve robustness to domain shift in undersampled neonatal MR reconstruction.

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

Curvature-Guided Geometric Representation for Protein-Ligand Binding Affinity Prediction

arXiv:2606.14159v1 Announce Type: new Abstract: Protein-ligand binding affinity (PLA) prediction is critical in drug discovery. Despite the notable advancements in machine learning-based approaches, existing methods struggle to jointly characterize local geometric organization and globally coordinated cross-molecular interactions, limiting their ability to model complex binding mechanisms. Here, we propose RicciBind, a geometric representation framework that integrates curvature-guided hierarchical structure learning with optimal transport (OT)-based cross-domain alignment to model molecular interactions. Specifically, RicciBind leverages Ricci curvature to capture local interaction tightness within molecular structures, enhancing structural awareness and organizing atomic interactions into curvature-aware hierarchical representations. An OT-based cluster matching mechanism then aligns protein and ligand clusters across heterogeneous domains under geometric constraints, enabling globally consistent correspondences and revealing higher-order interaction patterns beyond local neighborhoods. By coupling curvature-guided structure encoding with OT-driven cross-domain alignment, RicciBind effectively models complex interaction semantics and substantially improves both the accuracy and interpretability of binding affinity prediction. Extensive experiments demonstrate that RicciBind achieved superior predictive performance and generalization across PLA benchmarks and virtual screening tasks. Ablation studies further confirmed the essential role of Ricci curvature in enhancing molecular interaction representations.

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

EHRNote-ChatQA: A Benchmark for Evidence-Grounded Multi-Turn Clinical Question Answering over Longitudinal Discharge Summaries

Discharge summaries are crucial clinical documents containing the context of a patient's overall hospital stay, and are routinely reviewed by medical experts for patient readmission, ongoing care, and diagnostic decision-making. When reviewing them, medical experts often must iteratively synthesize information across multiple summaries while verifying the evidence supporting each answer. Although large language models (LLMs) are increasingly explored for clinical question answering, existing benchmarks do not sufficiently reflect this setting: they often evaluate exam-style medical knowledge or focus on single-turn question answering with limited evidence-grounding evaluation. We introduce EHRNote-ChatQA, the first benchmark for evidence-grounded multi-turn clinical question answering over patients' multiple discharge summaries. Built from de-identified MIMIC-IV discharge summaries, EHRNote-ChatQA contains 967 patient-level multi-turn samples spanning one to five notes and 16,072 medical-expert-verified QA pairs (8,036 content questions, each paired with an evidence-grounding question) across eight clinical categories. The benchmark is constructed through an expert-informed pipeline combining discharge-summary structuring schema, expert-curated multi-turn QA templates, and LLM-based generation, followed by review and revision of every single QA sample by 11 medical experts. Benchmarking 22 open- and closed-source LLMs reveals several challenges, including that LLMs struggle more with evidence grounding than content answering, multi-turn errors compound across turns, and single-turn clinical QA performance does not reliably transfer to this setting. These findings establish EHRNote-ChatQA as a rigorous and practical benchmark for evaluating clinical QA systems. The dataset will be made publicly available through PhysioNet credentialed access.

18.
arXiv (math.PR) 2026-06-15

The 1/4-phenomenon of placement probabilities of tilings in the Aztec diamond

arXiv:2512.08377v2 Announce Type: replace-cross Abstract: We consider domino tilings of the Aztec diamond. Using the Domino Shuffling algorithm introduced by Elkies, Kuperberg, Larsen, and Propp in arXiv:math/9201305, we are able to generate domino tilings uniformly at random. In this paper, we investigate the probability of finding a domino at a specific position in such a random tiling. We prove that this placement probability is always equal to $1/4$ plus a rational function, whose shape depends on the location of the domino, multiplied by a position-independent factor that involves only the size of the diamond. This result leads to significantly more compact explicit counting formulas compared to previous findings. As a direct application, we derive explicit counting formulas for the domino tilings of Aztec diamonds with $2\times 2$-square holes at arbitrary positions.

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

DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layers

arXiv:2605.30456v2 Announce Type: replace Abstract: Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches. At the same time, these problems are often accompanied by rich domain knowledge derived from physical laws, operational requirements, and expert heuristics. Such knowledge is frequently expressed as rules involving logical propositions and linear inequalities. Existing neuro-symbolic methods typically enforce these rules approximately through soft penalties, assume input-independent rules when designing specialized architectures, or rely on non-differentiable post-processing at inference time to achieve hard constraint satisfaction. While recent advances in differentiable optimization layers enable end-to-end feasibility enforcement within neural networks, extending these approaches to logical or mixed-integer rules remains challenging due to inherent nonconvexity. In this work, we propose a unified end-to-end framework for enforcing hard, input-dependent mixed integer linear constraints within neural networks. Our approach represents rules as disjunctive constraints and applies hierarchical convex relaxations to obtain convex hull formulations. These relaxations yield tractable linear constraints that can be embedded as differentiable optimization layers while enabling exact rule satisfaction. We demonstrate the effectiveness of the proposed framework on real-world datasets, achieving perfect rule satisfaction and strong predictive performance.

20.
arXiv (quant-ph) 2026-06-16

Minimum measurements quantum protocol for band structure calculation

arXiv:2511.04389v2 Announce Type: replace Abstract: Protocols for quantum measurement are an essential part of quantum computing. Measurements are no longer confined to the final step of computation but are increasingly embedded within quantum circuits as integral components of noise-resilient algorithms. However, each observable typically requires a distinct measurement basis, often demanding a different circuit configuration. As the number of such configurations typically grows with the number of qubits, measurements constitute a major bottleneck. Focusing on electronic structure calculations in crystalline systems, we propose a measurement protocol that restricts the required measurement configurations to an absolute minimum of just three, independent of the number of qubits. This makes it one of the few known protocols that do not scale with qubit number. In particular, we derive the measurement protocol from the symmetries of tight-binding (TB) Hamiltonians and implement it within the Orthogonal-Ansatz Variational Quantum Eigensolver (OA-VQE) algorithm. We demonstrate its performance on three systems, namely a two-dimensional CuO$_2$ square lattice (3 qubits), bilayer graphene with hexagonal (Honeycomb) lattice (4 qubits) and three-dimensional diamond lattice (10 qubits). Beyond tight-binding systems, the protocol can be extended to enable efficient initial state preparation for many-body Hamiltonians, such as multi-orbital Hubbard models in a momentum space.

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

Structured Cognitive Loop for Behavioral Intelligence in Large Language Model Agents (Extended Revision: From Behavioral Architecture to Epistemic Accountability)

Authors:

arXiv:2510.05107v5 Announce Type: replace Abstract: The central challenge for AI agents is not only performance but accountability. Agents that act through opaque prompt sequences may produce correct outputs, but they provide little basis for verifying why an action was permitted, where an error occurred, or how responsibility should be assigned. This paper presents the Structured Cognitive Loop as an architecture for accountable behavior in large language model agents. SCL separates cognition, memory, control, and action into distinct modules. The language model proposes. External memory preserves verified state. A lightweight controller checks preconditions, prevents redundant actions, and authorizes execution before tools are used. We evaluate SCL against ReAct and common LangChain agent variants across travel planning, conditional email drafting, and constraint guided image generation. Across 360 episodes, SCL achieves 86.3 percent task success compared with 70.5 to 76.8 percent for prompt based baselines. It also improves goal fidelity, reduces redundant tool calls, increases reuse of intermediate state, and lowers unsupported assertions. This extended revision situates SCL within a broader architecture of epistemic accountability. Subsequent extensions integrate context aware Human in the Loop control, Pool Gated Retrieval, and the Horizon Warrant Commitment framework. Together these components define an agent architecture in which the model proposes, structure decides, evidence is warranted before use, and human judgment is embedded in the trace rather than imposed after the fact. The result is a foundation for AI agents whose decisions are not only effective but also authorized, inspectable, and accountable.

22.
medRxiv (Medicine) 2026-06-16

MRMU: A New Paradigm for Mendelian Randomization by Accounting for Measured Covariates and Unmeasured Confounders

Mendelian randomization (MR) is a powerful approach for causal inference, however, its reliability is frequently compromised by unadjusted covariates and unmeasured confounders, such as unmeasured pleiotropy and sample structure. To address these challenges, we introduce MRMU, a novel paradigm for the MR framework. Unlike traditional single-variable or multivariable MR methods, MRMU selects instrumental variables only from the exposure of interest and estimates one exposure effect at a time, while jointly accounting for measured covariates and unmeasured confounders. This design improves the reliability of MR analyses. In simulations and real data, MRMU achieved better type I error control, higher statistical power, and more accurate effect estimation than existing MR methods. Applying to coronary artery disease (CAD), MRMU identified robust cardiometabolic risk factors, including LDL-C, APOB, systolic blood pressure, body mass index, and smoking initiation, with consistent evidence across multiple CAD datasets. In contrast, traits such as HDL-C, height, and educational attainment, which were found to be significant by existing MR methods, were no longer supported by MRMU. MRMU further supported blood pressure-related traits, rather than lipid traits, as the more relevant pathway linking urate to CAD. Finally, by integrating large-scale plasma proteomics data, MRMU identified candidate CAD drug targets beyond established HMGCR- and PCSK9-related pathways, highlighting its utility for therapeutic target prioritization.

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

Who Flips? Self- and Cross-Model Counterarguments Reveal Answer Instability in LLMs

Standard accuracy benchmarks are designed to test how closely large language models (LLMs) approach correct answers, but are not suitable for testing whether LLMs stick with a correct answer when that answer is challenged by a plausible counter-argument. We introduce a controlled protocol for evaluating answer stability: after a model answers a multiple-choice question correctly, we challenge the model's answer with a coherent argument for an incorrect option and measure whether the model flips. The setup a) isolates argumentative content from overt social pressure and b) varies argument length, self-attribution, and cross-model source. Across seven frontier models and 57 MMLU subjects, flip rates range from 17.5% to 97.3%, revealing large differences in stability that are not captured by accuracy metrics alone. We find that self-attribution consistently increases flip rates (mean +7.1pp, up to +18.7pp). Also, pooling wrong-answer arguments across models and selecting the most effective one per question yields stronger adversarial challenges than relying on any single source model. We further construct MaxFlip, a curated challenge set that amplifies flips by up to +23.6pp over standard self-generated challenges. We release the protocol, challenge records, and MaxFlip to support stability evaluation alongside standard accuracy benchmarks. Materials are available at https://github.com/nafisenik/WhoFlips and https://hf.co/datasets/nafisehNik/WhoFlips.

24.
arXiv (CS.AI) 2026-06-16

CoAgent: Concurrency Control for Multi-Agent Systems

arXiv:2606.15376v1 Announce Type: cross Abstract: Multi-agent LLM systems – coding agents, devops agents, document agents – now routinely run several agents in parallel against the same git tree, Kubernetes cluster, or document. As soon as two of them mutate shared state, they enter the regime classical concurrency control has studied for decades, but classical mechanisms fit LLM agents poorly. A single agent transaction spans minutes of inference, read sets are broad and opaque rather than statically inferable, and the live state agents act on admits neither fork nor buffer, so writes take effect the moment they execute. Locks block long inference intervals; OCC abort-and-retry discards minutes of work on every conflict. This paper builds concurrency control on a capability classical transactions lack: the LLM inside each agent can judge whether a conflicting write invalidates its plan, and can repair exactly the operations that depended on it. Control therefore turns advisory: the runtime informs, the agent repairs. Our protocol, MTPO (Monotonic Trajectory Pre-Order), fixes a serialization order at launch, serves each read the order-filtered value, and applies writes speculatively in place; a one-way notification asks an affected reader to re-judge and patch its plan, while the framework mechanically undoes and reorders misplaced writes through the saga-style inverse each tool registers in advance. At quiescence the run is serializable in the pre-decided order. We realize MTPO as CoAgent, toolcall middleware whose privileged ToolSmith grows footprint-declared, undoable tools online. On ten contended workloads, CoAgent stays within 5\% of serial correctness at a $1.4\times$ speedup and near-serial token cost, where 2PL and OCC surrender nearly all concurrency gains; on a bash-only target system, it grows a 25-tool library online and lifts the task pass rate from 45/71 to 63/71 at $0.80\times$ the time and $0.86\times$ the cost.

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arXiv (CS.CV) 2026-06-16

RealityBridge: Bridging Editable 3D Gaussian Splatting Driving Simulations and Real-World Videos

Long-tail hazardous scenarios are essential for safety-oriented autonomous driving, yet they are difficult to collect and reproduce at scale. Editable 3D Gaussian Splatting (3DGS) simulation offers a promising alternative by reconstructing real driving scenes and supporting controllable scene editing. However, edited 3DGS-rendered videos still suffer from a significant Sim-to-Real gap, including rendering artifacts, degraded foreground assets, inconsistent illumination, and temporal flickering. Existing restoration and video generation methods are insufficient for this task, as they often fail to jointly repair 3DGS-specific artifacts, improve visual realism, and ensure temporal consistency. To fill this gap, we propose RealityBridge, a structure-preserving and asset-aware Sim-to-Real framework for edited 3DGS driving videos. RealityBridge uses multimodal controls, including rendered videos, foreground masks, edge maps, and semantic masks, together with a lightweight GateNet for adaptive condition allocation across backbone layers. We further construct targeted training data and introduce autoregressive long-video training with reward-guided post-training to improve restoration quality, temporal stability, and hallucination suppression. Extensive experiments on internal and public driving datasets show that RealityBridge outperforms existing methods in artifact removal, illumination harmonization, and long-sequence temporal consistency.