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01.
arXiv (CS.AI) 2026-06-17

Can LLMs Be CEOs? Benchmarking Strategic Resource Reallocation with Multi-Role Agent Simulation

arXiv:2606.17459v1 Announce Type: new Abstract: Evaluating the decision-making capabilities of large language models (LLMs) is a growing research priority, yet existing benchmarks focus on isolated cognitive tasks such as reasoning, knowledge retrieval, and economic rationality in stylized settings. These evaluations overlook the defining challenge of real executive decision-making: integrating conflicting recommendations from specialized stakeholders under information asymmetry, organizational constraints, and temporal dependencies. We introduce \textsc{CEO-Bench}, a multi-agent benchmark that evaluates LLMs on CEO-level strategic resource reallocation – the process of redirecting capital across business units in a multi-round, constraint-rich organizational environment. In \textsc{CEO-Bench}, LLM agents receive conflicting advice from four role-conditioned C-suite advisors (CFO, CTO, COO, CMO), each with private signals and distinct priorities, and must synthesize these into a concrete allocation plan evaluated along four dimensions: role integration, conditional boldness, history-sensitive judgment, and plan validity. Experiments across five frontier models on 13 scenarios reveal that all models achieve high structural validity but diverge sharply on strategic calibration – the hardest capability layer. We identify systematic failure modes including single-advisor capture, conservative default under ambiguity, and historical amnesia, and uncover a structural integration-boldness tradeoff: models that engage more deeply with conflicting perspectives tend to produce less decisive action. These findings delineate the current capability boundary of LLMs as organizational decision-makers and inform the design of future AI-assisted executive systems.

02.
arXiv (CS.LG) 2026-06-18

Self-attention-based non-linear basis transformations for compact latent space modelling of dynamic optical fibre transmission matrices

arXiv:2406.07775v2 Announce Type: replace Abstract: Multimode optical fibres are hair-thin strands of glass that efficiently transport light. They promise next-generation medical endoscopes that provide unprecedented sub-cellular image resolution deep inside the body. However, confining light to such fibres means that images are inherently scrambled in transit. Conventionally, this scrambling has been compensated by pre-calibrating how a specific fibre scrambles light and solving a stationary linear matrix equation that represents a physical model of the fibre. However, as the technology develops towards real-world deployment, the unscrambling process must account for dynamic changes in the matrix representing the fibre's effect on light, due to factors such as movement and temperature shifts, and non-linearities resulting from the inaccessibility of the fibre tip when inside the body. Such complex, dynamic and nonlinear behaviour is well-suited to approximation by neural networks, but most leading image reconstruction networks rely on convolutional layers, which assume strong correlations between adjacent pixels, a strong inductive bias that is inappropriate for fibre matrices which may be expressed in a range of arbitrary coordinate representations with long-range correlations. We introduce a new concept that uses self-attention layers to dynamically transform the coordinate representations of varying fibre matrices to a basis that admits compact, low-dimensional representations suitable for further processing. We demonstrate the effectiveness of this approach on diverse fibre matrix datasets. We show our models significantly improve the sparsity of fibre bases in their transformed bases with a participation ratio, p, as a measure of sparsity, of between 0.01 and 0.11. Further, we show that these transformed representations admit reconstruction of the original matrices with < 10% reconstruction error, demonstrating the invertibility.

03.
arXiv (quant-ph) 2026-06-11

Exact Dynamics of Topological Order Across a CDW–SPT Transition

arXiv:2606.11303v1 Announce Type: cross Abstract: We investigate the nonequilibrium dynamics of a one-dimensional interacting system across a transition from a charge-density-wave (CDW) phase to a symmetry-protected topological (SPT) phase. Starting from a CDW initial state, we study both sudden quenches and slow ramps into the SPT regime. While the CDW order melts under both protocols, the fate of topological order is sharply different. Following a sudden quench, long-range SPT order does not emerge because the post-quench state contains a finite density of excitations above the topological ground state. In contrast, slow ramps allow the system to follow the instantaneous ground state away from the critical region, enabling the buildup of SPT order with deviations governed by Kibble-Zurek defect production. The dynamics is solvable via a unitary mapping to a quadratic fermionic Hamiltonian, allowing us to compute the Loschmidt echo, correlation functions, and string correlator. The Loschmidt rate function exhibits cusps signaling dynamical quantum phase transitions, while the correlation dynamics reveal the contrasting mechanisms governing quenches and ramps across the transition. These results demonstrate that entering the topological regime is not sufficient for the emergence of topological order; the decisive factor is the suppression of excitation production during the evolution.

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

Trajectory Geometry of Transformer Representations Across Layers

arXiv:2606.09287v2 Announce Type: replace Abstract: Understanding how transformer representations evolve across layers, not merely what they encode, remains an open problem in mechanistic interpretability. We recast the transformer forward pass as a discrete population trajectory through a high-dimensional representation manifold, drawing on geometric tools from computational neuroscience. Rather than probing for pre-specified features, we characterize trajectory geometry using five metrics computed directly in the ambient space: trajectory length, curvature, a semantic convergence index, layerwise cosine similarity, and representational stability. Across three model families (GPT-2, TinyLlama, Qwen2.5) and five controlled prompt families, we report four findings. First, semantically related prompts converge significantly in middle-to-late layers (peak CI 0.41–0.58, p

05.
arXiv (CS.AI) 2026-06-16

Advanced Machine Learning and Deep Learning Techniques for Enhanced Cattle Identification and Detection: A Comprehensive Review

arXiv:2606.15655v1 Announce Type: new Abstract: The need for effective cattle identification technology is now more acutely felt than ever in maintaining biosecurity, food safety, and supply chain efficacy in livestock management. This paper presents a systematic review of recent research in cattle identification using machine learning and deep learning techniques. The present systematic review measures the effectiveness of traditional and modern cattle identification techniques using studies from major academic databases, where articles were subjected to full-text review. Among these techniques, classical Machine Learning Techniques such as K-Nearest Neighbors and Support Vector Machines have demonstrated good results in cattle identification; however, Deep Learning Techniques, such as Convolutional Neural Networks, Residual Networks, and You Only Look Once, are better in cognition, detection, and identification tasks. Feature extraction relies on common techniques like Local Binary Pattern (LBP), Speeded-Up Robust Features (SURF), and Scale-Invariant Feature Transform (SIFT), while key features commonly used in these studies include muzzle prints and coat patterns. The review highlights key hurdles involving cattle identification, such as the limited number of publicly accessible datasets, issues with data quality susceptible to environmental changes and animal mobility, and high demand for real-time processing ability. The paper aims to inform researchers, policymakers, and stakeholders about implementing scalable, humane, and effective cattle identification systems to achieve sustainable livestock management.

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

Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networks

arXiv:2605.00725v2 Announce Type: replace Abstract: Topological neural networks have emerged as effective tools for modeling higher-order relational structures beyond pairwise graphs, including hypergraphs, simplicial complexes, and cell complexes. However, existing Weisfeiler-Leman type expressivity analyses are typically developed on different structural domains and rely on domain-specific neighborhood systems, making their expressive powers difficult to compare within a common formalism. In this paper, we introduce the Combinatorial Complex Weisfeiler-Leman (CCWL) framework, a unified expressive power refinement defined on combinatorial complexes. By exploiting the ability of combinatorial complexes to represent both set-type relations and part-whole hierarchies, CCWL performs topological color refinement through four structural neighborhoods: boundary, co-boundary, lower adjacency, and upper adjacency. We show that, under specified lifting maps, CCWL can simulate several domain-specific WL-type refinements, thereby providing a common theoretical baseline for analyzing topological message passing. We further study the neighborhood sufficiency problem and prove that, under explicit coverage conditions, a reduced refinement using only lower- and upper-adjacent bridge information preserves the distinguishing power of the full four-neighborhood CCWL refinement. Guided by this theoretical result, we instantiate the reduced refinement as the Combinatorial Complex Isomorphism Network (CCIN). Experiments on synthetic and real-world benchmarks demonstrate that CCIN achieves competitive performance against representative graph and topological neural network baselines. Ablation studies and resource-efficiency analyses further support the effectiveness of the proposed lower/upper-neighborhood design.

07.
arXiv (CS.AI) 2026-06-12

Reasoning as Pattern Matching: Shared Mechanisms in Human and LLM Everyday Reasoning

arXiv:2606.13607v1 Announce Type: new Abstract: When large language models (LLMs) fail to generalize or make haphazard errors in reasoning, it is often taken as evidence that LLMs are not truly reasoning, but rather performing a kind of pattern matching. The implication is that people's behavior does not exhibit the same types of failures because human reasoning uses principled and abstract world models. We evaluate human participants and 25 LLMs on their ability to engage in common-sense reasoning about a variety of everyday situations and observe similar patterns of errors in both people and models. We then identify the set of attention heads driving LLM responses and find that these heads implement a form of pattern-matching. These attention heads allow us to predict seemingly inexplicable reasoning errors in people caused by ostensibly irrelevant prompt details. Taken together, our results suggest that everyday causal reasoning in people and LLMs is more consistent with a form of pattern-matching than with abstract world models.

08.
arXiv (CS.LG) 2026-06-12

Central Limit Theorems for Stochastic Gradient Descent Quantile Estimators

arXiv:2503.02178v3 Announce Type: replace-cross Abstract: This paper develops asymptotic theory for quantile estimation via stochastic gradient descent (SGD) with a constant learning rate. The quantile loss function is neither smooth nor strongly convex. Beyond conventional perspectives and techniques, we view quantile SGD iteration as an irreducible, periodic, and positive recurrent Markov chain, which cyclically converges to its unique stationary distribution regardless of the arbitrarily fixed initialization. To derive the exact form of the stationary distribution, we analyze the structure of its characteristic function by exploiting the stationary equation. We also derive tight bounds for its moment generating function (MGF) and tail probabilities. Synthesizing the aforementioned approaches, we prove that the centered and standardized stationary distribution converges to a Gaussian distribution as the learning rate $\eta\rightarrow0$. This finding provides the first central limit theorem (CLT)-type theoretical guarantees for the quantile SGD estimator with constant learning rates. We further propose a recursive algorithm to construct confidence intervals of the estimators with statistical guarantees. Numerical studies demonstrate the effective finite-sample performance of the online estimator and inference procedure. The theoretical tools developed in this study are of independent interest for investigating general SGD algorithms formulated as Markov chains, particularly in non-strongly convex and non-smooth settings.

09.
arXiv (CS.LG) 2026-06-19

Folded Transport MCMC: Eliminating Label Switching by Sampling on a Fundamental Domain

作者:

arXiv:2606.04307v2 Announce Type: replace Abstract: In Bayesian mixture models and other exchangeable-component models, the posterior is invariant under permutation of component labels, creating m! equivalent modes-the label-switching problem. Standard MCMC methods either mix poorly across these modes or rely on post-hoc relabelling that cannot guarantee the sampler has converged. We propose Folded Transport MCMC (FolT-MCMC), which eliminates label switching before sampling by restricting the Markov chain to a fundamental domain-a sorted or reflected subspace containing exactly one representative from each symmetric mode. The proposal is a learned normalising flow whose density is symmetrised over the group orbits, ensuring correct targeting on the reduced space. We show that this construction preserves a computable convergence diagnostic based on the oscillation of the log-density ratio, and that the diagnostic becomes sharper on the fundamental domain whenever the original-space flow under-covers one or more symmetric modes. Experiments on Gaussian mixtures (d=2-20), label-switching targets (up to 24 equivalent modes), a standard Bayesian three-component mixture posterior, and real accelerometer data from a supertall building show improvement ratios of 2x to 145x, with the folded diagnostic stable across dimensions while the unfolded diagnostic collapses.

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

CoRe: A Continuously Reward-Finetuned LLM Query Rewriter for Multi-Stage Context-Aware Relevance in Web-Scale Video Search

LLM-based query rewriters in production face a tension: the training reward must reflect how the rewrite is consumed by the production ranker, yet the training procedure must be cheap enough to support continuous redeployment as data drifts. We present CoRe (Context Relevance), such a system, redeployed weekly for over five months in a major short-video search engine. Our reward uses the deployed multimodal relevance model as its source and a multiplicative ratio form mirroring the production fusion algebra, closing the simulation-production gap that offline reward proxies leave open. A semi-online Mixed Preference Optimization loop makes this reward affordable at multi-million-instance weekly scale: a DPO-style pairwise objective restricts the gradient pass to a small top-k/bottom-k subset of sampled trajectories, and a phase structure reduces trainer/inference-server parameter syncs from per-step to per-phase. An automated promotion gate over reward-like and stability metrics detected and recovered from a real reward-hacking incident in production. Rewriter output is consumed as parallel relevance signals at recall, rawrank, and finerank without displacing the original signals, bounding rewriter-failure blast radius. Online A/B from two sequential production launches, first deploying the rewriter at finerank, then extending consumption to recall and rawrank, delivers statistically significant reductions in change-query rate on rewrite-impacted queries, with all headline relevance and engagement metrics moving in the expected direction.

11.
arXiv (CS.CL) 2026-06-16

Beyond Monolingual Deep Research: Evaluating Agents and Retrievers with Cross-Lingual BrowseComp-Plus

Deep research agents are increasingly evaluated on their ability to search for evidence, reason over retrieved sources, and produce grounded answers. Existing browsing benchmarks, however, largely assume that the user's query and the supporting evidence are written in the same language, leaving open whether agentic search systems can operate when relevant evidence appears in another language. We introduce XBCP (Cross-lingual BrowseComp-Plus), a controlled benchmark that preserves the English question-and-answer space of BrowseComp-Plus but varies the languages of the supporting documents. XBCP instantiates two complementary settings: in the cross-lingual setting, each query is paired with evidence in a single assigned language. In the multilingual setting, the full evidence corpus is distributed equally and randomly across 12 languages spanning high-resource and low-resource regimes. We evaluate four deep research agents using sparse and dense multilingual retrievers, measuring answer accuracy, evidence recall, search behavior, calibration, citation fidelity, and oracle retrieval. Results reveal substantial degradation when evidence is translated. Even strong, dense retrievers lose evidence recall, and agents become less calibrated and cite evidence less reliably. Notably, accuracy remains lower even when all gold evidence is supplied directly. These findings suggest that cross-lingual deep research exposes both retrieval failures and an independent, agent-side difficulty in integrating language-mismatched evidence.

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

MaskWAM: Unifying Mask Prompting and Prediction for World-Action Models

World Action Models (WAMs) present a promising paradigm for robotic control via video prediction. However, current WAMs suffer from fundamental spatial bottlenecks: standard text inputs introduce referential ambiguity in cluttered scenes, while unstructured RGB predictions lack semantic grounding and remain biased by task-irrelevant backgrounds. To overcome these limitations, we introduce MaskWAM, an object-centric world-action model. By jointly integrating masks as both explicit inputs and predictions via a unified Mixture of Transformers (MoT), MaskWAM unlocks robust policy generalization. This design provides two key benefits: (1) predicting future masks yields object-centric semantic supervision that suppresses visual noise, significantly enhancing even standard text-conditioned WAMs; and (2) coupling this predictive supervision with first-frame visual prompts, such as target object masks, establishes a precise spatial anchor that substantially reduces language ambiguity. Crucially, as WAMs are inherently vision-driven architectures, direct mask conditioning yields substantially stronger guidance than text alone, establishing a precise and robust paradigm for manipulating unseen objects. Evaluations on LIBERO, RoboTwin, and real-world tasks demonstrate that MaskWAM significantly outperforms baselines in both language-clear and language-ambiguous tasks.

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

A 3D Isovist World Model – Revealing a City's Unseen Geometry and Its Emergent Cross-City Signature

arXiv:2606.03609v3 Announce Type: replace-cross Abstract: Embodied agents that navigate cities rely on world models that predict how their surroundings will change as they move. But for navigation, what matters is not what the buildings look like; it is where the agent can go. Most world models nonetheless predict appearance, learning how a scene looks rather than the space an agent can move through. Those that do target geometry, such as bird's-eye-view occupancy grids, flatten the three-dimensional environment onto a ground plane, discarding the above-ground and multi-level structure that shapes real navigation. What is missing is a predictive target that captures the navigable geometry an agent actually traverses, without photometric entanglement and without collapsing the third dimension. Our key idea is to model the open volume between buildings, the negative space, encoded as a 3D isovist: a spherical visibility-depth map recording the distance to the nearest surface in every direction. We introduce an embodied world model that predicts the next isovist from a short history of past isovists and a movement action. The prediction is formulated as a depth residual so the decoder inherits sharp building edges, trained with self-rollout scheduled sampling to keep corrupted context on the geometry manifold, and equipped with a persistent latent bird's-eye-view spatial map for cross-path consistency. Our central finding is emergent and unexpected: a single city-blind model trained on Manhattan and Paris develops a cross-city spatial signature, with city identity linearly decodable from its temporal latents far above single-frame baselines, so the signature lives in the learned dynamics rather than in appearance. The representation is lightweight, interpretable, and reproducible, offering a geometric substrate for spatial reasoning in embodied AI, robotics, and urban analysis, released with an open dataset and pipeline.

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

daVinci-kernel: Co-Evolving Skill Selection, Summarization, and Utilization via RL for GPU Kernel Optimization

GPU kernel optimization represents a paradigm where functional correctness is assumed and execution efficiency is the objective. We present daVinci-kernel, a reinforcement learning framework that couples skill discovery with skill exploitation through a dynamically evolving skill library. daVinci-kernel jointly trains three agents sharing one LLM backbone: a Skill Selection Agent that retrieves relevant techniques via BM25 and LLM reranking, a Policy Agent that generates multi-turn CUDA/Triton kernels conditioned on selected skills, and a Skill Summary Agent that distills successful rollouts into reusable skills. Candidate skills are added only after execution-based verification confirms reproducible speedups. All three agents share a single LLM backbone, are initialized via a structured SFT cold start on diversity-filtered data, and are then jointly optimized end-to-end with multi-turn REINFORCE and per-agent advantage estimation. On KernelBench, daVinci-kernel-14B achieves 37.2%, 70.6%, and 32.2% on Level 1, Level 2, and Level 3 under the Fast$_1$ threshold, outperforming the strongest prior RL-trained model, Dr.Kernel-14B.

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

Evaluating the Robustness of Proof Autoformalization in Lean 4

Proof autoformalization aims to translate a mathematical informal proof written in natural language into a formal proof in a formal language such as Lean~4. Several works have developed LLM-based models for proof autoformalization. However, existing evaluations have typically focused on translating well-formed informal proofs from curated datasets. We argue that a robust proof autoformalizer must remain faithful even for informal proofs that diverge from these idealized ones, and we present the first study on the robustness of proof autoformalization models. We formulate two categories of perturbations and evaluate robustness under each: a global perturbation paraphrases the informal proof in a different style, under which the formalization should remain consistent; a local perturbation alters a value, symbol, or proof step, possibly in a counterfactual way, and a robust formalization should faithfully reflect the perturbation rather than reverting to the original one or inferring a different one on its own. We build a benchmark with both perturbations on miniF2F and MATH-500, and automatically measure how stable a proof autoformalization's correctness is under global perturbations and how faithfully its output reflects local perturbations. We evaluate seven recent models, all of which are sensitive to global perturbations and mostly fail to remain faithful under local perturbations. Code and data are available via https://github.com/ucr-rai/robust-proof-autoformalization.

17.
arXiv (CS.CV) 2026-06-18

A Multi-Domain Benchmark for Detecting AI-Generated Text-Rich Images from GPT-Image-2

Text-rich images often contain privacy-sensitive, transactional, or decision-relevant information. As recent multimodal image generation models become increasingly capable of synthesizing realistic textual content and structured visual designs, detecting AI-generated text-rich images has become an important challenge for digital trust and content authenticity. Existing benchmarks, however, largely focus on object-centric images and provide limited coverage of scenarios where textual semantics and layout organization are central. In this paper, we introduce a multi-domain benchmark for detecting text-rich images generated by OpenAI's GPT Image 2. The benchmark contains 8,602 images across six representative categories: commercial posters, infographics, academic posters, receipts, tables, and UI screenshots. Using this benchmark, we evaluate five representative AI-generated image detectors in a zero-shot setting and analyze their overall, category-wise, and post-processing robustness. Our results show that detector performance is highly domain-dependent: methods that perform well in some categories often fail on others, and even the strongest conventional detector exhibits severe sensitivity to JPEG compression. We further conduct an exploratory evaluation with a multimodal vision-language model, revealing both its promise and its limitations on structured formats. These findings highlight the need for text- and layout-aware detection methods for modern AI-generated images. Our dataset is released at XXX.

18.
arXiv (CS.CV) 2026-06-17

MaineCoon: Pursuing A Real-Time Audio-Visual Social World Model

As an increasing majority of global video content is consumed on social platforms for interactive social purposes, video generation models built for social worlds are important but largely overlooked by previous studies. In this work, we define the position of social world models and build a prototype model as the first step towards this goal. While previous world models successfully simulate physical environments or gaming world exploration, they remain fundamentally detached from human-centric social dynamics. To bridge this gap as the first step to social world models, we present MaineCoon, the first real-time audio-visual autoregressive model that has 22B parameters and is capable of real-time streaming generation and sub-second interaction, with a record-breaking frame rate of up to 47.5 FPS, on a single GPU. To the best of our knowledge, MaineCoon is also the first real-time audio-visual generation model specifically optimized for social-interactive applications. To enable efficient and stable training, we introduce several novel techniques into MaineCoon, including self-resampling, cross-modal representation alignment, domain-aware preference optimization, and reinforced online-policy distillation (ROPD). We also design the first agentic streaming inference framework that supports thousand-second-scale or even longer generation while mitigating drift with agentic cache management and prompt planing. These innovations significantly accelerate training while optimizing real-time inference performance. We believe this work not only sets a new state-of-the-art (SOTA) performance benchmark for high-quality, low-latency, and long-horizon audio-visual autoregressive models, but also points out the paradigm shift desired for next-generation AI-native social platforms.

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

Dynamic Black-hole Emission Tomography with Physics-informed Neural Fields

With the success of static black-hole imaging, the next frontier is the dynamic and 3D imaging of black holes. Recovering the dynamic 3D gas near a black hole would reveal previously-unseen parts of the universe and inform new physics models. However, only sparse radio measurements from a single viewpoint are possible, making the dynamic 3D reconstruction problem significantly ill-posed. Previously, BH-NeRF addressed the ill-posed problem by assuming Keplerian dynamics of the gas, but this assumption breaks down near the black hole, where the strong gravitational pull of the black hole and increased electromagnetic activity complicate fluid dynamics. To overcome the restrictive assumptions of BH-NeRF, we propose PI-DEF, a physics-informed approach that uses differentiable neural rendering to fit a 4D (time + 3D) emissivity field given EHT measurements. Our approach jointly reconstructs the 3D velocity field with the 4D emissivity field and enforces the velocity as a soft constraint on the dynamics of the emissivity. In experiments on simulated data, we find significantly improved reconstruction accuracy over both BH-NeRF and a physics-agnostic approach. We demonstrate how our method may be used to estimate other physics parameters of the black hole, such as its spin.

20.
medRxiv (Medicine) 2026-06-19

Grey- and white-matter resilience to tau, cognition and sex in Alzheimer's disease

INTRODUCTION: Brain resilience to tau has been mainly studied in relation to grey matter, while its role in white matter remains unclear in Alzheimer's disease (AD). Sex may moderate associations between brain resilience and cognition. METHODS: We analyzed medial temporal lobe tau PET SUVR, entorhinal cortical thickness, cingulum-hippocampal mean diffusivity, and cognition in 205 amyloid-positive individuals from ADNI. Associations between grey- and white-matter resilience to tau and cognitive performance or decline were examined using linear and mixed-effects models, including sex interactions and stratified analyses. RESULTS: Higher grey-matter resilience to tau related to better cross-sectional memory and language performance (p

21.
arXiv (CS.LG) 2026-06-11

Geometric bias in eigenspace perturbation under random heterogeneous noise

arXiv:2606.11263v1 Announce Type: cross Abstract: Spectral methods rely fundamentally on the stability of principal eigenspaces under random perturbations. Classically, this stability is quantified by the Davis-Kahan and Wedin theorems, which bound the eigenspace error using the operator norm of the noise and the relevant spectral gaps. While these worst-case bounds are sharp for arbitrary deterministic perturbations, they can be wasteful in the low-rank signal-plus-random-noise setting, as they fail to capture the fine-grained interaction between the signal geometry and the noise distribution. In this paper, we study the spectral perturbation of signal-plus-noise matrices corrupted by sparse, random noise with an arbitrary, inhomogeneous variance profile. We demonstrate that under heterogeneous noise variances, the empirical eigenvectors suffer a systematic, deterministic geometric bias that is entirely invisible to classical perturbation bounds. By leveraging the Quadratic Vector Equation (QVE) and establishing fine-grained isotropic local laws, we derive near-optimal, non-asymptotic perturbation bounds for the leading eigenspaces in the operator and $2\to\infty$ norms. The bounds separate the usual signal-to-noise contribution, stochastic fluctuations, and structured geometric bias terms determined by the alignment between the signal eigenspaces and the row-wise variance profile.

22.
arXiv (quant-ph) 2026-06-12

Symmetry and Topology of Monitored Quantum Dynamics

arXiv:2412.06133v4 Announce Type: replace-cross Abstract: The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective non-Hermitian dynamical generators, thereby establishing the tenfold classification for symmetry and topology of monitored free fermions. Our classification elucidates the role of topology in measurement-induced phase transitions and identifies potential topological terms in the corresponding nonlinear sigma models. Furthermore, we establish the bulk-boundary correspondence in monitored quantum dynamics: nontrivial topology in spacetime manifests itself as topologically nontrivial steady states and gapless boundary states in Lyapunov spectra, such as Lyapunov zero modes and chiral edge modes, leading to the topologically protected slowdown of dynamical purification.

23.
arXiv (CS.LG) 2026-06-18

Do as the Romans Do: Learning Universal Behaviors from Heterogeneous Agents

arXiv:2606.18537v1 Announce Type: new Abstract: Humans often acquire new skills by observing others, since observed behaviors implicitly reveal how to act in an environment. However, observations drawn from a heterogeneous population introduce conflicting behavioral signals, making it difficult to determine which behaviors are worth imitating. We address this challenge with General Reward Inference and Disentanglement (GRID), a social learning method that extracts universally useful behaviors from a heterogeneous population of demonstrators pursuing different goals. GRID decomposes per-agent reward functions into a general reward, capturing behaviors shared across all agents, and specific rewards, capturing individual preferences and objectives. Training exclusively on the general reward provides a new paradigm of generalist pretraining. It yields a generalist agent that internalizes universal environmental competencies, such as safety and basic task proficiency, without the mode-averaging bias that afflicts standard learning from demonstration techniques. This generalist serves as a superior prior for fine-tuning to downstream tasks, including preferences unseen during training. Experiments across a synthetic basis function decomposition, multi-agent Craftax, and a continuous autonomous driving simulator (Highway-Env) confirm that GRID successfully disentangles reward structure in a semantically meaningful way, outperforms standard learning from demonstration baselines, and enables more efficient and stable specialization.

24.
arXiv (quant-ph) 2026-06-15

Geometric mechanisms enabling spin- and enantio-sensitive observables in one photon ionization of chiral molecules

arXiv:2603.02735v3 Announce Type: replace-cross Abstract: We examine spin-resolved photoionization of randomly oriented chiral molecules via circularly polarized light, and revisit earlier predictions of Cherepkov (J. Phys. B: Atom. Mol. Phys. 16, 1543, 1983). We will show that the dynamical origin of spin- and enantio-sensitive observables arise from two intrinsic mechanisms that are quantified by two pseudovectors stemming from the geometric properties of the photoionization dipoles in spin space and in real space, and an extrinsic mechanism which is a directional bias introduced by the well-defined direction of light polarization. These mechanisms arise solely from electric dipole interactions. Consequently, this means that the ten independent parameters that was earlier predicted by Cherepkov to fully describe spin-resolved photoionization of chiral molecules can be reduced as moments of these three pseudovectors. We also find that the molecular pseudoscalars describing the spin- and enantio-sensitive components of the yield can be described by the flux of these pseudovectors through the energy shell, which changes sign upon switching enantiomers. Our results provide compact expressions for these observables which provide an intuitive picture on what determines the strength of these spin- and enantio-sensitive observables. The approach can be readily generalized to photoexcitation, multiphoton processes, and arbitrary field polarizations. Regardless of the specific driving conditions, the resulting spin- and enantio-sensitive observables are still controlled by the same three pseudovectors, underscoring their universal role as the primary generators of chirality-induced spin asymmetries, emphasizing their fundamental geometric origin and the universality of the mechanism identified here.

25.
arXiv (CS.AI) 2026-06-19

FM-Agent: Scaling Formal Methods to Large Systems via LLM-Based Hoare-Style Reasoning

arXiv:2604.11556v2 Announce Type: replace-cross Abstract: LLM-assisted software development has become increasingly prevalent, and can generate large-scale systems, such as compilers. It becomes crucial to strengthen the correctness of the generated code. However, automated reasoning for large-scale systems remains challenging due to code complexity. Hoare logic offers an approach to decomposing a large system into smaller components and reasoning about them separately (i.e., compositional reasoning). However, existing works still struggle to scale, because Hoare logic requires writing formal specifications for each function, imposing a heavy human burden. The problem is exacerbated when code is generated by LLMs, as developers lack a deep understanding of each function's expected behavior. This paper presents FM-Agent, the first framework that realizes automated compositional reasoning for large-scale systems. Leveraging LLMs, FM-Agent introduces a top-down paradigm to automatically generate function-level specifications. Specifically, FM-Agent derives the specification of a function from how its callers expect the function to behave, so the generated specifications can reflect the developer's intent of a function even if the implementation is buggy. Developers' intent is usually expressed in natural language, while existing verifiers only support formulas. Therefore, FM-Agent generalizes Hoare-style inference to reason about functions against natural-language specifications. Finally, to confirm bug existence and explain bug causes, FM-Agent automatically generates test cases to trigger potential bugs. In our evaluation, FM-Agent successfully reasons about large-scale systems within 2 days, each of which has up to 143k LoC. These systems have already been tested by their developers, but FM-Agent still finds 522 newly discovered bugs. These bugs can cause serious consequences, including system crashes and incorrect execution results.