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01.
arXiv (CS.CV) 2026-06-16

A Comprehensive Survey of Medical Image Segmentation: Challenges, Benchmarks, and Beyond

Medical image segmentation plays a critical role in clinical diagnostics, treatment planning, disease monitoring, and neurological disorder identification. This article presents a comprehensive review of its systematic development, covering widely used public datasets, representative methods built on the U-Net, Transformer, and SAM architectures, and key evaluation metrics with their differences, followed by an analysis of major challenges from multiple perspectives. Unlike surveys that focus on a single model family or a specific clinical application, this review organizes U-Net-, Transformer-, and SAM-based methods within a unified analytical framework, with a particular focus on their effectiveness in improving segmentation accuracy and efficiency. This work aims to guide future research and support clinical translation of medical image segmentation, with all related resources publicly available in our GitHub repository: https://github.com/andrew-pengyu/Awsome_MedSeg/tree/main.

02.
arXiv (CS.LG) 2026-06-15

AGORA: Can Deliberation and Governance Gates Absorb Participation Bias in Transit Planning?

arXiv:2606.13696v1 Announce Type: cross Abstract: Transit network design depends not only on the optimization algorithm but also on who shows up to the public hearing. Current practice often collects one-directional comments from self-selected attendees, leaving participant mix as an uncontrolled source of outcome variation. We present AGORA, a framework that holds the network, demand, and solver fixed while systematically varying meeting composition through stakeholder agents, structured deliberation, and governance gates. Across two standard benchmark networks at different scales, we find that (i) aggregate outcomes vary little across compositions, but on tail risk and fairness disparity, representative sampling still tends to outperform skewed compositions; (ii) without deliberation, composition produces no variation at all, showing that deliberation is the mechanism through which who attends affects outcomes; and (iii) governance gates compress cross-profile variance without shifting the average outcome on Mandl, but low acceptance on Mumford0 shows thresholds require instance-specific calibration. These findings reframe participation bias from an uncontrollable input to a process-design problem: even without guaranteed representative attendance, well-structured deliberation and governance criteria can substantially reduce how much outcomes depend on who is in the room.

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

Necessary and Sufficient Conditions for Universal Gates with Pauli Strings and Beyond

arXiv:2606.12096v1 Announce Type: new Abstract: Any quantum computation consists of a sequence of unitary evolutions described by a finite set of Hamiltonians. For the case where this set consists of only products of Pauli operators, known as Pauli strings, we provide a necessary and sufficient condition for it to generate $\mathfrak{su}(2^n)$, i.e., to be universal for quantum computation on $n$ qubits. When combining Pauli strings with a general Hamiltonian, we show a sufficient (and in certain circumstances even necessary) condition for universality based on the Pauli-basis expansion of the Hamiltonian. As an application of these results, we prove two corollaries: (i) a necessary and sufficient condition for the universality of a general Hamiltonian given arbitrary single-qubit control on all qubits, and (ii) the universality of an XYZ Heisenberg Hamiltonian with local control of just two adjacent qubits.

04.
arXiv (CS.LG) 2026-06-18

Towards a future space-based, highly scalable AI infrastructure system design

arXiv:2511.19468v2 Announce Type: replace-cross Abstract: If AI is a foundational general-purpose technology, we should anticipate that demand for AI compute – and energy – will continue to grow. The Sun is by far the largest energy source in our solar system, and thus it warrants consideration how future AI infrastructure could most efficiently tap into that power. This work explores a scalable compute system for machine learning in space, using fleets of satellites equipped with solar arrays, inter-satellite links using free-space optics, and Google tensor processing unit (TPU) accelerator chips. To facilitate high-bandwidth, low-latency inter-satellite communication, the satellites would be flown in close proximity. We illustrate the basic approach to formation flight via an 81-satellite cluster of 1 km radius, and describe an approach for using high-precision ML-based models to control large-scale constellations. Trillium TPUs are radiation tested. They survive a total ionizing dose equivalent to a 5 year mission life without permanent failures, and are characterized for bit-flip errors. Launch costs are a critical part of overall system cost; a learning curve analysis suggests launch to low-Earth orbit (LEO) may reach $\lesssim$\$200/kg by the mid-2030s.

05.
arXiv (math.PR) 2026-06-15

Mixing Times for the Facilitated Exclusion Process

arXiv:2402.18999v2 Announce Type: replace Abstract: The facilitated simple exclusion process (FEP) is a one-dimensional exclusion process with a dynamical constraint. We establish bounds on the mixing time of the FEP on the segment, with closed boundaries, and the circle. The FEP on these spaces exhibits transient states that, if the macroscopic density of particles is at least $1/2$, the process will eventually exit to reach an ergodic component. If the macroscopic density is less than $1/2$ the process will hit an absorbing state. We show that the symmetric FEP (SFEP) on the segment $\{1,\ldots,N\}$, with $k>N/2$ particles, has mixing time of order $N^{2}\log(N-k)$ and exhibits the pre-cutoff phenomenon. For the asymmetric FEP (AFEP) on the segment, we show that there exists initial conditions for which the hitting time of the ergodic component is exponentially slow in the number of holes $N-k$. In particular, when $N-k$ is large enough, the hitting time of the ergodic component determines the mixing time. For the SFEP on the circle of size $N$, and macroscopic particle density $\rho \in(1/2,1)$, we establish bounds on the mixing time of order $N^{2}\log N$ for the process restricted to its ergodic component. We also give an upper bound on the hitting time of the ergodic component of order $N^{2}\log N$ for a large class of initial conditions. The proofs rely on couplings with exclusion processes (both open and closed boundaries) via a novel lattice path (height function) construction of the FEP.

06.
arXiv (quant-ph) 2026-06-19

Applications of quantum annealing to magnetic dipole hyperfine structure constants: First results beyond energies for atoms

arXiv:2606.20166v1 Announce Type: new Abstract: We report the first results of the magnetic dipole hyperfine structure (HFS) constants of neutral $\mathrm{Li}$, Li-like $\mathrm{Be}$, neutral $\mathrm{Na}$, and Na-like $\mathrm{Mg}$ using a modified version of the Quantum Annealer Eigensolver (QAE) algorithm on D-Wave's quantum hardware. The results are benchmarked against relativistic configuration interaction with multiconfiguration Dirac Hartree-Fock (MCDHF) calculations using the General-purpose Relativistic Atomic Structure Package (GRASP), and simulated annealing. In our modified QAE, a zooming-and-sigma-annealing approach with a floating-point encoding scheme is adopted to estimate the ground-state eigenvalue and eigenvector of the relativistic Dirac-Coulomb Hamiltonian matrices ($H_{\mathrm{DC}}$) constructed from 11 or fewer configuration state functions (CSFs). For calculations with extended correlation orbital sets, we applied a CSF truncation scheme, retaining only CSFs (up to 12) that make significant contributions to the ground-state wavefunction. Our modified QAE precision is kept limited to three decimal places (up to 10 qubits). Hardware demonstrations on the D-Wave quantum processing unit (QPU) yielded results that were completely consistent with GRASP (at the chosen precision) in determining the magnetic dipole HFS constants, with accuracy varying across systems and $H_{\mathrm{DC}}$ matrix dimensions.

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

Communication-Efficient Verifiable Attention for LLM Inference

arXiv:2606.16352v1 Announce Type: cross Abstract: Computation integrity of remote large language model (LLM) serving can be questionable. For conventional deep neural networks (DNNs), the existing TEE-shielded DNN partitioning (TSDP) approach uses Trusted Execution Environment (TEE) to compute non-linear components and verify the integrity of linear components offloaded to an untrusted GPU. However, directly applying TSDP to Transformer-based LLMs incurs significant TEE computation and TEE-GPU communication overhead. This paper presents Communication-efficient TEE-GPU Attention (\textsc{VeriAttn}) for accelerating verifiable LLM inference. \textsc{VeriAttn} offloads both linear and non-linear computations of attention to the GPU, while TEE performs verification. Moreover, for prefill, \textsc{VeriAttn} uses a two-level pipeline to overlap data movement, TEE pre-/post-processing, and GPU computation. For decoding, when the key-value cache exceeds available GPU memory, \textsc{VeriAttn} partitions attention across TEE and GPU to reduce repeated key-value transfers. Evaluation on an Intel TDX platform shows that \textsc{VeriAttn} achieves 2.60-3.38$\times$ and 3.86-5.42$\times$ acceleration over TSDP for 6k-token prompts and 10k-token outputs during prefill and decoding, respectively.

08.
arXiv (CS.LG) 2026-06-11

Querying Counterfactuals on Tissue Graphs with Supervised Disentanglement

arXiv:2606.08493v2 Announce Type: replace-cross Abstract: Tissue graph counterfactuals ask how a cell's expression would change under altered spatial neighbor contexts. Such queries are central to predicting cell behavior in tissues, but lack a unified definition, with existing methods targeting specific intervention types or treating cells as i.i.d. In this work, we first formalize tissue graph counterfactuals as a class of spatial interventions that either rewire connections between cells (edge perturbation) or modify the expression of their neighbors (node perturbation). We then introduce Cellina (https://cellina.readthedocs.io) - a framework that uses supervised disentanglement to decompose a cell's intrinsic state from its spatial context, using the latter as a conditioning input for counterfactual predictions. Across benchmarks spanning over 2.5 million spatially-resolved cells in colorectal cancer and mouse brain, Cellina outperforms spatially-informed and non-spatial competitors in in-silico graph perturbations, disentanglement, and scalability. Additionally, we show that Cellina reveals biologically distinct cancer subdomains in an unsupervised manner and enables targeted neighbor perturbation simulations.

09.
medRxiv (Medicine) 2026-06-22

How knowledge shapes community stigma and social support for women seeking abortion in the Democratic Republic of Congo: A cross-sectional study.

Background The Democratic Republic of Congo (DRC) bears one of the highest maternal mortality ratios globally (746 per 100,000 live births), with nearly 11% of deaths attributable to complications of unsafe abortion. Despite ratification of the Maputo Protocol and related national policies, access to safe abortion remains limited, largely due to entrenched stigma. Social support, encompassing emotional, informational, and instrumental assistance, is critical in shaping womens abortion-seeking behaviors and health outcomes. This study examines the influence of community-level knowledge on stigma and social support for women seeking abortion care. Methods A cross-sectional survey was conducted from May 2024 to June 2024 among 1,715 adults in Kinshasa and North Kivu provinces. Analyses focused on a sub-sample of 574 respondents reporting familiarity with women who had undergone abortion. Structural Equation Modeling (SEM) was applied to estimate direct and indirect pathways linking community knowledge, stigma, and social support. Results Two core knowledge indicators, recognition of abortion as a safe medical procedure and awareness of legal conditions for access, were significantly associated with outcomes. A one-unit increase in knowledge corresponded to a 0.39-point increase in social support and a 0.19-point reduction in stigma. Enhanced knowledge promoted empathetic attitudes, reinforced practical support, and mitigated moralizing judgments toward women seeking abortion. Conclusions Strengthening community knowledge emerges as a strategic lever to reduce abortion-related stigma and enhance social support in the DRC. These findings underscore the importance of integrating stigma-reduction and knowledge-enhancement interventions into reproductive health programs to improve womens access to safe and dignified abortion care.

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

A Tutorial on World Models and Physical AI

Authors:

arXiv:2606.12783v1 Announce Type: new Abstract: World modeling is emerging as a central principle for building intelligent systems capable of prediction, reasoning, and decision making. A central distinction can be drawn between explicit world models, which learn structured dynamics for rollout-based reasoning and planning, and implicit world models, which encode predictive structure within scalable learned representations. These complementary paradigms provide a foundation for physical AI in domains such as robotics and autonomous driving, enabling intelligence beyond reactive control under real-world constraints. Recent foundation models further suggest a pathway toward unified systems integrating perception, prediction, and action. Despite rapid progress, major challenges remain in hierarchical reasoning, long-horizon planning, and autonomous goal formation, which are critical for advancing toward artificial general intelligence. This tutorial presents a coherent framework in which diverse world modeling approaches are unified through shared predictive structure and differentiated by how such structure is represented and exploited.

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

SDFLoRA: Selective Decoupled Federated LoRA for Privacy-preserving Fine-tuning with Heterogeneous Clients

arXiv:2601.11219v3 Announce Type: replace-cross Abstract: Federated learning (FL) for large language models (LLMs) has attracted increasing attention as a privacy-preserving approach for adapting models over distributed data, where parameter-efficient methods such as Low-Rank Adaptation (LoRA) are widely adopted to reduce communication and memory costs. However, practical deployments often exhibit rank and data heterogeneity: clients operate under different low-rank budgets and data distributions, making direct aggregation of LoRA updates biased and unstable. Existing approaches either enforce a unified rank or align heterogeneous updates into a single shared subspace, which tends to mix transferable and client-specific directions and consequently undermines personalization. Moreover, under differential privacy (DP), perturbing such structurally mixed updates injects noise into directions that should remain purely local, leading to unnecessary utility degradation. To address these issues, we propose Selective Decoupled Federated LoRA (SDFLoRA), a structure-aware LoRA framework that decouples each client update into a shared component for aggregation and a private component that preserves client-specific semantics. Only the shared component participates in subspace alignment, while the private component remains local and uncommunicated, making the training DP-compatible and stabilizing aggregation under rank heterogeneity. By injecting noise only into the aggregated shareable update, this approach avoids perturbations to local directions and improves the utility-privacy trade-off. Experiments on multiple benchmarks demonstrate that SDFLoRA outperforms federated LoRA baselines and achieves a strong utility-privacy trade-off.

12.
arXiv (CS.AI) 2026-06-18

A DeepLearning Framework for Dynamic Estimation of Origin-Destination Sequence

arXiv:2307.05623v2 Announce Type: replace-cross Abstract: OD matrix estimation is a critical problem in the transportation domain. The principle method uses the traffic sensor measured information such as traffic counts to estimate the traffic demand represented by the OD matrix. The problem is divided into two categories: static OD matrix estimation and dynamic OD matrices sequence(OD sequence for short) estimation. The above two face the underdetermination problem caused by abundant estimated parameters and insufficient constraint information. In addition, OD sequence estimation also faces the lag challenge: due to different traffic conditions such as congestion, identical vehicle will appear on different road sections during the same observation period, resulting in identical OD demands correspond to different trips. To this end, this paper proposes an integrated method, which uses deep learning methods to infer the structure of OD sequence and uses structural constraints to guide traditional numerical optimization. Our experiments show that the neural network(NN) can effectively infer the structure of the OD sequence and provide practical constraints for numerical optimization to obtain better results. Moreover, the experiments show that provided structural information contains not only constraints on the spatial structure of OD matrices but also provides constraints on the temporal structure of OD sequence, which solve the effect of the lagging problem well.

13.
arXiv (CS.LG) 2026-06-16

How Controlling the Variance can Improve Training Stability of Sparsely Activated DNNs and CNNs

arXiv:2602.05779v2 Announce Type: replace Abstract: The Edge-of-Chaos (EoC) theory developed for the random initialization of deep networks allows more efficient training by both preserving information in the initial outputs of the network and minimising exploding or vanishing gradients through characterisation of the intermediate layers as Gaussian processes. This EoC theory provides formulae for the choice of the initialisation distribution variances of the weights and biases. For activations which are approximately linear around the origin, the EoC theory typically encourages the Gaussian process variance to converge towards zero with increasing depth. Here we consider the less studied setting of highly sparsity inducing activations where a large region of values near the origin are set to zero. In this setting we prove a new phenomenon whereby initialisations leading to larger fixed Gaussian processes are beneficial to training stability. This theory informs a new, yet simple, initialisation strategy that allows training DNNs and CNNs with as large as 90\% sparsity in the hidden layers.

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

Multi-Task Bayesian In-Context Learning

arXiv:2606.20538v1 Announce Type: new Abstract: Bayesian predictive inference provides a principled framework for uncertainty quantification, data efficiency, and robust generalization. However, exact inference is often intractable, and scalable approximations may remain computationally expensive or require restrictive modeling assumptions that degrade predictive performance. Prior-Data Fitted and in-context models have recently emerged as an amortized alternative by learning to map datasets directly to predictive distributions, but existing approaches are tightly coupled to the support of the training prior and lack explicit mechanisms for adapting to new priors at test time, resulting in limited robustness under distribution shift. We introduce a multi-task in-context learning framework for amortized hierarchical Bayesian predictive inference that explicitly represents prior information as a prefix of in-context datasets. A transformer trained on sequences of prior and target tasks learns to adapt its predictions across families of priors. On a suite of evaluations with increasing difficulty, including out-of-meta-distribution priors and priors with high-dimensional latent structures, our method matches oracle Bayesian predictors while being orders of magnitude faster. We further demonstrate its practical relevance on a real-world spatiotemporal temperature prediction benchmark. Code is available at https://github.com/martianmartina/multi-task-bayesian-icl/.

15.
arXiv (CS.LG) 2026-06-24

Robust and Fast Training via Per-Sample Clipping

arXiv:2605.02701v2 Announce Type: replace-cross Abstract: We propose a robust gradient estimator based on per-sample gradient clipping and analyze its properties both theoretically and empirically. We show that the resulting method, per-sample clipped SGD (PS-Clip-SGD), achieves optimal in-expectation convergence rates for non-convex optimization problems under heavy-tailed gradient noise. Moreover, we establish high-probability convergence guarantees that match the in-expectation rates up to polylogarithmic factors in the failure probability. We complement our theoretical results with multiple numerical experiments. In particular, we demonstrate that PS-Clip-SGD outperforms both vanilla SGD with momentum and standard gradient clipping when training AlexNet on the CIFAR-100 dataset, even after accounting for the additional computational time caused by per-sample clipping. We also empirically show that, in the presence of gradient accumulation, applying clipping at the mini-batch level can improve training performance while incurring virtually no additional computational cost. This finding is particularly interesting, as it contradicts the common practice of applying clipping only after all accumulation steps have been completed.

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

Reroute, Don't Remove: Recoverable Visual Token Routing for Vision-Language Models

Vision-language models (VLMs) project images into hundreds to thousands of visual tokens, making decoder inference expensive in both attention computation and KV-cache memory. Existing visual-token reduction methods largely follow a rank-and-remove paradigm: they score visual tokens, keep a compact subset, and permanently discard the rest. We show that this irreversible action is fragile because visual-token importance changes across decoder depth; tokens ranked low at one stage may become relevant in later layers, especially for grounding-sensitive queries. We propose Reroute, a training-free plug-in that replaces removal with recoverable routing. At each routing stage, selected vision tokens pass through decoder blocks, while deferred tokens bypass the stage and re-enter the candidate pool at the next routing decision. Reroute reuses existing attention-score ranking rules and stage-wise schedules, preserving the theoretical TFLOPs and KV-cache budget class of the pruning method it augments. Across FastV, PDrop, and Nüwa variants on LLaVA-1.5 and Qwen backbones, reroute improves grounding under aggressive token reduction while maintaining general VQA performance. These results suggest that VLM token reduction should not be viewed only as irreversible pruning, but also as recoverable routing. The code can be found here: https://github.com/elmma/mllm-reroute/

17.
arXiv (CS.LG) 2026-06-24

WiFi-Based People Counting Using Beam-Steerable Antennas: A Test-bed Study

arXiv:2606.23710v1 Announce Type: cross Abstract: Ubiquitous perception through RF signals is a pivotal opportunity for future technology: it enables personalized services such as smart living, remote healthcare, automated logistics or interaction through free-space gestures. The ubiquity of Wi-Fi and cellular networks presents a promising platform for the development of innovative sensing tools. Future standards will also introduce dedicated sensing features which, for example, will allow routers to work as frequency modulated continuous wave radios targeting radar applications. Most of the current chip designs support ad-hoc firmware for CSI extraction with MIMO arrangements of the transmitter (TX) and receiver (RX) antennas and OFDM subcarriers. The CSI describes the phase shift and amplitude attenuation of multiple propagation paths on each subcarrier. The latest IEEE 802.11be standard (Wi-Fi 7) offers a wider subcarrier bandwidth of 160MHz (up to 320MHz), providing at least 120 usable pilot subcarriers for CSI or CIR estimation. Additionally, Wi-Fi signals have been recently exploited to track daily human movements and behaviors, while Wi-Fi signal variations have been shown to differ between different people and can consequently be used for their re-identification.

18.
arXiv (math.PR) 2026-06-16

Structure preserving properties of higher order moment closures for TASEP

arXiv:2604.15925v2 Announce Type: replace-cross Abstract: The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional flow of interacting particles on a 1D-lattice that is much used in systems biology and statistical physics. Its master equation describes the evolution of the probability distribution on the configuration space. The size of the master equation grows exponentially with the length of the lattice. It is known that the complexity of the system may be reduced using mean-field approximations. We provide a rigorous definition of a family of such models using moments of any order and an extension to the pair approximation for obtaining closures for the system. The dimension of these models grows linearly with the lattice size and exponentially in the order of the approximation. Moreover, we show that the states of these models still have a probabilistic interpretation and that basic structural properties of the master equation are preserved. This extends known results on the Ribosome Flow Model which can be viewed as the first order approximation for TASEP.

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

ROSE: Benchmarking the Perception-to-Action Gap in Multimodal Models

arXiv:2606.19965v1 Announce Type: cross Abstract: Multimodal large language models (MLLMs) are increasingly expected to act on visual information, yet the same scene may require different actions under different task contexts. How reliably can a model turn the same visual evidence into the action required by the current context? To answer this question, we introduce \textsc{ROSE} (Reference-conditioned Oddity and Symbolic Execution), a controlled benchmark that holds the visual scene fixed while varying region constraints and required symbolic outputs. Through coupled counting and coordinate-action tasks, \textsc{ROSE} tests whether models can infer an implicit majority reference and act on the resulting fine-grained visual evidence under changing contexts. Across nine recent MLLMs, performance drops by as much as 44.5 percentage points from counting-oriented tasks to region-conditioned action, despite 98.8\% human performance. The gap persists on paired scenes and regions for which the same model returns the correct count, while global-click and matched local controls show that coordinate grounding explains only part of the loss, revealing a distinct, model-dependent bottleneck in turning shared visual evidence into context-specific actions.

20.
arXiv (CS.LG) 2026-06-17

Characterizing Nash Equilibria in Zero-Sum Games: A Physics-Inspired, Parallelizable Approach with a Linear Number of Gradient Queries

arXiv:2507.11366v2 Announce Type: replace-cross Abstract: We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based methods (time-average convergence) or contraction-map-based methods (last-iterate convergence). We propose a new method based on Hamiltonian dynamics in physics and prove that it can characterize the set of NE in a finite (linear) number of iterations of alternating gradient descent in the unbounded setting, modulo degeneracy, a first in online optimization. Unlike standard methods for computing NE, our proposed approach can be parallelized and works with arbitrary learning rates, both firsts in algorithmic game theory. Experimentally, we support our results by showing our approach drastically outperforms standard methods.

21.
arXiv (CS.CV) 2026-06-17

Detail++: Training-Free Detail Enhancer for Text-to-Image Diffusion Models

Recent advances in text-to-image (T2I) generation have led to impressive visual results. However, these models still face significant challenges when handling complex prompt, particularly those involving multiple subjects with distinct attributes. Inspired by the human drawing process, which first outlines the composition and then incrementally adds details, we propose Detail++, a training-free framework that introduces a novel Progressive Detail Injection (PDI) strategy to address this limitation. Specifically, we decompose a complex prompt into a sequence of simplified sub-prompts, guiding the generation process in stages. This staged generation leverages the inherent layout-controlling capacity of self-attention to first ensure global composition, followed by precise refinement. To achieve accurate binding between attributes and corresponding subjects, we exploit cross-attention mechanisms and further introduce a Centroid Alignment Loss at test time to reduce binding noise and enhance attribute consistency. Extensive experiments on T2I-CompBench and a newly constructed style composition benchmark demonstrate that Detail++ significantly outperforms existing methods, particularly in scenarios involving multiple objects and complex stylistic conditions.

22.
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.

23.
arXiv (math.PR) 2026-06-24

On the packing dimension of projected measures

arXiv:2604.18222v2 Announce Type: replace-cross Abstract: We study the packing dimension of Borel measures under orthogonal projections. We give a necessary and sufficient condition such that typical projections of Borel probability measures have full packing dimension and derive general lower bounds in the complementary case. Our approach shows that the Assouad dimension of the support influences the behavior of projected measures.

24.
arXiv (CS.CL) 2026-06-19

JAMER: Project-Level Code Framework Dataset and Benchmark on Professional Game Engines

Current AI-driven game development has made substantial progress in asset generation, gameplay design, and web-based game coding, yet project-level code engineering on professional game engines remains largely unexplored due to the absence of large-scale datasets and deterministic evaluation methods. We present JamSet and JamBench, the first project-level game code framework dataset and benchmark built on a professional game engine. Our key insight is that Game Jam competitions, community events where developers build complete games under tight time constraints, yield thousands of open-source projects suitable for this purpose. Building on the Godot engine's text-based format and headless execution mode, we design a deterministic verification pipeline from file integrity to runtime behavior collection, distilling 8,133 verified projects from over 240,000 repositories. Of these, 300 manually verified projects form JamBench; the rest constitute JamSet. JamBench defines theme-driven generation and code completion tasks, evaluated through a pipeline combining compilation pass rates, Structural Completeness Score (SCS), and Behavioral Alignment Score (BAS). Evaluation of 9 frontier models reveals a capability cliff as project scale increases, with runtime pass rates dropping from 80.4% on small projects to 5.7% on large ones (Task2a). Code Agents improve compilation rates yet yield no gains in runtime behavioral quality, indicating that the bottleneck lies in architectural design rather than syntactic correctness. Experiments validate JamSet as effective training data. All data and code are publicly available.

25.
arXiv (math.PR) 2026-06-24

On the convergence of doubly stochastic Markov chains

arXiv:2606.24584v1 Announce Type: new Abstract: We characterize the asymptotic behavior of time-homogeneous doubly stochastic Markov chains. Our investigation revolves around understanding the dynamics of products of doubly stochastic matrices, which in turn allows us to fully characterize three distinct behaviors: cyclicity, convergence towards a special equilibrium matrix, and divergence. Notably, we introduce a novel and comprehensive sufficient condition for the convergence of an infinite product of doubly stochastic matrices.