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01.
arXiv (CS.CV) 2026-06-24

A Dual Edge Spatial Jacobian Image Graph for Interpretable Diabetic Retinopathy Grading

Automated diabetic retinopathy (DR) grading from colour fundus photographs can achieve strong predictive performance, but clinical interpretation requires more than an image-level label. It requires understanding how lesion evidence is distributed around retinal vessels and how this evidence relates to quantitative vascular biomarkers. We present a dual-edge spatial-Jacobian image graph for interpretable DR grading. Each fundus image is represented as a graph node with four aligned evidence streams: AutoMorph vessel information ($X_1$), DR-XAI-style lesion evidence maps ($X_2$), a 128-dimensional lesion-based contrastive image embedding ($X_3$), and AutoMorph morphometric biomarkers ($X_4$). The spatial edge branch ($X_{12}$) encodes vessel-lesion geometry, while the Jacobian branch ($X_{34}$) models embedding-biomarker sensitivity. Lightweight two-token attention fuses both edge families into a final image graph. On 2,910 matched non-augmented APTOS images, the full graph achieves 0.8076 accuracy, 0.8312 quadratic weighted kappa, 0.5915 macro-F1, and 0.9330 adjacent-grade accuracy; referable DR reaches 0.9055 accuracy and 0.9711 AUROC. The framework is positioned as an explainable representation-learning tool for lesion-biomarker hypothesis generation, rather than as a deployment-ready clinical classifier. The code is available at https://github.com/Inamullah-Colab/dual-edge-dr-graph-xai.

02.
arXiv (math.PR) 2026-06-12

Sub-Riemannian spectral distance

arXiv:2606.12804v1 Announce Type: cross Abstract: We study eigenvalues and eigenfunctions of the ``div-grad type" sub-Laplacian with respect to Popp's volume on a compact equiregular sub-Riemannian manifold $M$. Since Popp's volume is canonically determined by the sub-Riemannian structure of $M$, the spetra of the sub-Laplacian carry geometric meanings. In this paper, we first embed $M$ into the Hilbert space of square-summable sequences using eigenfunctions and then define a spectral distance between two compact equiregular sub-Riemannian manifolds. Our result is a sub-Riemannian analogue of Berard-Besson-Gallot's classical work in the Riemannian case.

03.
arXiv (CS.AI) 2026-06-17

Handling Feature Heterogeneity with Learnable Graph Patches

arXiv:2606.17667v1 Announce Type: cross Abstract: In recent years, the rapid development of foundation models and graph pre-training technologies has spurred increasing interest in constructing a universal pre-trained graph model or Graph Foundation Model (GFM). However, a significant challenge is that existing models are unable to address feature heterogeneity in graph data without textual information, which hinders the transferability of graph models across different datasets. To bridge this gap, we propose the concept of learnable graph patches, which we regard as the smallest semantic units of any graph data. We decompose the graph into learnable graph patches by unfolding the node features and constructing corresponding patch structures separately. We then design a framework that mines transferable information from graph data across domains. Specifically, after extracting graph patches, we propose a patch encoder to extract knowledge from each unit and a patch aggregator to learn how the units are combined into a whole. Due to its domain-agnostic nature, the model can be applied to downstream data across different domains. Furthermore, we analyze the connection between our method and existing graph models, as well as the transferability of the node embeddings it generates. Empirically, our method not only achieves the capability to use multi-domain graphs for pre-training, but also shows enhanced performance across various downstream datasets and tasks. Moreover, we observe consistent improvement in downstream performance as the volume of pre-training data increases.

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

Finite-Time Convergence of Distributionally Robust Q-Learning with Linear Function Approximation

arXiv:2510.01721v3 Announce Type: replace Abstract: Distributionally robust reinforcement learning (DRRL) seeks policies that perform well when the deployment transition model differs from the nominal model generating the data. Most finite-sample guarantees for DRRL are tabular, model-based, rely on generative access, or obtain function-approximation guarantees only under additional structure, such as linear-transition models or restrictive discount-factor conditions. We study discounted model-free robust Q-learning under an $(s,a)$-rectangular chi-square uncertainty set, with linear approximation of the robust Q-function, using only a single Markovian trajectory from an unknown nominal model. Our algorithm combines a target-network outer loop with a dual function-approximation scheme for the chi-square robust Bellman update. The dual procedure uses moment-tracking critics, suffix averaging, a fresh-evaluation stage for the variance-like moment, and a tunable smoothing parameter to have a Lipschitz-continuous chi-square dual gradient. We prove a finite-time convergence bound to the optimal robust Q-function up to approximation error, without imposing a small-discount-factor assumption. Our results help close a gap between the empirical use of robust RL algorithms and the non-asymptotic guarantees available for their non-robust counterparts.

05.
arXiv (math.PR) 2026-06-16

Hua-Chen New Theory of Economic Optimization

arXiv:2504.19134v4 Announce Type: replace-cross Abstract: Between 1957-1985, Chinese mathematician Loo-Keng Hua pioneered economic optimization theory through three key contributions: establishing economic stability's fundamental theorem, proving the uniqueness of equilibrium solutions in economic systems, and developing a consumption-integrated model 50 days before his death. Since 1988, Mu-Fa Chen has been working on Hua's theory. He introduced stochastics, namely Markov chains, to economic optimization theory. He updated and developed Hua's model and came up with a new model (Chen's model) which has become the starting point of a new economic optimization theory. Chen's theory can be applied to economic stability test, bankruptcy prediction, product ranking and classification, economic prediction and adjustment, economic structure optimization. Chen's theory can also provide efficient algorithms that are programmable and intelligent. {Stochastics} is the cornerstone of Chen's theory. There is no overlap between Chen's theory, and the existing mathematical economy theory and the economics developments that were awarded Nobel Prizes in Economics between 1969 and 2024. The distinguished features of Chen's theory from the existing theories are quantitative, calculable, predictable, optimizable, programmable and can be intelligent. This survey provides a theoretical overview of the newly published monograph [5rw24]. Specifically, the invariant of the economic structure matrix, also known as the Chen's invariant, was first published in this survey.

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

Runtime Enforcement of Hybrid System Properties

arXiv:2606.12022v1 Announce Type: cross Abstract: Runtime enforcement has emerged as a promising approach for ensuring the safety of autonomous and cyber-physical systems operating in uncertain and dynamic environments. Unlike traditional runtime verification, runtime enforcement actively intervenes during execution to prevent property violations by modifying unsafe system behaviors. Existing enforcement frameworks primarily focus on untimed or discrete-time specifications and are often limited to delaying or suppressing events, making them inadequate for reactive systems exhibiting complex continuous dynamics. In this paper, we propose a runtime enforcement framework where safety requirements are modeled using Hybrid Automata (HA). The framework combines discrete-event editing with continuous-time monitoring to support enforcement actions such as suppression, delay, and insertion of events at arbitrary time instants. Upon observing environmental inputs, the automaton is initialized, and runtime reachability analysis is used to synthesize safe corrective actions. We formally define the enforcement problem for safety hybrid automata, establish enforceability conditions, and present an online enforcement algorithm for reactive systems. A detailed case study on an Adaptive Cruise Control (ACC) system demonstrates the effectiveness of the proposed approach in maintaining safety properties under unsafe controller behaviors. Experimental results show that the framework introduces minimal computational overhead while ensuring continuous compliance with safety requirements in real time.

07.
arXiv (quant-ph) 2026-06-12

Effective Geometry and Position-Dependent Mass in Dual-$q$ Quantum Mechanics

arXiv:2606.12444v1 Announce Type: new Abstract: This work investigates the deformed-derivative formalism introduced by Borges, with emphasis on the relation between the linear operator $D_{(q)}$ and its nonlinear dual counterpart $D^{(q)}$. Directly inserting the dual derivative into the kinetic term leads to a nonlinear Schrödinger equation and obscures the usual interpretation of superposition and probability. We show that this nonlinearity can be removed by a simultaneous transformation of the coordinate and of the wave function. The transformed problem is an ordinary linear Schrödinger equation in a deformed coordinate, and its representation in the physical coordinate is equivalent to a Hermitian position-dependent-mass (PDM) Hamiltonian. In this formulation, the deformation parameter $q$ determines both the effective mass profile and the associated metric. The formalism is applied to the free particle, the infinite square well, the rectangular barrier, and the harmonic oscillator in the weak-deformation regime. Comparison with the nonadditive-translation approach of Costa Filho et al. shows that the Borges dual-$q$ framework provides an alternative route to the same effective geometric structure. For $q1$, the effective length is increased, which lowers the spectrum and suppresses tunneling relative to the undeformed limit $q=1$.

08.
arXiv (CS.LG) 2026-06-19

Self-Adaptive Scale Handling for Forecasting Time Series with Scale Heterogeneity

arXiv:2606.20010v1 Announce Type: new Abstract: Current time series forecasting (TSF) research predominantly focuses on scale-homogeneous data, where different time series share similar numerical magnitude ranges. However, in real-world industrial scenarios such as financial product sales, different time series often differ by orders of magnitude (scale heterogeneity). Since these series share similar temporal patterns, joint modeling is desirable for better data utilization, yet existing scaling methods either compress low-scale signals (global normalization) or destroy semantic discriminability and amplify inverse-scaling errors (window-based scaling). This paper proposes a self-Adaptive Scale-handling (AS) module that learns adaptive scale factors tailored to each input, preserving semantic discriminability while reducing inverse-scaling errors. AS consists of Scale Calibrating (SC), which calibrates prior mean scaling factors through neural networks, and Scaling Selection (SS), which decides whether to apply calibration or retain the original factor, avoiding over-calibration. Experiments on real-world fund sales datasets from Ant Fortune and Alipay show that AS seamlessly integrates into popular TSF models and consistently improves their performance. The code and dataset are available at the link https://github.com/Meteor-Stars/ASTSF.

09.
arXiv (quant-ph) 2026-06-11

Q-DICE: Quantum Distributed Interconnect Compiler and Emulator

arXiv:2606.11340v1 Announce Type: new Abstract: As distributed quantum computing (DQC) offers a leading path towards scalable quantum computation, the ability to benchmark distributed algorithms under realistic conditions becomes critical for system co-design. However, without access to physical systems, researchers lack tools to evaluate distribution protocols. We introduce Q-DICE (Quantum Distributed Interconnect Compiler and Emulator), a hardware-aware emulation environment for benchmarking distributed quantum circuits on classical simulators and on NISQ-era monolithic hardware. This work provides three core contributions: (1) a programmatic scheme to construct distributed QPU backends, utilizing two novel techniques - QPU slicing and stitching - to facilitate distributed circuit mapping, (2) a methodology for modeling nonlocal link noise using physically motivated Kraus operators and stochastic error channels, and (3) a boundary-aware circuit mapping algorithm enforcing distributed QPU topology constraints during transpilation. Together, these components constitute a distribution-aware compiler and noise-modeling engine that faithfully enforces the physical limitations of distributed quantum hardware within existing execution environments. We validate Q-DICE against a multitude of experimentally demonstrated quantum circuits, including a distributed Grover's search on optically linked trapped-ion hardware, achieving a worst-case fidelity deviation of 4% between simulated and experimental results. These findings demonstrate Q-DICE's capacity to accurately reproduce real distributed quantum system behavior across platforms, streamlining experimentation with distributed quantum algorithms and architectures.

10.
medRxiv (Medicine) 2026-06-11

What level of expertise is necessary to generate ACLS training test questions: pre-med students vs. artificial intelligence?

Abstract Introduction In-hospital cardiac arrest carries high mortality despite standardized ACLS training. Educators face increasing time constraints in developing assessment tools for ACLS training. Two possible solutions to this problem are using pre-medical students or using artificial intelligence to generate test questions. This study compared the quality of pre-medical student-generated ACLS test questions vs. AI-generated ACLS test questions, testing the hypothesis that AI-generated questions are non-inferior to student-generated questions. Methods Ten pre-medical students created ACLS questions following predefined criteria, while an AI model (Northwell's Artificial Intelligence Hub) generated comparable questions. A blinded ACLS-certified physician evaluated questions on the qualities of Alignment, Clarity, Cognitive Level, and Question Design using a standardized rubric (Likert scale: 1 = poor quality, 5 = excellent). Student's T-test and Chi-square analysis were used to compare the quality of questions on different rubric domains within each arm (student vs. AI) and within one domain (eg, question Clarity) between arms. The Student's T test was used when 2 comparator groups were compared (eg, Clarity of student-generated vs. AI-generated questions) within one arm. The ANOVA test was used when comparing more than 2 comparator groups (eg, Alignment vs. Clarity vs. Cognitive Level) within one arm. Statistical significance was set as a priority at p

11.
arXiv (CS.CV) 2026-06-12

Selecting Samples on Graphs: A Unified Dataset Pruning Framework for Lossless Training Acceleration

The rapid growth of modern training datasets has significantly increased computational cost, motivating dataset pruning~(DP) methods which retain only a subset of informative samples to reduce training cost. Existing pruning criteria typically rely on either intrinsic signals that assess samples independently or extrinsic signals that promote diversity via pairwise relations. While effective in their own specific regimes, each captures only one aspect of sample utility and lacks robustness across different pruning ratios or data distribution. In this work, we present a unified graph-based DP framework. By modeling the dataset as a weighted graph, where node weights encode intrinsic value and edge weights encode extrinsic value, DP can be cast as a Maximum Weight Clique Problem (MWCP). Although MWCP is NP-hard, its structure admits a principled greedy solution based on sample-wise marginal gains. Under a few mild conditions, we further prove that this unified objective enjoys a formal approximation guarantee, which applies to a broad family of importance metrics and provides practical design guidelines. Extensive experiments show that our method outperforms existing DP methods while substantially reducing training cost, reducing training time by over 40\% without sacrificing accuracy on ImageNet-1k with ResNet-50.

12.
arXiv (CS.CV) 2026-06-11

MFEN:Multi-Frequency Expert Network for Visible-Infrared Person Re-ID

Visible-infrared person re-identification (VI-ReID) is challenging due to the large modality discrepancy between visible and infrared images. We contend that this discrepancy is largely related to differing lighting conditions, including differences in light wavelength and light source type. Recently, frequency-based VI-ReID approaches have achieved notable success because frequency information can better extract identity-relevant contours and details while excluding irrelevant lighting and color. However, existing methods either do not distinguish different frequency bands or focus on only one band, which is insufficient under diverse lighting conditions. To perform comprehensive frequency domain learning, we propose a Multi-Frequency Expert Network (MFEN) that enables multi-frequency modulation and adaptively combines different bands through a mixture-of-experts design. We further introduce Random Frequency Augmentation (RFA) and Frequency Auxiliary Optimization (FAO) to better train MFEN. The three modules are complementary and jointly capture critical frequency-domain details for robust representation learning. Extensive experiments on three VI-ReID datasets demonstrate the effectiveness of our approach.

13.
arXiv (CS.AI) 2026-06-11

APPO: Agentic Procedural Policy Optimization

arXiv:2606.12384v1 Announce Type: cross Abstract: Recent advances in agentic Reinforcement Learning (RL) have substantially improved the multi-turn tool-use capabilities of large language model agents. However, most existing methods assign credit over coarse heuristic units, such as tool-call boundaries or fixed workflows, making it difficult to identify which intermediate decisions influence downstream outcomes. In this work, we study agentic RL from two perspectives: where to branch and how to assign credit after branching. Our pilot analysis shows that influential decision points are broadly distributed throughout the generated sequence rather than concentrated at tool calls, while token entropy alone does not reliably reflect their impact on final outcomes. Motivated by these observations, we propose Agentic Procedural Policy Optimization (APPO), which shifts branching and credit assignment from coarse interaction units to fine-grained decision points in the sequence. APPO selects branching locations using a Branching Score that combines token uncertainty with policy-induced likelihood gains of subsequent continuations, enabling more targeted exploration while filtering out spurious high-entropy positions. It further introduces procedure-level advantage scaling to better distribute credit across branched rollouts. Experiments on 13 benchmarks show that APPO consistently improves strong agentic RL baselines by nearly 4 points, while keeping efficient tool-calls and maintaining behavior interpretability.

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

Doeblin Curves

arXiv:2606.19859v1 Announce Type: cross Abstract: Recent research on Doeblin coefficients has shed light on their usefulness as a multi-way generalization of the Dobrushin contraction coefficient for TV distance, in a separate vein from their classic role in the theory of Markov chain ergodicity. However, strong conditions, such as being bounded away from 0, are typically necessary for Doeblin coefficients to establish the existence of information contraction. Building on recently formulated concepts of nonlinear information contraction, we aim to propose a finer-grained Doeblin-based characterization of multi-way contraction behavior which yields non-vacuous contraction guarantees even for channels whose Doeblin coefficient is 0. To this end, we introduce the notion of a Doeblin curve – a nonlinear function which quantifies the contraction behavior of a Markov kernel on collections of input distributions at specific levels of divergence and power. Through the course of our analysis, we develop a new variational characterization of Doeblin coefficients, present several properties of Doeblin curves, define several versions of power-constrained Doeblin curves, and derive upper and lower bounds using our aforementioned variational characterization. We then utilize these results in diverse areas, including generalization bounds for noisy iterative optimization, error bounds for reliable computation with noisy circuits, and differential privacy guarantees for online iterative algorithms. In particular, we extend results in these areas to broader domains or group settings, leveraging Doeblin curves to reveal finer-grained contraction phenomena than Doeblin coefficients.

15.
arXiv (quant-ph) 2026-06-16

A New Definition of Quantum Superposition

arXiv:2606.15607v1 Announce Type: new Abstract: The usual description of the superposition of two (pure quantum) states is ambiguous, since the binary operation of summation in a Hilbert space does not pass down to the quotient projective space. Even though Dirac noted this as early as 1930, it is often asserted that the superposition is a binary operation acting on two states with a value that is a unique state. The goal for this note is to motivate a rigorous, geometrical definition of the superposition of states in the setting of complex projective space, which has been argued elsewhere to be the natural geometric phase space for quantum theory. The upshot is that the new definition of the superposition of two pure states, viewed as two distinct points in the projective space, is the unique (complex) line on which those two points lie. Finally, a comparison is given between superposition and expansion in an orthonormal basis.

16.
medRxiv (Medicine) 2026-06-24

Development and Validation of Machine Learning Models for Predicting Initiation of Emergency Dialysis in Advanced Chronic Kidney Disease

Background: Initiation of emergency dialysis, often requiring temporary catheter owing to unprepared definitive vascular access, is associated with infectious and vascular complications and suggests advanced chronic kidney disease (CKD) care gaps. Previous studies focused on kidney failure or dialysis timing. This study aimed to predict initiation of emergency dialysis using machine learning and baseline data. Methods: This retrospective cohort study used the Japan Medical Data Center claims data (2014-2022). Adults with an estimated glomerular filtration rate (eGFR)

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

SHERLOC: Structured Diagnostic Localization for Code Repair Agents

LLM agents solve repository-level coding tasks through multi-turn tool use, but utilize half their budget on locating faults before editing. Dedicated localization frameworks have emerged, yet are still evaluated as file retrieval rather than actionable diagnosis, producing locations without the diagnostic context a repair agent needs. We introduce SHERLOC (Structured Hypothesis-driven Exploration and Reasoning for Localization), a training-free framework pairing a reasoning LLM with compact repository tools and self-recovery, without fine-tuning or multi-agent orchestration. SHERLOC reaches state-of-the-art localization across model scales: 84.33% accuracy@1 on SWE-Bench Lite and 81.27% recall@1 on SWE-Bench Verified; at ~30B parameters, it matches or outperforms other agentic methods. Injecting our locations and diagnostic findings into repair agents yields, on average, +5.95 pp resolve rate on SWE-Bench Verified while cutting localization and total tokens by 36.7% and 23.1%.

18.
arXiv (CS.CL) 2026-06-19

LaViSA: A Language and Vision Structural Ambiguity Benchmark

Structural ambiguity arises when a single sentence admits multiple valid interpretations due to its syntactic structure, posing a fundamental challenge for language understanding. Visual scenes serve as useful cues for resolving such ambiguity, and Vision and Language Models (VLMs) need to be capable of deriving possible semantic interpretations from visual scenes. We introduce Language and Vision Structural Ambiguity (LaViSA), a benchmark designed to evaluate the ability of VLMs to resolve structural ambiguity leveraging visual scenes. LaViSA consists of ambiguous sentences, their disambiguated sentences, and corresponding images of these disambiguated sentences across seven ambiguity categories. Using LaViSA, we conduct a comprehensive evaluation of diverse VLMs, including both proprietary and open-source models with varying parameter scales and reasoning capabilities. Experimental results show that although recent VLMs can leverage visual scenes to resolve structural ambiguity to a some extent, they still struggle with certain ambiguity types and visually subtle semantic distinctions, indicating remaining limitations in resolving structural ambiguity using visual scenes.

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

Let LLMs Judge Each Other: Multi-Agent Peer-Reviewed Reasoning for Medical Question Answering

Objective: To enhance the accuracy, interpretability, and robustness of large language models (LLMs) in medical question answering (MedQA). Method: We designed a multi-agent peer-reviewed reasoning method in which multiple LLM agents independently generate chain-of-thought reasoning with candidate answers, then act as peer reviewers to evaluate each other's reasoning for factual correctness and logical soundness. The highest-rated reasoning chain is selected to produce the final answer. Experiments were conducted with five state-of-the-art LLMs (Llama-3.1-8B, Qwen2.5-7B, Phi-4, DeepSeek-LLM-7B, GPT-oss-20B) on three benchmark datasets: HeadQA, MedQA-USMLE, and PubMedQA. Performance was compared against single-model chain-of-thought reasoning and chain-of-thought-based majority voting. Results: Peer-reviewed reasoning consistently outperformed both baselines. The best model combination achieved an average accuracy of 0.820 across datasets, exceeding the strongest single model (0.777) and majority voting ensembles (up to 0.789). The method also scaled effectively with more participating models, while peer assessments reliably distinguished high- from low-quality reasoning chains. Conclusion: The proposed multi-agent peer-reviewed reasoning method enables LLMs to act as both solvers and evaluators, yielding superior performance in MedQA. By emphasizing reasoning quality rather than answer agreement alone, this approach improves accuracy, interpretability, and robustness, offering a promising direction for trustworthy biomedical AI systems.

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

Appearance-Invariant Detection of Suggestive Motion via Laban Movement Descriptors

Content moderation in online multiplayer 3D virtual environments is increasingly automated, yet detection has focused on images, video, and audio, leaving suggestive motion a blind spot. We present a motion-only classification pipeline that detects suggestive and explicit movement from SMPL skeleton trajectories using Laban Movement Analysis (LMA) descriptors. On a dataset spanning everyday, artistic, suggestive, and explicit movement (17+ hours of video), a logistic regression trained on 61-feature LMA descriptors reaches 68% binary SFW/NSFW accuracy (70% random forest) under a leak-free evaluation protocol. At this level, our descriptor performs comparably to a learned video model trained on the same motion re-rendered as appearance-free video, a gray figure with no clothing, skin, or scene. The indirectness (tortuosity) of each joint's trajectory, measured as the ratio of the joint's path length to its net displacement, peaks at the suggestive tier, showing that the Direct-to-Indirect polarity of Laban's Space factor provides an interpretable marker of the shift from functional to suggestive motion. Ultimately, Laban-based kinematic descriptors offer a lightweight, interpretable approach to suggestive-motion detection: every decision decomposes into named, theory-grounded features. Because the classifier operates on pose trajectories alone, moderation can run directly on avatar poses in virtual environments, with no appearance data.

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

Hubs or Fringes: Pretraining Data Selection via Web Graph Centrality

The performance of modern language models depends critically on pretraining data composition. Yet existing data selection methods rely on auxiliary classifiers for document scoring or mixture optimization, adding computational overhead and dependence on labeled data. We propose WebGraphMix, a lightweight data selection framework that computes structural centrality scores over the Common Crawl host-level web graph and uses them to vary the proportion of central versus peripheral documents in the pretraining mixture. We hypothesize that central hosts expose models to reusable abstractions, while peripheral hosts encode specialized, long-tail knowledge. WebGraphMix computes centrality scores efficiently at web scale, requiring no model training, labeled data, or downstream supervision. We integrate WebGraphMix into the DataComp-LM pipeline and train models at 400M and 1B parameter scales with 8B and 28B tokens respectively, evaluating on 23 tasks ranging from factual knowledge to symbolic reasoning. Our experiments show that central and peripheral web regions encode complementary capabilities. Mixture combining both at a ratio of 1:1 achieves 41.4% on average, compared to 39.8% for uniform sampling. Combining structural scores with document-level quality classifier scores further improves performance to 43.8%. These findings demonstrate that web graph topology is a meaningful axis for pretraining data curation, capturing information that is largely orthogonal to existing content-based approaches.

22.
arXiv (CS.AI) 2026-06-16

TNODEV: Toolbox for Neural ODE Verification

arXiv:2606.16567v1 Announce Type: new Abstract: Neural ordinary differential equations (neural ODE) have started to appear in safety critical settings such as continuous-time controllers for cyber-physical systems and classifiers integrated into automated decision pipelines, raising the question of whether their behavior can be formally verified. Existing tools dedicated to neural ODE provide only a single reachability call without iterative input set refinement, limiting the precision of their verdicts to whatever one reachability call can deliver. We present TNODEV, the first sound formal verifier for neural ODE that integrates a falsification checker, a fast interval-based reachability backend based on continuous-time mixed monotonicity, a verification and refinement loop with three input-set splitting heuristics, and a parallel scheduler in a single end-to-end pipeline. TNODEV supports safe-set inclusion verification on pure neural ODE, neural ODE in closed loop with a neural network controller and general neural ODE (GNODE), with the safe set specified either as an interval or as the half-space intersection induced by a target classification label. We evaluate TNODEV on a range of benchmarks across safe-set inclusion and classification-robustness properties, including a direct reachability comparison against NNV~2.0 and CORA and a verification comparison against NNV2.0 on MNIST general neural ODE classifiers.

23.
arXiv (CS.CV) 2026-06-25

UniTeD: Unified Temporal Diffusion for Joint Perception and Planning in Autonomous Driving

Diffusion models have shown strong potential for multi-modal planning in end-to-end autonomous driving. However, most existing methods confine diffusion to the planning module, conditioning on fixed outputs from separate discriminative perception networks. This decoupled design propagates perception errors to the planner, increasing optimization difficulty and reducing robustness. To overcome these limitations, we propose UniTeD, a Unified Temporal Diffusion framework that jointly models perception and planning through iterative denoising in a shared generative space. By enabling bidirectional information exchange, the framework facilitates mutual refinement between tasks and improves robustness via noise-conditioned multi-task training. We further extend this unified diffusion paradigm to a streaming setting by incorporating temporal context. A Temporal Transition Module (TTM) is introduced to resolve the noise-level mismatch between historical and current frames. In addition, we propose an Anchor Refresh Strategy (ARS) to alleviate the training-inference distribution shift commonly observed in sparse diffusion-based end-to-end driving frameworks. Without bells and whistles, UniTeD achieves state-of-the-art performance across multiple benchmarks, surpassing both recent discriminative end-to-end methods and diffusion-based planning approaches.

24.
bioRxiv (Bioinfo) 2026-06-18

A unified smoothing framework for protein domain bigram model

Biomolecular sequences can be represented as strings over an alphabet, an analogy that has motivated many applications of computational linguistic techniques to biological problems. However, such methods must be adapted to the characteristic scale and organization of biomolecular data. Here, we consider the problem of bigram smoothing for multidomain protein architectures, where domain bigram frequency data is extremely sparse and differs from textual data in alphabet size, string length distribution, the relationship between bigram and unigram frequencies, tandem repeat lengths, and the distribution of domain adjacencies. Moreover, some domain combinations are unobserved because they are biologically incompatible, others because the data are incomplete. A smoothing method that distinguishes these two cases is required. We propose a unified smoothing framework based on interpolation that can be tuned to accommodate different bigram data characteristics. Within this framework, we design specific model variants suited to protein domain bigram data: these assign low adjusted counts to pairs that are likely incompatible, while making appropriate adjustments for undersampled pairs. We demonstrate empirically that this approach distinguishes the two cases while preserving the characteristic signatures of multidomain data.

25.
arXiv (math.PR) 2026-06-12

Temporal Conductance and Bounds on the Voter Model for Dynamic Networks

arXiv:2606.13374v1 Announce Type: cross Abstract: The voter model is a classical stochastic process that models how opinions might spread through a network: at each step, every node lazily adopts the opinion of a random neighbour; eventually all nodes share the same opinion (consensus). Stronger connectivity should yield faster consensus. Berenbrink, Giakkoupis, Kermarrec, and Mallmann-Trenn (ICALP 2016) make this precise via the network's conductance: if the network has $m$ edges, minimum degree $d_{\min}$, and conductance at least $\phi$, then the voter model reaches consensus in expected $O(m/(d_{\min}\phi))$ steps. Their results extend to dynamic networks with fixed vertex degrees by considering the network's conductance at each time step. We introduce temporal conductance $\Phi$, a more general connectivity measure for dynamic networks. Unlike static conductance, which collapses to $0$ whenever some snapshot is disconnected, $\Phi$ captures connectivity through edges that appear at different times. We generalise the results of Berenbrink et al. from static conductance to temporal conductance, showing that the expected consensus time of the standard voter model is at most $O(m/(d_{\min}\Phi))$. Moreover, we prove that this bound is tight up to constant factors. We expect temporal conductance to be a useful primitive for analysing other dynamics on temporal networks, and potentially time-inhomogeneous Markov chains more generally.