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版本更新 · v3arXiv:2504.08639

Constructing Witnesses for Lower Bounds on Behavioural Distances

Ruben Turkenburg, Harsh Beohar, Franck van Breugel, Clemens Kupke, Jurriaan Rot

原文摘要

Behavioural distances provide a robust alternative to notions of equivalence such as bisimilarity in the context of probabilistic transition systems. They can be defined as least fixed points, whose universal property allows us to exhibit upper bounds on the distance between states, showing them to be at most some distance apart. In this paper, we instead consider the problem of bounding distances from below, showing states to be at least some distance apart. Contrary to upper bounds, it is possible to reason about lower bounds inductively. We exploit this by giving an inductive derivation system for lower bounds on an existing definition of behavioural distance for labelled Markov chains. This is inspired by recent work on apartness as an inductive counterpart to bisimilarity. Proofs in our system will be shown to closely match the behavioural distance by soundness and (approximate) completeness results. We further provide a constructive correspondence between our derivation system and formulas in a modal logic with quantitative semantics. This logic was used in recent work of Rady and van Breugel to construct evidence for lower bounds on behavioural distances. Our constructions provide smaller witnessing formulas in many examples.

cs.LO

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2603.15300

GATE-AD: Graph Attention Network Encoding For Few-Shot Industrial Visual Anomaly Detection

Aggelos Psiris, Yannis Panagakis, Maria Vakalopoulou, Georgios Th. Papadopoulos

原文摘要

Few-Shot Industrial Visual Anomaly Detection (FS-IVAD) is a critical task in modern manufacturing, where automated product inspection systems must identify rare defects using only a handful of normal, defect-free training samples. Existing approaches typically model normality by assessing each patch largely through its individual appearance, e.g., through similarity to stored normal features, reconstruction from support samples, or distance from a learned normal representation. This paper introduces GATE-AD, whose key contribution is to instead model few-shot normality through local contextual relations: a patch is considered normal when it can be consistently recovered from its learned dependencies with its spatial neighbors. To realize this formulation, frozen self-supervised ViT patch tokens are organized on a spatial neighbor graph and processed by a Graph Attention Network (GAT), while representation alignment and a Scaled Cosine Error (SCE) objective enable reconstruction-based anomaly scoring. Node masking and attention dropout further regularize learning in the low-shot regime. On MVTec AD, VisA, and MPDD, GATE-AD achieves strong detection and localization performance across $1$- to $8$-shot settings, attaining the highest image-level AUROC in $10$ of $12$ settings and the highest image-level AP in $8$ of $12$ settings under a unified evaluation protocol, while also achieving the lowest inference latency among the compared methods. In order to facilitate reproducibility and further research, the source code of GATE-AD is available at https://github.com/gthpapadopoulos/GATE-AD.

cs.CV

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2606.18157

Reducing Prize-Collecting Stroll and Related Routing Problems to Prize-Collecting TSP

Hong Li

原文摘要

We consider prize-collecting variants of the metric traveling salesperson problem (TSP). The prize-collecting stroll problem (PCS) is the path version of the prize-collecting TSP (PCTSP). Given a complete metric graph, two distinct prescribed terminal vertices $s,t$, and nonnegative penalties on vertices, PCS asks for an $s$-$t$ tour minimizing its length plus the total penalty of vertices that are not visited by it. We study a common generalization of PCTSP, PCS, and several related prize-collecting routing problems, which we call the prize-collecting $Φ$-TSP. In this model, an interface $Φ$ specifies a set of prescribed vertices together with their parity and connectivity requirements. We show that, if a polynomial-time $ρ$-approximation algorithm for PCTSP is available, then, for every fixed $\varepsilon>0$, there is a polynomial-time $(ρ+\varepsilon)$-approximation algorithm for the prize-collecting $Φ$-TSP when the number of prescribed vertices is bounded by a fixed constant. Consequently, PCS can be approximated as well as PCTSP up to an arbitrarily small additive loss, closing the gap between the best-known approximation guarantees for the two problems.

cs.DS

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2610.11991

Quantitative Verification of Infinite-State Networks

Dhruv Nevatia, David Basin

原文摘要

Many network protocols and distributed systems combine recursion, unbounded local state, and quantitative behaviour such as cost, latency, or reliability. Existing decidability results for networks of pushdown systems are largely qualitative, and do not extend to quantitative analyses, which must jointly track traces and weights. We present a framework for the quantitative verification of acyclic networks of weighted pushdown systems. Finitely summarising a recursive network component requires collapsing the infinite family of runs obtained by pumping its nested loops, and doing so exactly, rather than by over-approximation, is a standing difficulty. We give a class of weight domains where this is possible: pumping semirings, those in which the weights accumulated by such a family collapse to a closed form; informally, the domain must be unable to count iterations. The class admits domains with infinite ascending chains, such as the arctic semiring and downward-closed languages. Over these, we give a terminating saturation algorithm computing quantitative reachability exactly, resting on two ideas: segment tree algebras, a compositional representation of runs, and thermal extensions, which symbolically separate accelerated weights so that further acceleration remains exact. We use this to compute upward and downward closures of context-free languages uniformly, and to lift the algorithm to acyclic networks over "thin" pumping semirings, yielding the first quantitative safety and reachability analyses for networks of pushdown systems.

cs.FL · cs.LO · cs.PL

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2605.15906

A Causally Grounded Taxonomy for Image Degradation Robustness Evaluation

Stefan Becker, Simon Weiss, Wolfgang Hübner, Michael Arens

原文摘要

Image degradations arise throughout acquisition, processing, and transmission, altering both visual appearance and downstream machine-perception performance. They are studied across synthetic corruption benchmarks, perceptual image quality assessment (IQA), low-level vision, and physically grounded imaging-system analysis. However, these communities rely on incompatible grouping schemes and backend-specific severity definitions, making results difficult to compare across datasets, degradation models, and tasks. We propose a causally grounded framework for organizing and interpreting image degradations. Rather than introducing new degradations or redefining existing benchmarks, we provide an interpretive representation and measurement layer that makes implicit assumptions explicit. Each degradation is characterized by two orthogonal axes: its dominant causal source in the imaging pipeline and its dominant perceptual effect. This dual-axis abstraction yields a compact taxonomy spanning algorithmic corruptions, perceptual distortions, low-level imaging artifacts, and physically motivated camera or system failures. To make severity semantics observable without modifying existing implementations, we quantify each native severity level using full-reference image quality metrics: PSNR, SSIM, and LPIPS. This separates causal origin, perceptual appearance, measured distortion strength, and downstream task impact while preserving native parameterizations. We demonstrate the framework through COCO-Degradation, a taxonomy-aligned benchmark for evaluating object detector robustness under diverse low-level imaging conditions. By connecting causal source, perceptual effect, and measured severity, the proposed framework supports more interpretable and reproducible evaluation of how low-level visual degradations affect machine perception.

cs.CV

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2607.29549

AMTFV: Agentic Mathematical Tool-Flow Verification for LLM Self-Correction

Rui Zou, Yutao Zhu, Mengqi Wei, Ji-Rong Wen

原文摘要

Large language models have demonstrated strong mathematical problem-solving capabilities, yet reliably verifying their candidate answers remains challenging. Existing representative methods mainly revise outputs through natural-language reflection or assist verification by directly generating verification programs; the former may not reliably support exact computation, whereas the latter prematurely couples mathematical modeling with low-level implementation. We propose AMTFV (Agentic Mathematical Tool-Flow Verification). By introducing Mathematical Tool Flow (MTF) as an interrupt--execute--resume interface, AMTFV decouples verification modeling from concrete execution and supports exact computation through a mathematical toolbox. Specifically, the verification agent first constructs a verification workflow, encodes the mathematical objects and computational intent requiring reliable execution in an MTF request, and sends it to the mathematical toolbox agent. The latter parses the request, generates executable calls, and dispatches them to the backend for exact computation. Tool outputs then support candidate-answer adjudication, answer revision, and verification-workflow revision. We evaluate AMTFV on five challenging mathematical reasoning datasets with seven model configurations from DeepSeek, GPT, and Gemini. Experimental results show that AMTFV outperforms the representative baselines evaluated in this study overall; under an individual model configuration, it improves average accuracy over the strongest baseline by up to 8.3 percentage points, with larger gains on samples of medium and high verification complexity.

cs.AI

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2310.01830

AI-Generated Images as Data Source: The Dawn of Synthetic Era

Zuhao Yang, Yu Wei, Fangneng Zhan, Kunhao Liu, Muyu Xu, Xiaoqin Zhang, Ling Shao, Shijian Lu

原文摘要

The advancement of visual intelligence is intrinsically tethered to the availability of large-scale data. In parallel, generative Artificial Intelligence (AI) has unlocked the potential to create synthetic images that closely resemble real-world photographs. This prompts a compelling inquiry: how much visual intelligence could benefit from the advance of generative AI? This paper explores the innovative concept of harnessing these AI-generated images as new data sources, reshaping traditional modeling paradigms in visual intelligence. In contrast to real data, AI-generated data exhibit remarkable advantages, including unmatched abundance and scalability, the rapid generation of vast datasets, and the effortless simulation of edge cases. Built on the success of generative AI models, we examine the potential of their generated data in a range of applications, from training machine learning models to simulating scenarios for computational modeling, testing, and validation. We probe the technological foundations that support this groundbreaking use of generative AI, engaging in an in-depth discussion on the ethical, legal, and practical considerations that accompany this transformative paradigm shift. Through an exhaustive survey of current technologies and applications, this paper presents a comprehensive view of the synthetic era in visual intelligence. A project associated with this paper can be found at https://github.com/mwxely/AIGS .

cs.CV

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2510.20608

Convergence Analysis of SGD under Expected Smoothness

Yuta Kawamoto, Hideaki Iiduka

原文摘要

Stochastic gradient descent (SGD) is the workhorse of large-scale learning, yet classical analyses rely on assumptions that can be either too strong (bounded variance) or too coarse (uniform noise). The expected smoothness (ES) condition has emerged as a flexible alternative that ties the second moment of stochastic gradients to the objective value and the full gradient. This paper presents a self-contained convergence analysis of SGD under ES. We (i) refine ES with interpretations and sampling-dependent constants; (ii) derive bounds of the expectation of squared full gradient norm; and (iii) prove sublinear convergence rates with explicit residual errors for various step-size schedules. Furthermore, we empirically validate our theoretical framework by training a ResNet-18 model on the CIFAR-100 dataset. We uncover a two-phase dynamic in the gradient noise structure, transitioning from a suboptimality-dominated regime to a geometry-dominated regime. Our treatment unifies and extends recent theoretical threads in the literature.

cs.LG

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2512.17473

Alternating Direction Method of Multipliers for Nonlinear Matrix Decompositions

Atharva Awari, Nicolas Gillis, Arnaud Vandaele

原文摘要

We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD). Given an input matrix $X \in \mathbb{R}^{m \times n}$ and a factorization rank $r \ll \min(m, n)$, NMD seeks matrices $W \in \mathbb{R}^{m \times r}$ and $H \in \mathbb{R}^{r \times n}$ such that $X \approx f(WH)$, where $f$ is an element-wise nonlinear function. We evaluate our method on several representative nonlinear models: the rectified linear unit activation $f(x) = \max(0, x)$, suitable for nonnegative sparse data approximation, the component-wise square $f(x) = x^2$, applicable to probabilistic circuit representation, and the MinMax transform $f(x) = \min(b, \max(a, x))$, relevant for recommender systems. The proposed framework flexibly supports diverse loss functions, including least squares, $\ell_1$ norm, and the Kullback-Leibler divergence, and can be readily extended to other nonlinearities and metrics. We illustrate the applicability, efficiency, and adaptability of the approach on real-world datasets, highlighting its potential for a broad range of applications.

eess.SP · cs.LG · math.OC · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2602.18394

Self-Aware Object Detection via Degradation Manifolds

Stefan Becker, Simon Weiss, Wolfgang Hübner, Michael Arens

原文摘要

Object detectors achieve strong performance under nominal imaging conditions but can fail silently when exposed to blur, noise, compression, adverse weather, or resolution changes. In safety-critical settings, it is therefore insufficient to produce predictions without assessing whether the input remains within the detector's nominal operating regime, which we refer to as self-aware object detection. We introduce a degradation-aware framework based on degradation manifolds, which structure a detector's feature space according to image degradation rather than semantic content. Our method augments a standard detection backbone with a lightweight embedding head trained via multi-layer contrastive learning, where images sharing the same degradation composition are pulled together while differing configurations are separated. Unlike prior contrastive IQA approaches, our method performs detector-aligned input-fidelity monitoring: it uses task-backbone features and a nominal prototype to detect degradation-induced shifts, rather than estimating perceptual image quality in a standalone representation. To anchor the representation, we estimate a pristine prototype from clean training embeddings, defining a nominal operating point in feature space. Self-awareness is then derived as geometric deviation from this reference, providing an intrinsic image-level signal of degradation-induced shift that is independent of detection confidence. Experiments on synthetic corruptions, cross-dataset zero-shot transfer, and natural weather-induced shifts show strong pristine-degraded separability, consistent behavior across detector architectures, and robust generalization across datasets with substantial content variation. These results suggest that degradation-aware detector representations provide a reliable signal for monitoring input-fidelity shifts.

cs.CV

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2510.00666

Blind Image Restoration via Merging the Manifold Hypothesis, Kernel Method and a Diffusion-like Flow

Leah Bar, Liron Mor Yosef, Shai Zucker, Neta Shoham, Inbar Seroussi, Nir Sochen

原文摘要

Blind Image Restoration (BIR) aims to restore degraded images without knowledge of either the type or severity of the degradation. This is a challenging ill-posed inverse problem for which an image prior is essential. We view the prior of an image class as a probability distribution supported on a low-dimensional manifold embedded in the high-dimensional image space. Existing generative approaches primarily model the probability distribution, while the geometric structure is implicit or disregarded. Conversely, geometric approaches do not account for the non-uniform probability distribution on the manifold. We propose a geometric-probabilistic framework for BIR that models these aspects. The probability distribution on the manifold is approximated using a kernel-based method, while a distance from the manifold function induces a geometry-based probability function on the ambient space. This formulation leads to the (Latent) Manifold-Probabilistic Projection Model ((L)MPPM), a restoration model defined in both image and latent spaces. (L)MPPM induces a flow guided by a score field that jointly incorporates geometric and probabilistic information. Evaluated on image restoration tasks and datasets, (L)MPPM consistently outperforms existing approaches, providing empirical evidence for the benefit of incorporating both geometric and probabilistic information into the image prior.

cs.CV · cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2607.27277

Complexity of Strong Popularity in Hedonic Games

Matan Gilboa

原文摘要

In a hedonic game, agents are partitioned into coalitions and have preferences over the coalitions they may join. A partition is called strongly popular if it strictly beats every other partition in a majority vote among the agents. We study the complexity of determining the existence of strongly popular partitions in two fundamental classes of hedonic games: additively separable and fractional hedonic games (ASHGs and FHGs), where agents' utilities are determined, respectively, by the sum and average of their valuations for the members of their coalitions. We prove that this problem is PCW-complete for ASHGs and for FHGs even with non-negative valuations, where PCW is a subclass of $Σ^P_2$ associated with unambiguous problems (which have at most one witness), recently introduced by Gilboa et al. (2025). These are the first natural complete problems for PCW, in the sense that their formulations do not involve arbitrary Boolean circuits. Our results resolve open problems posed by Brandt and Bullinger (JAIR 2022) and Bullinger and Gilboa (IJCAI 2025). The two reductions employ substantially different techniques, reflecting both the distinct utility models and the stringent non-negativity constraint in FHGs. Furthermore, in contrast with FHGs, we show that in ASHGs restricting valuations to be non-negative makes the problem polynomial-time solvable.

cs.GT · cs.CC

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2605.11953

PROTECT-DB: Protecting Data using Replicated State Machines: Efficient Corruption Detection & Recovery

Anant Utgikar, S. Sudarshan

原文摘要

Data is critical for the operation of any organization and needs to be protected, especially against attacks that compromise the state of the database. In this paper, we explore an approach based on Byzantine-fault tolerant replicated state machines, built on top of a deterministic extension of PostgreSQL. Each replica deterministically executes transactions recorded in a shared log/blockchain. Our focus is on creating a practical system that is designed for efficient and quick detection of corruption, as well as quick repair concurrent with execution of transactions. We also present a performance study showing the efficiency and practicality of our approach. We believe our work lays the foundations for the practical use of the BFT replicated state machine approach in the context of databases.

cs.DB · cs.CR

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2601.20983

Monotone Optimisation with Learned Projections

Ahmed Rashwan, Keith Briggs, Chris Budd, Lisa Kreusser

原文摘要

Optimisation algorithms typically assume oracle access to objectives and constraints, yet in many applications these functions are available only through data. To recover them, a common approach learns a surrogate for each function and optimises over it, but this can be unnecessarily expensive and may fail to preserve the structure required by the optimisation algorithm. We study this problem for monotone optimisation, a class of non-convex problems which can be solved globally using the Polyblock Outer Approximation (POA) algorithm. Our key observation is that POA does not require the constraint functions themselves, but only a scalar quantity we call the radial inverse. Learning this quantity directly replaces POA's inner bisection loop over a learned constraint with a single radial inverse evaluation. We characterise exactly which maps arise as radial inverses of monotone constraints, and relate their approximation error to perturbations of the feasible set and optimal objective value. Building on these results, we introduce Homogeneous-Monotone Radial Inverse (HM-RI) networks, structured min-max models that enforce the monotonicity and positive-homogeneity of radial inverses by construction. Across synthetic monotone optimisation problems and a cellular transmit-power application, HM-RI improves solution quality over direct constraint surrogates and local optimisation baselines by up to 58.6 percentage points relative to the Oracle reference objective, while achieving a 3.0-4.7x speed-up over bisection-based POA with learned constraint surrogates, with the largest solution-quality gains occurring in data-limited and piecewise-constant settings.

cs.LG · math.OC

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2607.19266

Toward Auditable Fraud Detection: Combining Graph Features, Model Explanations, and Agentic Case Investigation

Rahil Sharma

原文摘要

Fraud detection systems must scale with rising transaction volume while remaining explainable and reviewable. We study a layered pipeline on the PaySim dataset that combines a gradient-boosted classifier, graph-derived structural features, an autoencoder-based anomaly signal, TreeSHAP explanations, and a bounded LLM investigation agent applied to cases the classifier scores uncertainly. Before any model comparison, we identify and remove a simulator-specific balance shortcut that would otherwise inflate baseline performance. After this correction, neither the graph features nor the anomaly signal improves Average Precision on the full test set. Both, however, rank fraud better within the subset of cases receiving intermediate baseline scores. In a controlled experiment with injected multi-account fraud rings, engineered structural features recover all injected test transactions, while the tabular baseline misses roughly a quarter of them. The investigation agent underperforms direct thresholding of the classifier it relies on, reaching 65.0% accuracy against 71.7% on a balanced 60-case sample, despite having access to model explanations, graph context, and retrieved reference cases. Of the eight decisions the agent changed, six replaced correct classifier outputs with errors, and it produced a coherent written rationale in each case. An exploratory disagreement-based escalation rule flagged two of these agent errors for human review without flagging any correct decision. We conclude that each component of a layered fraud system contributes only under specific conditions, and that a plausible rationale from an investigation agent is not evidence of a better decision.

cs.LG · cs.AI

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2607.04689

RCT-AD: Reliability-Aware Context and Temporal BEV Reasoning for End-to-End Autonomous Driving

Argho Dey, Yunfei Yin, Swachha Ray, Md Minhazul Islam, Zheng Yuan, Sijing Xiong, Hongyu Liu, Zhiqiu Huang

原文摘要

Reliable temporal representation learning is important for end-to-end autonomous driving, particularly when visual observations are degraded by occlusion, motion blur, illumination variation, and sensor noise. Existing Bird's-Eye-View (BEV) approaches provide a unified representation for perception and planning; however, temporal features are commonly aggregated across frames without explicitly accounting for the reliability of individual observations. Consequently, low-quality or inconsistent features may propagate through temporal representations and degrade downstream perception, prediction, and planning. To address this problem, we propose RCT-AD, a Reliability-Aware Context and Temporal BEV Reasoning framework for end-to-end autonomous driving that explicitly models feature reliability and temporal consistency within a shared BEV representation. RCT-AD introduces a Reliable Context Awareness (RCA) module that estimates frame-level reliability using spatial, semantic, temporal, and visual-quality cues, and selectively preserves trustworthy information through a reliability-guided temporal memory mechanism. When the current observation is unreliable, historical high-reliability features are aligned and integrated to construct a more stable temporal BEV representation. A Temporal Trajectory Planner models long-term temporal dependencies and multi-agent interactions, while semantic segmentation and motion-guided detection provide complementary supervision for refining the shared BEV representation. Experiments on the nuScenes benchmark demonstrate consistent improvements across perception, motion prediction, and trajectory planning. RCT-AD achieves 61.5 NDS, 52.9 mAP, and 52.3 mIoU while maintaining competitive computational efficiency. These results demonstrate the effectiveness of reliability-aware temporal BEV reasoning for unified perception, prediction, and planning.

cs.RO · cs.CV

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2605.05877

Understanding Simulated Annealing: from Weak Poincaré Inequalities to a Discrete Optimal Transport Framework

Yuchen He, Tianhui Jiang, Zhehan Lei, Sihan Wang, Chihao Zhang

原文摘要

Simulated annealing follows a path of distributions from an easy initial law to a target. Standard analyses require rapid mixing at every fixed temperature, which can fail for multimodal targets even when annealing succeeds. Motivated by the continuous optimal-transport analysis of annealed Langevin dynamics by Guo, Tao, and Chen (ICLR 2025), we develop a discrete optimal-transport framework for finite-state annealing. The discrete action of the path integrates the minimum electrical energy needed to route the demand $-\partial_sπ_s$ through the chain's transition capacities. Like a path-dependent inverse conductance, it penalizes a bottleneck only when the path must move mass across it. We also introduce weak action, which leaves an $\varepsilon$ amount of this motion unrouted. Up to initialization error, action $\mathcal A$ gives reverse-KL error at most $\mathcal A/(4T)$ after $T$ expected updates, while weak action gives TV error at most $\varepsilon+\sqrt{\mathcal A^{w}_\varepsilon/(8T)}$. Paralleling canonical paths and Poincaré inequalities, we develop flow and spectral bounds, showing that pathwise (weak) Poincaré inequalities imply (weak) action bounds. We also show that a weak Poincaré inequality yields a genuine one after removing a small amount of mass. As a pathwise analogue of chain decomposition, we obtain a componentwise algorithm for mixtures with phase weights supplied at initialization. Applications include mean-field Ising and Potts models and bipartite spin systems. For every fixed $δ>0$, we give a polynomial-time single-site annealing sampler for uniform independent sets in $(d,D)$-biregular bipartite graphs with $D/d\geq1+δ$ and large $D$. To our knowledge, this is the first polynomial-time sampler requiring only a fixed multiplicative degree imbalance, strictly extending the $D\geq7d\log d$ regime of Cannon and Perkins (SODA 2020).

cs.DS · math.PR

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2510.10648

JND-Guided Light-Weight Neural Pre-Filter for Perceptual Image Coding

Yangyang Wu, Chenlong He, Yuanheng Chen, Yibo Fan

原文摘要

Just Noticeable Distortion (JND)-guided pre-filter is a promising technique for improving the perceptual compression efficiency of image coding. However, existing methods are often computationally expensive, and the field lacks standardized benchmarks for fair comparison. To address these challenges, this paper introduces a twofold contribution. First, we develop and open-source FJNDF-Pytorch, a unified benchmark for frequency-domain JND-Guided pre-filters. Second, leveraging this platform, we propose a complete learning framework for a novel, lightweight Convolutional Neural Network (CNN). Experimental results demonstrate that our proposed method achieves state-of-the-art compression efficiency, consistently outperforming competitors across multiple datasets and encoders. In terms of computational cost, our model is exceptionally lightweight, requiring only 7.15 GFLOPs to process a 1080p image, which is merely 14.1% of the cost of recent lightweight network. Our work presents a robust, state-of-the-art solution that excels in both performance and efficiency, supported by a reproducible research platform. The open-source implementation is available at https://github.com/viplab-fudan/FJNDF-Pytorch.

eess.IV · cs.CV · cs.MM

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.20619

pcNN-SN: a physics-enhanced predictor-corrector neural network algorithm coupled with the discrete ordinates method for neutron transport equations

Cong Liu, Junxia Wei, Shuai Wang, Heng Yong

原文摘要

Super-resolution machine learning methods hold promise for addressing the high computational costs associated with high-dimensional features in traditional transport simulations. This paper proposes a physics-enhanced neural network coupling algorithm for discrete ordinates (SN) transport calculations. Based on high- and low-accuracy data, we develop a predictor-corrector neural network (pcNN) to predict correction factors for coarse-grid solutions. Based on transport equations, local physical features containing subgrid-scale information are selected as network inputs. Dimensionless transformation of physical quantities reduces the input space dimensionality and narrows the range of parameter distributions, thereby facilitating network training. Physical constraints are incorporated into the network model, and the corrected solution retains its original conservation properties. pcNN and SN transport sweeps are internally coupled, and numerical solutions are corrected online. Numerical results demonstrate that this algorithm can effectively improve coarse-grid solutions to achieve a level of accuracy comparable to that of fine-grid results. The physics-based network design enables the model to demonstrate a certain degree of reusability under different computational conditions. Compared to mesh refinement, the pcNN-SN algorithm reduces the computation time for the three-dimensional test problems by more than 60%.

physics.comp-ph · cs.LG

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2609.34660

Rewarding Novel Deductions: Solver-guided Process Supervision for Logical Reasoning

Muhammad Asif Ali, Wenqing Wang, Huan Wang, Mohammad Raza

原文摘要

Logical reasoning remains a major challenge for large language models (LLMs), particularly on structured problems that require precise constraint tracking, consistency preservation, and multi-step deduction. This challenge is especially acute for small-scale LLMs, which are more prone to producing inconsistent, redundant, or brittle reasoning trajectories. Existing approaches for improving logical reasoning largely optimize for final-answer correctness, providing only weak supervision over the intermediate reasoning process. In this work, we propose SPRING: (Solver-guided Process Rewards for Novel LogIcal ReasoNing Step Generation). SPRING uses an SMT solver as a training-time verifier of intermediate reasoning steps to provide process-level supervision. It introduces the notion of a novel reasoning step, namely, a step that is logically valid, consistent with the evolving reasoning state, and not already implied by previously accepted non-contradictory deductions. Based on this solver-based assessment, it designs process rewards that encourage novel inferential progress while penalizing contradictory and uninformative reasoning steps. Evaluation across three logical reasoning benchmarks: ZebraLogic, AR-LSAT, and Knights and Knaves, and four LLMs shows that SPRING consistently outperforms base LLMs, outcome-only reward baselines, and Logic-LM. On ZebraLogic, SPRING improves puzzle accuracy by up to 49.71 and 15.43 points over the base LLM and strongest outcome-only baseline, respectively. On AR-LSAT, it improves overall accuracy by up to 64.43 and 11.39 percentage points over the base LLM and strongest outcome-only baseline, respectively. On Knights and Knaves, SPRING achieves up to 93.14 puzzle accuracy and 96.05 person accuracy.

cs.CL

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2603.14094

Maximin Robust Bayesian Experimental Design

Hany Abdulsamad, Sahel Iqbal, Christian A. Naesseth, Takuo Matsubara, Adrien Corenflos

原文摘要

We address the brittleness of Bayesian experimental design under model misspecification by formulating the problem as a max--min game between the experimenter and an adversarial nature subject to information-theoretic constraints. We demonstrate that this approach yields a robust objective governed by Sibson's $α$-mutual information~(MI), which identifies the $α$-tilted posterior as the robust belief update and establishes the Rényi divergence as the appropriate measure of conditional information gain. To mitigate the bias and variance of nested Monte Carlo estimators needed to estimate Sibson's $α$-MI, we adopt a PAC-Bayes framework to search over stochastic design policies, yielding rigorous high-probability lower bounds on the robust expected information gain that explicitly control finite-sample error.

stat.ML · cs.LG · math.ST · stat.CO · stat.ME

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2606.21023

Demystifying Numerical Instability in LLM Inference: Achieving Reproducible Inference for Mission-Critical Tasks with HEAL

Zhenting Zhu, Lucas Thai, Shan Yu, Yicheng Liu, Yifan Qiao, Chenxi Wang, Harry Xu, Junyi Shu

原文摘要

As Large Language Models (LLMs) deploy into mission-critical domains (e.g., finance, medicine, and law), output reproducibility has become a strict system requirement. While practitioners use greedy decoding to eliminate algorithmic stochasticity, empirical deployments with 16-bit precisions still exhibit catastrophic output divergence across heterogeneous GPUs. Through SASS-level profiling, we reveal that this inconsistency is fundamentally driven by truncation errors introduced during downcasting at kernel boundaries. However, achieving reproducibility via a global FP32 pipeline incurs prohibitive system penalties: bypassing 16-bit hardware accelerators hurts compute efficiency, while upcasting the KV cache doubles memory overhead. To bridge this gap, we propose Hybrid Error ALleviation (HEAL), a targeted intervention that approximates FP32 precision while resolving hardware constraints through two targeted mechanisms. First, recognizing that floating-point formats underutilize their bit-width for Q, K, V tensors, HEAL applies INT16 quantization that preserves numerical stability without expanding the KV cache footprint. Second, HEAL synthesizes high-precision matrix multiplications via an algebraic error compensation strategy, executing entirely on high-throughput 16-bit Tensor Cores. To evaluate our approach practically, we introduce MCR-Bench, a benchmark targeting reproducibility in mission-critical tasks. HEAL achieves the same level of reproducibility on downstream tasks as the FP32 baseline while reducing the performance overhead by up to 6.0$\times$.

cs.LG

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2611.07644

Neural Image Compression with Internal-External Prior Fusion and Alignment

Tiancheng Si, Wenlong Xu, Dahua Gao

原文摘要

Existing context models for learned image com- pression rely primarily on internal priors from the current image, overlooking common patterns and typical textures shared across natural images. To address this limitation, we propose an Internal-External Prior Fusion-Alignment (IE-PFA) context model built upon quadtree spatial-channel joint modeling, where a learnable dictionary shared by the encoder and decoder serves as an external prior. Specifically, an RWKV-based Spatial- Channel Prior Fusion (RSCPF) module efficiently fuses inter- nal and external priors along spatial and channel dimensions with linear complexity, while a training-only Self-Distilled Prior Alignment (SDPA) mechanism aligns them without inference overhead. Moreover, our model supports variable-rate coding over 64 quality levels within a single network and is accelerated by custom CUDA operators. Experiments on seven benchmarks demonstrate state-of-the-art rate-distortion performance, achiev- ing an average BD-Rate saving of 21.65% over VTM-22.0-Intra, with only 29.9M parameters and the fastest coding speed among advanced neural codecs (61 ms encoding and 52 ms decoding). Code is available at https://github.com/stcnjtech/DCVC-X-Intra.

cs.CV · cs.AI

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2605.12683

Parallel-in-Time Training of Recurrent Neural Networks for Dynamical Systems Reconstruction

Florian Hess, Florian Götz, Daniel Durstewitz

原文摘要

Reconstructing nonlinear dynamical systems (DS) from data (DSR) is a fundamental challenge in science and engineering, but it inherently relies on sequential models. Recent breakthroughs for sequential models have produced algorithms that parallelize computation along sequence length $T$, achieving logarithmic time complexity, $\mathcal{O}(\log T)$. Since sequence lengths have been practically limited due to the linear runtime complexity $\mathcal{O}(T)$ of classical backpropagation through time, this opens new avenues for DSR. This paper studies two prominent classes of parallel-in-time algorithms for this task, both of which leverage parallel associative scans as their core computational primitive. The first class comprises models with linear yet non-autonomous dynamics and a nonlinear readout, such as modern State Space Models (SSMs), while the second consists of general nonlinear models which can be parallelized using the DEER framework. We find that the linear training-time recurrence of the first class of models imposes limitations that often hinder learning of accurate nonlinear dynamics. To address this, we augment DEER with Generalized Teacher Forcing (GTF), a novel variant within the more general nonlinear framework that ensures stable and effective learning of nonlinear dynamics across arbitrary sequence lengths. Using GTF-DEER, we investigate the benefits of training on extremely long sequences ($T$ approaching $10^5$) for DSR. Our results show that access to such long trajectories significantly improves DSR if the data features long time scales. This work establishes GTF-DEER as a robust tool for data-driven discovery and underscores the largely untapped potential of long-sequence learning in modeling complex DS.

cs.LG · cs.AI · cs.DC · physics.comp-ph

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2510.12026

Mamba Can Learn Low-Dimensional Targets In-Context via Test-Time Feature Learning

Junsoo Oh, Wei Huang, Taiji Suzuki

原文摘要

Mamba, a recently proposed linear-time sequence model, has attracted significant attention for its computational efficiency and strong empirical performance. However, a rigorous theoretical understanding of its underlying mechanisms remains limited. In this work, we provide a theoretical analysis of Mamba's in-context learning (ICL) capability by focusing on tasks defined by low-dimensional nonlinear target functions. Specifically, we study in-context learning of a single-index model $y \approx g_*(\langle \boldsymbolβ, \boldsymbol{x} \rangle)$, which depends on only a single relevant direction $\boldsymbolβ$, referred to as feature. We prove that Mamba, pretrained by gradient-based methods, can achieve efficient ICL via test-time feature learning, extracting the relevant direction directly from context examples. Consequently, we establish a test-time sample complexity that improves upon linear Transformers -- analyzed to behave like kernel methods -- and is comparable to nonlinear Transformers, which have been shown to surpass the Correlational Statistical Query (CSQ) lower bound and achieve near information-theoretically optimal rate in previous works. Our analysis reveals the crucial role of the nonlinear gating mechanism in Mamba for feature extraction, highlighting it as the fundamental driver behind Mamba's ability to achieve both computational efficiency and high performance.

cs.LG · stat.ML

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.35112

Subspace Crystallization in Grokking: Rank Compression Tracks the Phase Transition

Shlok Mehendale, Paras Chopra

原文摘要

Grokking describes understanding something deeply and intuitively. In neural networks, it is the phenomenon where a network generalizes long after memorizing its training data. This delay has been linked to a fall in the effective rank of the network's weight matrices, but whether this rank compression drives grokking or follows it is still unresolved. We study a mean-field MLP and a one-layer transformer trained on modular arithmetic and observe that: (i) Compression follows the onset, not memorization. Every transformer memorizes its training data within 250 steps, while the grokking onset (the first step at which test accuracy reaches 95%) varies from 6,500 to 21,000 steps. The steepest fall in effective rank comes about 900 steps after the onset, however late the onset occurs, and networks that memorize without grokking compress far less. (ii) Subspace crystallization. We call the span of the fewest top singular directions of a weight matrix that preserve 99% of test accuracy its sufficient subspace. Its size can shrink as the margin between the correct and the best wrong output grows, so we also count the directions needed to keep the outputs within 10%. In the transformer, this count falls during the transition from a quarter or more of the available directions to about a tenth, which we call subspace crystallization. (iii) Imposing low rank does not speed up grokking. Against a factorized full-rank control, capping the rank of the transformer's MLP input weights delays the onset, and capping the rank of its embedding stops 15 of 20 runs from grokking. Compression is therefore a signature of grokking rather than its cause.

cs.LG · cs.AI

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2512.21781

The State of SBOM Tools: A Comparative Analysis of SPDX and CycloneDX

Zhimin Zhao, Abdul Ali Bangash, Tongxu Ge, Arshdeep Singh, Zitao Wang, Bram Adams

原文摘要

A Software Bill of Materials (SBOM) provides transparency and accountability for software releases by documenting component metadata and dependencies, making it essential to modern development. Adoption and utility depend heavily on tools that generate, analyze, and manage SBOMs. SPDX and CycloneDX are the two leading formats, but tools supporting them differ in maturity, features, and community engagement. Understanding these differences is vital to improving SBOM practices. We quantitatively compare use cases for 108 open-source and 62 proprietary tools advertised for SPDX and CycloneDX, identifying feature gaps. We compare community-health metrics of OSS tool repositories on GitHub (145 CycloneDX and 456 SPDX observations, 573 distinct repositories). We analyze 26,853 issue reports since 2018 from these repositories, categorizing 26,772 using an LLM-assisted approach calibrated against manual annotations. We also compare community-health metrics of the top 250 OSS projects using CycloneDX tools versus the top 250 using SPDX tools. Findings reveal distinct characteristics: CycloneDX projects show higher developer engagement and certain community-health metrics, while SPDX has more OSS tool repositories. This research provides insights for developers, contributors, and practitioners on complementary strengths and opportunities for mutual enhancement across both formats.

cs.SE

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2611.00887

Multi-quadrotor systems interconnected via structurally unknown forces and moments

Kaiyue Xing, Shivansh Pratap Singh, Sarthak Mishra, Di Liu, Spandan Roy, Simone Baldi, Leonid Fridman

原文摘要

This work addresses the challenge of controlling multi-quadrotor systems subject to tight uncertain couplings. We consider interconnection forces and moments among the quadrotors to be state-dependent functions of the coordination errors, without assuming knowledge of their functional/parametric structures, e.g., no linear-in-parameters assumptions are made. We only rely on general state-dependent quadratic bounds valid for several Euler-Lagrange mechanical systems. We propose a coordination strategy embedding adaptive laws dedicated to compensating for the lack of structural knowledge. Unlike conventional decoupled position-attitude designs, we present a coupled stability analysis accounting for the position-attitude couplings induced by the interconnection forces and moments. The analysis, along with real experiments involving cooperative aerial transportation of rope-interconnected payloads, demonstrates the effectiveness of the proposed solution in compensating for these complex interconnections. Comparative experiments show that, when a payload drop induces a disturbance propagating through the ropes across the whole formation, the proposed strategy reduces significantly post-disturbance transients.

cs.RO

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2609.09108

Distributed Linear Programming on GPU Clusters at Extreme Scale

Arnaud Deza, Santanu S. Dey, Pascal Van Hentenryck

原文摘要

Large linear programs can exceed the memory of a single compute node. Although first-order methods replace sparse factorizations with GPU-suited matrix-vector products, other solver phases can reintroduce a single-node memory limit. We present SHARDLP, a distributed GPU LP solver that keeps the matrix and primal-dual state partitioned from sharded input through solution output. On the Google PDLP benchmark, SHARDLP solves ten of eleven instances, compared with eight in the published CPU PDLP study. On the largest benchmark, eight H200 GPUs solve a 1.185-billion-variable, 6.338-billion-nonzero LP in 9.9 minutes; the published CPU experiment reports 21.06 hours on different hardware. Beyond this benchmark, separately checked multi-node solves reach up to 13.604 billion variables and 40.807 billion nonzeros, while validated executions span up to 76 GPUs across 29 compute nodes. For column-partitioned solves, support-aware communication skips GPUs that store no coefficients for a row; on an LP with 2.76 billion nonzeros, it cuts modelled communication by 92.97% and improves solver time by 1.27x-1.52x. The code for SHARDLP is available at https://github.com/ArnaudDeza/ShardLP.

math.OC · cs.DC

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2609.12021

Fast Odd-Permutation Sums in Characteristic Two and Shortest Even Directed Cycles

Boxuan Chen, Bin Cui, Hanqing Li, Xupeng Miao, Haoze Wang

原文摘要

For an $n\times n$ matrix over a field of characteristic two, let $Φ$ denote the sum of the odd permutation monomials. We give a deterministic algorithm that evaluates $Φ$ and all its first partial derivatives using $O(n^ω)$ field operations, where $2<ω\le3$ is any fixed admissible exponent for square matrix multiplication. As an application, we obtain faster randomized algorithms for shortest even directed cycles. Given an $n$-vertex directed graph whose shortest even cycle has length $\ell$, with high probability we compute $\ell$ and the union of the arcs of all shortest even cycles in $\widetilde O(n^ω\ell)$ time, and find one such cycle in $\widetilde O(n^ω\ell+n^2\ell^2)$ time. The resulting general bounds are $\widetilde O(n^{ω+1})$ and $\widetilde O(n^4)$, respectively, improving on the $\widetilde O(n^{ω+3})$ and $\widetilde O(n^{ω+4})$ bounds of Björklund, Husfeldt, and Kaski [BHK24].

cs.DS

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arXiv ↗PDF ↗