arXiv:2603.14945v3 Announce Type: replace Abstract: Linear wave theory captures the essential physics of free-surface flows at a fraction of the computational cost of nonlinear and viscous methods, making it attractive for design, real-time control, and surrogate modeling applications. However, the Kelvin Green's function for a translating point-source generates unbounded wave energy in the $z\to 0$ limit, causing both numerical difficulties and physical inconsistencies. This paper develops a modified kernel for the Kelvin potential incorporating an elliptic spanwise line integration that naturally resolves this ill-posedness, yielding finite wave energy over the entire free surface. We then present a fast evaluator for both point and line kernels using contour deformation adapted to the non-analytic Kelvin phase, achieving $10^4$-$10^5$ speedup over direct quadrature while preserving the wake asymptotics. Predictions on the most challenging $z=0$ limit demonstrate physically consistent wave patterns and wave resistance trends. An open-source Julia implementation is provided.
Science Journals
arXiv:2603.15269v3 Announce Type: replace Abstract: The tortuosity of corneal nerve fibers are used as indication for different diseases. Current state-of-the-art methods for grading the tortuosity heavily rely on expensive segmentation maps of these nerve fibers. In this paper, we demonstrate that self-supervised pretrained features from ImageNet are transferable to the domain of in vivo confocal microscopy. We show that DINO should not be disregarded as a deep learning model for medical imaging, although it was superseded by two later versions. After careful fine-tuning, DINO improves upon the state-of-the-art in terms of accuracy (84,25%) and sensitivity (77,97%). Our fine-tuned model focuses on the key morphological elements in grading without the use of segmentation maps.
arXiv:2604.13349v2 Announce Type: replace Abstract: Communication in Large Language Model (LLM)-based multi-agent systems is moving beyond discrete tokens to preserve richer context. Recent work such as LatentMAS enables agents to exchange latent messages through full key-value (KV) caches. However, full KV relay incurs high memory and communication cost. We adapt KV-cache eviction methods to this setting and introduce \textbf{Orthogonal BackFill (OBF)} to mitigate information loss from hard eviction. OBF injects a low-rank orthogonal residual from discarded KV states into the retained KV states. We evaluate OBF against full KV relay on nine benchmarks spanning mathematical reasoning, expert and commonsense QA, and coding. With only 9.9%-20.2% of the prompt KV states retained, H-OBF delivers between $97%$ and $120%$ of full KV relay's per-benchmark accuracy across the nine benchmarks. This suggests that more information does not necessarily lead to better communication; preserving the most useful information matters more. Our codebase is included in the supplementary material. Our codebase is publicly available on https://github.com/markli404/When-Less-Latent-Leads-to-Better-Relay.
arXiv:2607.00277v1 Announce Type: new Abstract: We present Aegis, a joint-embedding predictive architecture for breast cancer detection and density assessment in mammography. We train three Vision Transformer variants (Small/Base/Large) using self-supervised joint-embedding predictive architecture (JEPA) pre-training on 71,103 studies from 14 clinical sites, followed by supervised fine-tuning with progressive resolution scaling up to 2048x1536. On a curated 785-study test set, our largest model achieves area under the receiver operating characteristic curve (AUC) 0.949 for breast cancer triage with 93% sensitivity and 75% specificity at the optimal operating point. An ensemble combining our model with a U.S. Food and Drug Administration-cleared baseline further improves discrimination to 0.952 AUC. For breast density classification, the model achieves 0.953 AUC for binary (dense vs. non-dense) classification and 62.6% exact accuracy across four Breast Imaging Reporting and Data System (BI-RADS) categories, with 98.8% adjacent accuracy comparable to reported human inter-reader agreement. External validation on the public VinDr-Mammo dataset provides evidence of cross-population transfer under a different reference standard, with the largest model achieving 0.871 AUC for triage in a zero-shot setting.
arXiv:2607.00399v1 Announce Type: new Abstract: End-to-end autonomous driving models often encounter performance bottlenecks, as training-time scaling leads to high computational costs and diminishing marginal returns. Existing planners typically adopt a one-shot generation paradigm, lacking secondary validation and active correction mechanisms to detect and revise suboptimal or unsafe trajectories during inference. To address this issue, we propose DriveVer, a lightweight, plug-and-play Test-Time Verifier that leverages the test-time scaling paradigm to enable autonomous driving systems to validate and refine trajectories without costly and heavy training. We construct a dedicated trajectory dataset based on the NAVSIM benchmark through condition-driven clustering and balanced sampling according to ego-vehicle states and navigation commands. Employing a dual-head architecture, DriveVer efficiently fuses candidate trajectories with multi-view visual representations and ego-vehicle kinematic features to simultaneously predict a safety confidence score and an absolute geometric refinement vector. Extensive experiments on the NAVSIM benchmark show that DriveVer significantly improves the performance of base planning models. Notably, as an extremely compact model with only 34M parameters, DriveVer introduces minimal computational overhead, achieving competitive results while maintaining real-time inference efficiency.
arXiv:2607.01041v1 Announce Type: new Abstract: Optical networks are critical infrastructure that underpins global communications, and detecting security breaches that jeopardize them is essential to maintaining worldwide connectivity. As malicious actors continuously evolve their attack techniques, dynamically updated intrusion detection models have become a key component of modern defense mechanisms. By incorporating newly acquired telemetry data, these models can adapt to emerging threats while maintaining high detection performance. However, when previously encountered attacks reappear after a prolonged period of absence, adaptive models may fail to recognize them due to the phenomenon of catastrophic forgetting. In contrast, statically trained models can reliably detect attacks represented in the original training data but lack the ability to adapt to previously unseen attack patterns. Consequently, intrusion detection systems face a fundamental tradeoff between adaptability to evolving threats and long-term retention of previously acquired knowledge. In this work, we propose a data-driven mechanism to cope with catastrophic forgetting in dynamic attack detection systems. Our approach balances the model update datasets by using parts of past attack data. We utilize a threshold-based mechanism to trigger data balancing after accuracy drops due to an active attack change. Applied to an experimental optical network security dataset, the proposed approach reduces the average model adaptation time by 37% compared to its dynamic counterpart that does not employ data balancing. Compared to a baseline from the literature that relies on neural network depth increasing, our approach requires 6% fewer data batches to adapt to changing conditions and regain performance.
arXiv:2607.01063v1 Announce Type: new Abstract: Large input spaces and complex inter-operation dependencies make black-box REST API testing challenging. AutoRestTest combines a Semantic Property Dependency Graph, multi-agent reinforcement learning, and large language models to intelligently explore large API input spaces. In the SBFT 2026 REST League, AutoRestTest ranked first in all three evaluation categories -- fault detection, overall efficiency, and overall effectiveness -- on 11 APIs (317 operations, approximately 29 per API), averaging 67.09 unique server errors and 17.27 successfully processed operations per API under a one-hour testing budget.
arXiv:2607.01042v1 Announce Type: new Abstract: Program comprehension is a central research topic in software engineering, focusing on how developers understand a program's structure, behavior, and intent. Eye-tracking studies have traditionally relied on display-based measurements, where gaze positions are represented as screen coordinates. However, syntax-based analyses have recently emerged. Prior work proposed methods to convert eye movements into transitions between nodes in an abstract syntax tree, but the relationship between task correctness and eye-movement features for specific syntactic elements remains unclear. This study converts eye-tracking data into transitions between syntactic nodes and analyzes fixation proportions and gaze transition patterns. We investigate the relationship between these patterns and task correctness, comparing correct and incorrect groups. Our results reveal distinct differences in gaze transition patterns between the two groups. In particular, successful participants exhibit more systematic transitions across syntactic elements, suggesting the use of structured reading strategies.
arXiv:2607.00451v1 Announce Type: new Abstract: This paper proposes an inner--outer (IO) iterative algorithm with optimal parameters for solving stochastic Lyapunov matrix equation associated with discrete-time stochastic linear system. First, under the assumption that the underlying stochastic linear system is asymptotically mean-square stable, the monotonicity and boundedness of the iterative sequence generated by the proposed algorithm are analyzed. On this basis, a sufficient convergence result is established for the zero initial condition. Second, by deriving the spectral radius of the corresponding iteration matrix, several necessary and sufficient convergence conditions are obtained for arbitrary initial conditions. In addition, the optimal parameter-selection strategies are developed to improve the convergence performance of the algorithm. Finally, numerical examples are presented to verify the theoretical results and demonstrate the advantages of the proposed algorithm over several existing iterative methods.
arXiv:2607.00013v1 Announce Type: new Abstract: Retrieval-Augmented Generation (RAG) systems are widely used in institutional question answering settings where responses must be grounded in authoritative documentation (Gao et al., 2023). In entity-dense domains where relevant information is distributed across heterogeneous documents, vector-only retrieval often produces fragmented evidence and increases dependence on inference-time reasoning (Zhao et al., 2024). This paper introduces GRACE-RAG, a retrieval-governed, graph-augmented RAG architecture that externalizes structural reasoning from the generative stage to a structured retrieval layer, resolving structural ambiguity offline, enabling deployment on self-hosted lightweight models calibrated to closed-domain institutional vocabulary. Experiments across three model capacities: Mistral 24B, GPT OSS 120B, and Gemini 2.5 Flash show consistent improvements in completeness, depth, and anticipatory coverage, with overall quality gains of up to 20% under mid-scale models, indicating that retrieval architecture governs structural quality over model scale, reducing computational and latency footprint without dependence on proprietary systems.
arXiv:2607.00297v1 Announce Type: new Abstract: When LLM agents use evaluator feedback to adapt their behavior in closed loops, evaluator biases propagate through the agent's strategy distribution -- a phenomenon known as evaluator preference coupling. Prior work has documented coupling across multiple evaluator families and model versions, but the field lacks a standardized protocol that enables third-party researchers to (i) reproduce coupling measurements, (ii) compare results across evaluators and time points, and (iii) detect measurement decay as proprietary evaluators silently update. This paper provides the protocol. We specify EPC (Evaluator Preference Coupling) -- a detailed, RFC-style protocol specification for the four-phase isolation paradigm, covering executor and evaluator configuration, strategy and task design, the TTRL update rule, metric computation (gamma, JSD, ECE, Brier), and output schema. We accompany the protocol with a versioned Reference Snapshot v1.0: coupling measurements for eight evaluator conditions (N=122 unique experimental repetitions across GPT-4o, Qwen, DeepSeek, and others) derived from five independent studies, annotated with evaluator version identifiers, API endpoints, and measurement dates. The snapshot is explicitly time-bound: all values are conditional on specific model versions and are expected to decay as proprietary evaluators update. We define a versioning convention (vX.Y-Z, encoding protocol version, snapshot version, and evaluator generation) and provide a usage guide covering adoption, interpretation, and known pitfalls. The protocol, reference snapshot, and implementation code are released as open infrastructure.
arXiv:2607.00309v1 Announce Type: new Abstract: We present a real-time musical interface that converts natural-language scene descriptions into evolving procedural soundscapes. A performer types a prompt such as "warm jazz cafe at midnight" and steers it through direct parameter adjustments - stepping brightness down, switching a rhythm style - each producing a predictable, audible shift without re-prompting. Where GPU-bound text-to-audio systems synthesize monolithic waveforms, our instrument generates human-readable configurations over a categorical schema, enabling fine-grained performer control; most valid combinations are designed to sound musically coherent. Three interchangeable backends - embedding retrieval for sub-second CPU-only use, hosted LLMs via API, and a fine-tuned 270M local model - all emit the same schema. A live generator architecture continuously emits audio while resolving new instructions in the background, crossfading seamlessly when ready; even when an LLM takes 5-12 seconds to respond, the audience hears uninterrupted sound - reframing text-to-music as an ongoing performable stream rather than a one-shot generation. We evaluate text-audio semantic alignment using LAION-CLAP on held-out prompts as a technical proxy, finding that retrieval-based configuration outperforms random valid configurations on this metric, while noting that LAION-CLAP also informed retrieval-map construction. We report performance observations, informal listener feedback, and release materials for the SDK, dataset artifacts, model, and audiovisual performance interface.
arXiv:2607.00336v1 Announce Type: new Abstract: The ab initio calculation of photoelectron angular distributions (PADs) for negative ions remains a significant theoretical challenge. In this work, we report a joint experimental and theoretical investigation of PADs for a series of molecular anions with varying polarities, including the nonpolar O2-, the weakly polar NO-, and the strongly polar AsO- and SbO-. To accurately describe the long-range electronic wavefunctions -- where photodetachment contributes most strongly -- we modified the standard Gaussian-type orbitals (GTOs) by augmenting them with a correct exponential Slater-tail basis set (~e^(-{\xi}r)). This simple yet effective approach significantly improves the agreement between the experimental and theoretical PADs for O2- and NO-. However, notable discrepancies persist for NO- for transitions to the v = 0 and v = 1 vibrational levels of neutral NO even after this correction. Given that our methodology successfully reproduced PADs for strongly polar anions (e.g., AsO- and SbO-), these residual discrepancies are unlikely to stem from "exit-channel scattering" induced by long-range dipole fields. Instead, we tentatively attribute the failure for NO- to the breakdown of the Born-Oppenheimer approximation or the frozen orbital approximation, arising from the extremely weak binding of the excess electron.
arXiv:2607.00620v1 Announce Type: new Abstract: Generalized Category Discovery (GCD) aims to recognize known classes while autonomously discovering novel ones in open-world settings. However, current approaches primarily focus on designing clustering objectives, often overlooking a critical bottleneck: standard vision backbones yield high-rank, entangled token representations that are ill-suited for unsupervised discovery of latent concepts and structures. In this paper, we propose Compositional Primitive Fields (CPF-GCD), a novel representation learning framework that reshapes the feature space to make such latent structure identifiable by enforcing a low-rank compositional organization. Our core hypothesis is that all categories, whether known or novel, can be expressed as compositions and spatial arrangements of a finite set of learnable visual primitives that capture reusable concepts. CPF instantiates this geometric constraint via a spatial field mechanism. Inserted between the backbone and the head, it rewrites noisy patch tokens through low-rank primitive mixtures, effectively decomposing images into reusable atomic parts and their spatial layouts. By explicitly modeling the spatial distribution of primitives, CPF enables novel categories to emerge naturally as new activation patterns over a shared vocabulary. This shifts the focus of representation from merely partitioning global embeddings to constructing a structured and separable primitive field. Extensive experiments demonstrate that CPF serves as a generic, plug-and-play module that consistently boosts performance across diverse GCD baselines, validating that identifying and leveraging low-rank compositional structure is a crucial inductive bias for open-world recognition.
arXiv:2606.30552v2 Announce Type: replace Abstract: Cross-embodiment transfer in vision-language-action (VLA) models remains challenging because low-level state and action spaces differ fundamentally across robot platforms. We observe that the high-level cognitive process underlying manipulation, including scene perception, object identification, task planning, and sub-task decomposition, is largely shared across embodiments. Based on this observation, we present ZR-0, a 2.6 billion parameter end-to-end VLA model that uses dense Embodied Chain-of-Thought (ECoT) supervision to align cross-embodiment representations within the vision-language model (VLM). ZR-0 adopts a dual-stream architecture: a pre-trained VLM (System 2) generates structured ECoT reasoning during training, while a Diffusion Transformer-based action expert (System 1) produces continuous action chunks via flow matching. The two components are coupled through cross-attention, with an attention mask that restricts the action expert to input prompt features only, enabling ECoT generation to be entirely skipped at inference without any performance loss. ZR-0 is pre-trained on ProcCorpus-60M, a large-scale dataset comprising approximately 60 million frames (approximately 1,000 hours) from over 400K trajectories, with dense ECoT annotations covering 96.8% of all frames. We evaluate ZR-0 on three simulation benchmarks spanning single-arm (LIBERO), bimanual (RoboTwin 2.0), and humanoid (RoboCasa GR-1 Tabletop) embodiments, as well as real-world experiments on the xArm platform, demonstrating strong performance across all settings. Code and model checkpoints are available at https://github.com/RUCKBReasoning/ZR-0.
arXiv:2607.00121v1 Announce Type: new Abstract: This work considers a Differential Reflecting Modulation (DRM) scheme for Reconfigurable Intelligent Surfaces (RIS) not requiring channel state information (CSI). When operating over time-varying fading channels, such schemes with Conventional Differential Demodulation (CDD) receivers experience high error floors and performance degradation. To address these issues, we propose a Decision Feedback Differential Detection (DFDD) technique for DRM. We explore the application of DFDD for RIS DRM and conduct extensive Monte-Carlo simulations to analyze performance. Results demonstrate the viability of our DFDD technique across various RIS scenarios and highlight the importance of proper parameter selection to achieve good performance. The DFDD scheme is also compared with uncoded and Differential Space-Time Modulation (DSTM) coded DRM using CDD based receivers. We observe that at low SNR, the DFDD scheme performs almost as well as the DRM with CDD scheme, but worse than the DSTM coded DRM. As the SNR increases however, both CDD-detected systems encounter high error floors while the error rate of DFDD based scheme continues to improve until it reaches a relatively low error floor. It is shown that the chief merits of employing DFDD receivers in such RIS systems is the low error floors they provide over time varying fading channels, albeit at expense of a small increased complexity.
MG-SpaIR: Multi-grade Sparse-guided Implicit Representation for Training-Data-Free Image Restoration
arXiv:2607.00138v1 Announce Type: new Abstract: MG-SpaIR is a training-data-free framework for restoring a clean image from a single observation corrupted by a mixture of blur, downsampling, noise, and missing pixels. Building on implicit neural representations (INRs), we introduce a multi-grade coarse-to-fine residual hierarchy that progressively refines the reconstruction across resolution grades, improving representational fidelity and mitigating spectral limitations. To stabilize reconstruction optimization and suppress INR-induced artifacts, we further propose an explicit sparse proximal regularization (e.g., $\ell_0$-type) applied directly in the high-resolution image domain, which discourages spurious high-frequency patterns while preserving sharp structures. The resulting optimization is solved efficiently via a multi-grade proximal alternating scheme, and we establish convergence guarantees for the associated updates under standard regularity conditions. Experiments on mixed-degradation benchmarks demonstrate that MG-SpaIR consistently outperforms strong training-data-free baselines such as Deep Image Prior, providing a stable, interpretable, and data-efficient alternative to conventional learning-based restoration methods.
arXiv:2607.00579v1 Announce Type: new Abstract: We introduce \textbf{Edge-based Pose Optimization (EPO)}, a trackless geometric optimization framework specifically designed to boost the Structure-from-Motion reconstructions generated by 3D Foundation Models. These models achieve rapid inference by bypassing the time-consuming feature extraction and matching stages of traditional pipelines, where explicit correspondences between each 3D point and multiple images, referred to as tracks, are established. However, their geometric accuracy currently falls short of traditional pipelines. While this can be addressed in a post-processing step via Bundle Adjustment-like refinement, doing so requires extracting feature tracks, thus defeating the original speed advantage. Instead, our fully differentiable framework uses edge map alignment as a proxy for geometric optimization, avoiding feature extraction and track construction entirely. Through extensive evaluation across multiple datasets and tasks, we demonstrate that EPO matches or outperforms Bundle Adjustment-like methods while requiring significantly lower runtime and memory. Notably, its reduced memory footprint makes EPO suitable for consumer-grade hardware, where competing refinement methods cannot run.
arXiv:2607.00580v1 Announce Type: new Abstract: Vision Transformers (ViTs) commonly rely on injected positional mechanisms to address self-attention's permutation invariance. Motivated by the spatial regularities of natural images, we ask whether spatial organization can be induced from data rather than explicitly injected. Under controlled, matched from-scratch training, we propose Active Spatial Guidance (Guidance), a training-only objective that disables positional injection and applies an auxiliary 2D coordinate-regression loss to the final-layer patch tokens. The guidance head is used only during training and removed for inference; the deployed model consists of a positional-injection-free ViT encoder and the task-specific prediction module. Using DINOv3 ViT backbones, Guidance consistently improves performance on ImageNet-100 classification, ADE20K semantic segmentation, and Hypersim monocular depth estimation, outperforming strong injected baselines such as learned absolute positional embeddings and rotary positional embeddings under identical training protocols. On ImageNet-100, broader comparisons against representative injected positional designs further support Guidance's effectiveness. Guidance also improves robustness under resolution transfer, and multi-resolution training further strengthens accuracy across input sizes. Overall, our results suggest that spatial inductive bias in ViTs need not be architecturally injected, but can be shaped through training-time supervision. The code used for training and evaluation is publicly available in https://github.com/cloudlc/asg.
arXiv:2607.00035v1 Announce Type: new Abstract: LLMs and agents can generate web scrapers from natural-language requirements, but direct generation remains unreliable because of dependency errors, broken selectors, schema mismatches, and heterogeneous page structures. We propose a constrained, verifiable agent framework that shifts LLM output from free-form code to typed JSON collector configurations, combining a six-type collector taxonomy, template and utility-function constraints, static Airflow DAG execution, rule-based quality checking, and structured feedback correction. Experiments on 138 tasks show that the taxonomy supports description-based requirement typing, while confirming that stable instantiation requires completing source, field, and execution constraints beyond the initial description. On 80 independently source-verified tasks, the framework runs with zero execution-stage LLM tokens and the lowest average wall-clock time, trading moderate one-shot quality for a reusable, deterministic, and verifiable execution path suited to repeated scheduled collection. These results position the framework as a reusable, low-cost, and verifiable execution path for repeated open-web data collection.
arXiv:2607.00144v1 Announce Type: new Abstract: Active learning (AL) performance is known to be budget-dependent, yet regimes are typically defined by heuristic label counts that fail to generalize across datasets or architectures. We characterize AL dynamics by reframing budget regimes as shifts in the dominant generalization mechanism. By reinterpreting PAC-style risk components as dynamic interacting terms, we prove that dominance shifts are structurally unavoidable, creating a moving bottleneck for generalization. We operationalize this using measurable proxies and a segmented regression procedure to identify a tripartite taxonomy: data-driven, transition, and model-driven phases. Our framework explains the long-standing observation that representativeness, coverage, and uncertainty strategies excel at different stages. Experiments across natural and medical imaging show that AL efficiency depends on the alignment between the strategy's inductive bias and the active bottleneck. Moreover, self-supervised representation shift transitions earlier along the labeling trajectory, highlighting the role of representation quality in shaping AL dynamics. Overall, this work provides a unified framework for the next generation of transition-aware AL algorithms.
arXiv:2607.00004v1 Announce Type: new Abstract: While advanced foundation models like ModernBERT significantly outperform older architectures in dense retrieval, they surprisingly lag behind the aging BERT-base baseline in learned sparse retrieval (LSR). We identify the root cause as the \textit{Vocabulary Gap}: modern tokenizers utilize raw, case-sensitive vocabularies designed for lossless reconstruction, which map single semantic units to redundant surface forms, wasting model capacity on morphological noise and hindering lexical matching. We formalize this intuition through a theoretical framework, demonstrating that appropriate vocabulary coarse-graining can tighten the generalization bounds by reducing complexity of the hypothesis class, provided that semantic integrity is preserved. To resolve this, we propose \textbf{Vocabulary Transfer (VT)}, a model-agnostic framework that migrates advanced encoders to sparse-friendly, normalized vocabularies with minimal computational cost. VT utilizes a novel \textbf{Semantic Initialization} via spatial topology to preserve geometric structure and an \textbf{Activation Potential Calibration (APC)} mechanism to align pre-trained manifolds with sparsity constraints, preventing the dead neuron and dense collapse observed in standard fine-tuning. Empirically, VT is universally effective: it enables ModernBERT to achieve state-of-the-art performance on the BEIR benchmark (\textbf{52.4} nDCG, a \textbf{+4.7} improvement), resuscitates failing models like RoBERTa-large, and generalizes seamlessly to inference-free architectures and specialized domains. These results confirm that the performance lag is not an architectural deficiency but a solvable vocabulary mismatch. We've released our code and models.\footnote{https://anonymous.4open.science/r/vocab-transfer/. All details included.}
arXiv:2604.14262v2 Announce Type: replace Abstract: GUI grounding models report over 85% accuracy on standard benchmarks, yet drop 27-56 percentage points when instructions require spatial reasoning rather than direct element naming. Current benchmarks miss this because they evaluate each screenshot once with a single fixed instruction. We introduce GUI-Perturbed, a controlled perturbation framework that independently varies visual scenes and instructions to measure grounding robustness. Evaluating three 7B models from the same architecture lineage, we find that relational instructions cause systematic accuracy collapse across all models, a 70% browser zoom produces statistically significant degradation, and rank-8 LoRA fine-tuning with augmented data degrades performance rather than improving it. By perturbing along independent axes, GUI-Perturbed isolates which specific capability axes are affected-spatial reasoning, visual robustness, reasoning calibration-providing diagnostic signal that aggregate benchmarks cannot. We release the dataset, augmentation pipeline, and a fine-tuned model.
arXiv:2606.01330v2 Announce Type: replace Abstract: We resolve the thin matching problem proposed by Anari, Charikar and Ramakrishnan [ACR23] up to polylogarithmic factors. Given a fractional perfect matching $x$, we say a perfect matching $M$ is $\alpha$-thin w.r.t. $x$ if for any cut $(S,\overline{S})$, we have $$ |M \cap E(S,\overline{S})| \leq \alpha\cdot x(S,\overline{S}).$$ [ACR23] conjectured that for any fractional perfect matching $x$, there exists a perfect matching $M$ which is $O(1)$-thin w.r.t. $x$. First, we show that if $M$ is restricted to be in the support of $x$, then $\alpha \geq \Omega(n)$ and we complement this by designing an efficient algorithm that outputs an $O(n\log n)$-thin perfect matching where $n$ is the number of vertices. Then, we relax this constraint and show that for any fractional perfect matching $x$, there is a perfect matching $M$ (which is not necessarily in the support of $x$) such that $M$ is $\text{polylog}(n)$-thin w.r.t. $x$. All results work for both bipartite and non-bipartite graphs. We also discuss applications to the metric distortion problem.
arXiv:2607.01171v1 Announce Type: new Abstract: Sample-based generative models are increasingly used for probabilistic forecasting in high-stakes decision settings, yet their training objectives are blind to the decision maker's cost structure. These models are commonly trained with strictly proper scoring rules, such as the energy score, which allocate their training signal in proportion to data density, with no awareness of where forecast errors are most costly for downstream decisions. We therefore propose decision-aware training for sample-based generative models, augmenting the energy score objective with a differentiable decision loss that directly penalises the cost incurred by acting on the model's forecast. This combined loss is theoretically grounded, as the decision loss is itself a proper scoring rule. We validate our method on one synthetic and two real-world tasks, showing targeted improvements in cost-sensitive regions while retaining full probabilistic forecasts.