arXiv:2606.02119v1 Announce Type: new
Abstract: Machine unlearning aims to remove the influence of specific forget training data due to privacy, copyright or bias concerns while maintaining the model performance on the remaining retain data. Existing unlearning algorithms, such as optimizing a weighted combination of losses, have tried to achieve these objectives of improving forget quality and maintaining retain utility. However, they do not guarantee that these objectives can be improved by a specified extent for all forget and retain data. In this work, we address this limitation with a novel and theoretically-grounded approach from a constrained optimization perspective. Firstly, we identify that the hardness of reconciling both objectives can be quantified by the similarity between the forget data and the retain data. Next, we derive an unlearning algorithm (HAMU) with the overall goal of guaranteeing a specified improvement in forget quality while minimizing the retain utility cost/degradation by updating the model weights based on our hardness measure. Our hardness measure also informs users when retain utility degradation is unavoidable, i.e., both objectives cannot be improved simultaneously, and stopping should be considered. Our algorithm is applicable to non-convex models and is easily parallelizable, making it readily deployable in real-world scenarios. We empirically demonstrate HAMU's superior performance over baselines on both image and text datasets using large models. Our code is available at https://github.com/aoi3142/HAMU.
Science Journals
arXiv:2606.02016v1 Announce Type: new
Abstract: Algorithm Selection (AS) aims to automatically identify the most suitable optimization algorithm for a given problem instance by leveraging measurable problem characteristics and historical performance data. In this study, we investigate the generalization ability of AS models across both synthetic and real-world optimization landscapes. We consider two widely used academic benchmark suites (BBOB and CEC) and two real-world problem sets (robotics trajectory optimization tasks and unmanned aerial vehicle path-planning problems). Through a systematic cross-benchmark evaluation, we analyze how AS models transfer between domains, identify where generalization succeeds or breaks down, and highlight the challenges that arise when applying AS in realistic, domain-specific contexts. Our findings provide insights into the robustness of current AS approaches and inform the development of more reliable, broadly applicable AS systems for real-world optimization.
arXiv:2606.01691v1 Announce Type: new
Abstract: Industrial Internet systems face increasing threats from sophisticated industrial control system (ICS) attacks, resulting in critical safety incidents. However, existing tools exhibit limited effectiveness in real-time anomaly detection due to the complex dependencies among sensors and actuators. To tackle this, we present IstGPT, the first industrial anomaly detection tool based on LLMs and graph learning to provide real-time protection against a wide range of ICS attacks. IstGPT achieves fine-grained and precise modeling on spatial-temporal dependencies in industrial cyber-physical systems. It first leverages industrial multi-modal knowledge, including operational data, technical documents, and system diagrams, to extract sensor-actuator dependency graphs via multi-stage prompt engineering. Then, LLM-Optimation iteratively refines the graph based on node accuracy, edge consistency, and logical coherence. Finally, IstGPT integrated improved graph neural networks with an encoder-decoder architecture to detect anomalies via reconstruction errors. We evaluate IstGPT against 12 state-of-the-art baselines on 9 datasets, including 2 public, 6 simulated, and a real-world robotic arm dataset. IstGPT achieves the best F1-scores and eTaF1 (a newer time-aware metric) across nine datasets. We further discuss the feasibility of deploying IstGPT in real-world industrial scenarios.
arXiv:2606.01694v1 Announce Type: new
Abstract: Thermal pedestrian MOT remains challenging because weak appearance cues and frequent detection interruptions cause severe trajectory fragmentation. We study whether lightweight post-processing can recover identity continuity without relying on heavy re-identification models or complex online association. Starting from a YOLOv8 and SORT baseline, we add a modular identity-repair backend consisting of online short-gap remapping and offline tracklet relinking based on temporal, spatial, motion, and border cues. Controlled ablations on a fixed validation split and evaluation on the official PBVS Thermal Pedestrian MOT benchmark show that the main identity gains arise from conservative relinking, improving IDF1 from 82.25 to 84.93 while preserving MOTA, whereas many heuristic thresholds remain stable across broad operating ranges. These results suggest that, in low-information thermal imagery, robust identity recovery can be achieved more effectively through high-precision trajectory relinking than through increasing tracker complexity. These results provide a controlled analysis of identity recovery in thermal video, showing that scene-level spatial-temporal consistency plays a dominant role in identity continuity compared to local frame-to-frame association.
arXiv:2603.23398v3 Announce Type: replace
Abstract: Generative modeling of discrete data, such as graphs, underpins many scientific and industrial applications, including molecular discovery and materials design. In these domains, probabilistic inference is particularly valuable, as it enables composable generation and principled incorporation of desired constraints, such as structural or functional properties. Energy-based models naturally support this goal by capturing relative likelihoods and enabling composable inference by directly enforcing constraints during inference. However, discrete energy-based models typically struggle with efficient and high-quality sampling, as off-support regions often contain spurious local minima, trapping samplers and causing training instabilities, resulting in a fidelity gap compared to discrete diffusion models. To address this gap, we introduce Graph Energy Matching (GEM), a discrete generative framework inspired by the Jordan-Kinderlehrer-Otto (JKO) transport-map optimization perspective. GEM learns a permutation-invariant potential energy that simultaneously guides discrete transport from noise toward high-likelihood graph regions and refines samples within these regions. We further introduce a sampling protocol leveraging an energy-based switching strategy, seamlessly bridging rapid, gradient-guided transport and a local mixing regime for effective exploration. On molecular graph benchmarks, GEM matches or surpasses strong discrete diffusion baselines on most reported metrics. Beyond improving generation quality, GEM's relative likelihood modeling enables targeted exploration, facilitating compositional generation, property-constrained sampling, and interpolation between graphs. Project page: https://michalbalcerak.ai/graph-energy-matching/.
arXiv:2412.15378v3 Announce Type: replace
Abstract: The functioning of complex systems depends on the coordination of diverse components, often supported by regulatory structures that incur costs. In human organizations, such costs manifest as administrative burden, which has been rising despite often reducing efficiency. Classic explanations point to bureaucrat self-interest or regulation, yet they do not explain variation across organizations or clarify how this burden can be reduced. Here, we develop a dynamical model of administrative growth that integrates known behavioral mechanisms of process creation, obsolescence, and removal. The model conceptualizes processes as developed for problem solving, but becoming obsolete as conditions change, while continuing to consume resources until actively pruned. This interplay generates two long-term outcomes: stable equilibrium or run-away growth. The threshold separating these outcomes is shaped by organizations' propensity to create new processes when faced with problems, and their propensity to prune obsolete ones in response to administrative burden. Importantly, their effects are asymmetric: sufficiently high creation propensity leads to bloat regardless of pruning propensity. Faster environmental change shifts this threshold, making bloat more likely. Simulations of interventions show that lasting reductions in administrative costs and waste require permanent shifts in priorities and investments in distinguishing obsolete from useful processes. Temporary efforts or indiscriminate cuts provide only short-lived relief, and counterintuitively, prioritizing direct production can increase waste. Our work highlights a general mechanism by which well-intentioned problem-solving can create self-reinforcing inefficiencies in complex systems, offering insights possibly generalizable to broader applications, such as legal, policy, and software systems where obsolete elements accumulate.
arXiv:2606.01895v1 Announce Type: new
Abstract: With the growing number of satellites in low Earth orbit (LEO) constellations, the near-Earth space environment has become increasingly congested, making space object detection (SOD) a pressing challenge for space safety and sustainability. To mitigate collision risks and ensure the continuity of space operations, SOD systems must deliver fast and accurate detection under stringent onboard constraints. In this paper, we investigate the potential of multi-viewpoint observation fusion within a deep learning (DL) framework to enhance SOD performance. We design a practical multi-view pipeline and several input representations for feeding multi-view data into YOLO-based detectors. Our experiments show that using multi-view inputs is feasible in most cases and typically produces better results for mAP50 and mAP50-95. For example, in model YOLOv9-m, single-view compared to a three-view fused RGB setting, mAP50 increases from 0.638 to 0.732, while mAP50-95 improves from 0.227 to 0.276. Compared with the single-view setting, the best three-view grayscale configuration improves mAP50 by 36.3% and mAP50-95 by 46.5%. These findings establish multi-view fusion as a viable and effective strategy for SOD, with broad implications for space situational awareness in LEO constellation deployments.
arXiv:2606.02387v1 Announce Type: new
Abstract: One of the most significant achievements of equilibrium logic was the characterization of strong equivalence, a property crucial for program transformation and optimization in Answer Set Programming (ASP). While ASP has recently been extended to a higher-order setting to enhance its expressive power, the lack of a comparable purely logical foundation has made verifying strong equivalence for higher-order programs or even proving the correctness of simple program transformations, a difficult challenge. This paper addresses this gap by developing a logical semantics for higher-order ASP by extending the equilibrium logic framework. Within this extended framework we demonstrate that every stratified higher-order logic program possesses a unique equilibrium model. Moreover, we establish definability results demonstrating that the syntax of our higher-order language is sufficiently expressive to capture its semantic domains. Finally, and most importantly, we generalize the classical theorem of strong equivalence to the higher-order setting: we prove that two programs are strongly equivalent if and only if they share the same higher-order models.
arXiv:2606.02406v1 Announce Type: new
Abstract: This paper presents a competitive solution to the S23DR Challenge 2026, which aims to reconstruct 3D house roof wireframe models from sparse SfM point clouds and ground-level semantic segmentations and depth maps. Our proposed method utilizes an end-to-end Transformer encoder-decoder architecture inspired by DETR. To effectively process the geometric and semantic data, the sparse SfM point cloud input is dynamically subsampled based on semantic priority and augmented with Gestalt and ADE20k class features. To further increase segmentation context, we fuse the point features with additional Gestalt feature encodings which are obtained by projecting the points into latent feature maps produced by a frozen autoencoder. Learned query embeddings are then decoded directly into 3D wireframe edges via cross-attention mechanisms. Evaluated on the "HoHo 22k" dataset, our approach significantly outperforms both handcrafted and learned baselines, achieving a Hybrid Structure Score (HSS) of 0.6476 and securing the second-highest position on the challenge's private leaderboard.
arXiv:2606.01943v1 Announce Type: cross
Abstract: Absolutely maximally entangled (AME) states and, more generally, $k$-uniform states in $(\C^q)^{\otimes n}$ are central objects in multipartite entanglement theory, with applications to quantum secret sharing, quantum masking, and quantum error correction. In the extremal case $k=\lfloor n/2\rfloor$, Scott (2004) proved a sharp nonexistence bound showing that AME states cannot exist once the number of parties $n$ exceeds a threshold of order $2q^{2}$ (with a parity dependence on $n$), where $q$ is the local dimension. Recently, Ning et al.\ studied \emph{defective} AME states (i.e., $k=\lfloor n/2\rfloor-l$ with $l>0$), gave explicit Scott-type bounds for defects $l=1,2$ and conjectured a general $(2l+2)q^{2}+o(q^{2})$ behavior. In this paper, we solve this conjecture and establish a fully explicit Scott-type upper bound for AME states with arbitrary defect $l\ge 0$, yielding Scott's bound for $l=0$ and Ning et al.'s bounds for $l=1,2$ as special cases. Equivalently, this gives nonexistence bounds for one-dimensional pure quantum error-correcting codes near the quantum Singleton regime. The proof uses a truncated MacWilliams linear-programming system and an explicit infeasibility certificate. As a direct application, we derive explicit asymptotic upper bounds on $k/n$ for fixed local dimension $q$, improving the implicit upper bounds given by Ning et al.
arXiv:2606.02111v1 Announce Type: new
Abstract: As multimodal large language models (MLLMs) have advanced to process video inputs, concerns have emerged about their potential for malicious misuse. Prior jailbreak studies have shown that safety alignment in MLLMs can be bypassed through visual inputs, yet it remains unclear which properties of video inputs induce this vulnerability. To address this gap, we introduce Multi-Clip Video (MCV) SafetyBench, a dataset of 2,920 videos designed to evaluate how the diversity of video inputs affects the vulnerability of MLLMs. Each video consists of multiple short clips depicting diverse contexts related to a harmful query. Experiments on eight representative video MLLMs show that attack success consistently increases with the number of clips. Our results further indicate that the video modality is (1) more vulnerable than the image modality, (2) more vulnerable to dynamic videos than to static videos, and (3) more vulnerable when videos contain more diverse contexts. Building on these findings, we propose a defense strategy that leverages the relative robustness of the image modality.
arXiv:2606.02079v1 Announce Type: new
Abstract: The main goal of active finetuning is to improve a pretrained model's performance on a specific task or domain by finetuning it with carefully selected informative or challenging data. Previous research has predominantly focused on the active aspect (i.e., data selection) while uniformly employing full finetuning for model adaptation, which inevitably distorts pretrained features due to distribution shift. This issue becomes particularly pronounced when the model size is large relative to the finetuning data quantity, leading to heightened overfitting risks. To address this critical gap, we formally outline the FiAF task that emphasizes systematic exploration of finetuning methodologies in active learning. We propose FACT, a three-phase hierarchical finetuning framework featuring both efficiency and simplicity, specifically designed for active finetuning scenarios. Our comprehensive experiments span: (1) Three major dataset categories encompassing classic (CIFAR10, CIFAR100, ImageNet-1k), imbalanced (CIFAR10-LT, CIFAR100-LT), and fine-grained (StanfordCars, FGVCAircraft) image classification datasets, each evaluated under 3-5 distinct sampling ratios; (2) Diverse pretrained architectures including Convolutional Neural Network (ConvNeXt), Vision Transformer (ViT), and Vision LSTM (ViL) networks; (3) A systematic investigation of frozen feature augmentation (FroFA) strategies. (4) A comprehensive and rigorous analysis of efficiency and generalizability. The results demonstrate significant improvements with strong generalization and robustness. Notably, under low sampling ratios, our framework achieves remarkable performance gains of over 20% on the ViT model for CIFAR10, CIFAR100, and ImageNet-1k benchmarks. This systematic approach establishes new state-of-the-art performance while maintaining parameter efficiency, proving particularly effective when labeled data is scarce.
arXiv:2606.02374v1 Announce Type: new
Abstract: Earth Observation (EO) has fundamentally transformed the monitoring of environmental processes and human activities up to planetary scale. Recent advances in self-supervised learning have given rise to Earth Observation Foundation Models (EOFMs), which leverage petabyte-scale unlabeled EO data to learn transferable representations across a wide range of downstream geospatial tasks. Despite these advances, current EOFMs remain largely confined to raster modalities, overlooking the rich, structured information encoded in openly-accessible vector data sources such as OpenStreetMap and Overture. Vector data provides explicit and compact representations of geographic entities, including geometry, topology, and semantic relationships, offering critical contextual signals that are often ambiguous or inaccessible in imagery alone. Raster and vector data thus represent complementary views of geographic space: raster data captures continuous physical and spectral patterns, while vector data encodes discrete objects and their relational structure and often represents more of the human rather than the physical systems (e.g. social or demographic data). However, existing geospatial representation learning paradigms treat these modalities in isolation, relying on imperfect and often lossy transformations to bridge them. This perspective paper calls for a paradigm shift toward joint Spatial Representation Learning (SRL) in an unified embedding space that integrate raster perception with vector-based reasoning. Building on emerging efforts in multimodal geospatial learning, we highlight conceptual foundations, technical challenges, and promising directions for aligning heterogeneous spatial data sources. We contend that such integration is essential for developing next-generation geospatial AI systems capable of more accurate, interpretable, and semantically grounded understanding of the Earth.
arXiv:2606.02134v1 Announce Type: new
Abstract: Deep neural networks achieve strong performance on many supervised learning tasks but remain vulnerable to adversarial perturbations. Neural network verification provides mathematically rigorous robustness guarantees, yet at substantial computational cost. To mitigate this, certified training techniques optimise for verifiable robustness during training, typically inducing a trade-off between natural and certified accuracy controlled by method-specific hyperparameters. Because these metrics are inherently conflicting, the common practice of reporting a single configuration is problematic: it can mislead conclusions about overall performance and prevents unbiased assessments of the state of the art. We address this by evaluating certified training methods via Pareto front comparisons over the natural--certified accuracy trade-off. To enable fair, method-agnostic comparisons, we perform efficient automated multi-objective hyperparameter optimisation to identify a set of Pareto-optimal configurations for each method. This approach often uncovers substantial undertuning in previously reported configurations, yielding superior performance and establishing a new state of the art. Leveraging these fronts, we present the first comprehensive multi-objective comparison of certified training approaches, showing that prior advancements are less pronounced than assumed and revealing previously unreported performance complementarities.
arXiv:2509.02558v2 Announce Type: replace
Abstract: Retrieval benchmarks for large language models (LLMs) should reflect the long, reasoning-intensive queries typical of retrieval-augmented generation (RAG). We present a systematic study of BRIGHT, a reasoning-focused retrieval benchmark, along with strong, reproducible reference methods integrated into Anserini, Pyserini, and RankLLM. We evaluate lexical, sparse, dense, and fusion-based retrievers, as well as LLM rerankers, under long-query settings. In reproducing BRIGHT's lexical baseline, we identify a key under-documented detail: query-side BM25 (BM25Q), which applies BM25 weighting to the query itself. On long, multi-sentence queries, BM25Q consistently outperforms standard BM25, making it the strongest lexical baseline for reasoning-oriented retrieval. We further audit the BRIGHT corpus, uncovering data quality issues that impact evaluation, and offer mitigation. Finally, we study the generalizability of BM25Q across five additional benchmarks, finding its gains largely specific to BRIGHT, while fusion with standard BM25 provides the most consistent improvements across datasets.
arXiv:2504.20238v2 Announce Type: replace
Abstract: Atmospheric predictability research has long held that rapid error growth at small spatial scales imposes an intrinsic limit of roughly two weeks on deterministic weather forecast skill. We challenge this limit using GraphCast, a machine-learning weather model, by optimizing initial conditions for twice-daily forecasts spanning 2020. This approach yields an average error reduction of 86% at ten days relative to control forecasts from reanalysis initial conditions, with skill lasting beyond 30 days. Mean optimal initial-condition perturbations reveal large-scale, spatially coherent corrections primarily reflecting an intensification of the Hadley circulation. Forecasts using GraphCast-optimal initial conditions in the Pangu-Weather model achieve a 21% error reduction, peaking at four days, indicating that analysis corrections reflect adjustments that target both model and analysis error. These results demonstrate the existence of initial conditions producing skillful deterministic forecasts far beyond two weeks. Whether such initial conditions can be identified in real-time for improving operational weather forecasts remains a topic of future research.
arXiv:2606.02136v1 Announce Type: new
Abstract: Neural asymmetric routing models increasingly encode directionality through matrix representations and asymmetry-aware attention. The final routing action, however, is not a node in isolation but a directed transition chosen under the current partial route. This creates a representation--decision mismatch: pairwise cost information may be encoded upstream while the final candidate logit is still largely parameterized as context--node compatibility. We propose a decoder-design principle for neural asymmetric routing: the final score should explicitly expose transition-level quantities suggested by the problem's cost-to-go structure. We instantiate this principle with an edge-aware decoder that adds candidate-specific terms for the current directed edge, return-to-start closure, and static lightweight lookahead, while keeping the representation backbone fixed. On a controlled SVD/Sinkhorn asymmetric backbone, the decoder improves over the RADAR reference when trained on ATSP-100 and evaluated zero-shot on ATSP-100/200/500/1000, reducing the ATSP-1000 gap from $4.13\%$ to $2.73\%$. On ACVRP, the same score-level modification shows the same qualitative trend under a richer routing state. ATSP ablations and directed-transition diagnostics sharpen the mechanism: the strongest evidence concerns sensitivity to the current directed edge, while closure and static lookahead act as heuristic continuation cues. The results support a mechanism study: a key decoder-side signal in neural asymmetric routing is decision-time exposure of transition-level edge information.
arXiv:2606.02449v1 Announce Type: new
Abstract: Multimodal agents are increasingly expected to operate interfaces on behalf of users, raising a central deployment question: can they truly substitute for humans in workflows that services deliberately protect against automation? CAPTCHA verification makes this question concrete. It is not merely a visual puzzle, but a human-verification boundary placed before account creation, content access, form submission, and other protected actions. We introduce \textbf{Humanity's Last Line of Verification (HLL)}, a controlled benchmark that uses interactive CAPTCHA verification to evaluate whether agents can cross this boundary through grounded, human-like interaction rather than recognition alone. HLL covers diverse CAPTCHA interactions and exposes agents to controlled realism stressors, including cluttered webpages, harder task variants, and trace-conditioned validation of the solving process. We evaluate eight frontier multimodal agents in a closed-loop GUI environment. The results show that current agents remain brittle at this human-substitution boundary: performance varies sharply across verification types, degrades under realistic interface conditions, and drops further when correct answers must be supported by valid action traces. By exposing gaps in localization, action calibration, state tracking, and process consistency, HLL provides a concrete testbed for measuring how close multimodal agents are to acting as human substitutes in protected real-world workflows. Our code is available at https://github.com/XinhaoS0101/HLL
arXiv:2606.01362v1 Announce Type: new
Abstract: Video generative models have achieved remarkable progress in synthesizing photorealistic video sequences. However, enabling broader and more creative downstream applications requires fine-grained instance-level video editing, including object insertion, object removal, and texture editing, which has emerged as a prominent yet challenging problem. Existing approaches either propose unified generative frameworks with only coarse semantic control, or design task-specific frameworks for individual editing tasks, limiting their flexibility and applicability across diverse real-world scenarios. To address these limitations, we propose AlbedoEdit, a unified generative video editing framework that jointly supports object insertion, object removal, and texture editing. Our key insight is that the intrinsic albedo map, which is invariant to lighting and contains no specularity, shadowing and inter-reflection effects, provides an effective and user-friendly mechanism for specifying fine-grained appearance edits. Built upon video foundation models, AlbedoEdit is fine-tuned to translate source RGB videos into edited RGB videos, conditioned on a user-edited first-frame albedo. Trained on a new paired synthetic dataset covering all three editing tasks, AlbedoEdit implicitly learns to harmonize edited contents and simulate complex real-world visual effects triggered by editing operations, including specular highlights, soft shadows, and mirror reflections. AlbedoEdit demonstrates superior performance over state-of-the-art video editing approaches, both qualitatively and quantitatively. Project webpage is https://vcai.mpi-inf.mpg.de/projects/AlbedoEdit/.
arXiv:2606.02451v1 Announce Type: new
Abstract: Programmable photonic meshes provide a promising platform for analog matrix-vector multiplication, but their scalability is often limited by the large phase-shift ranges required in universal interferometer circuits. We introduce a perturbative programming method that operates the circuit near a fixed reference configuration and realizes the target transformation through interferometric subtraction, thereby reducing the required programmable phase excursion. We develop this approach for photonic matrix-vector multiplication architectures based on universal unitary meshes, and low-depth non-unitary constructions based on sums of unitaries. We identify favorable reference configurations through a local conditioning criterion, analyze the phase statistics obtained for random target matrices, and show that perturbative programming produces phase distribution shrinking as the matrix size increases. We further quantify the trade-off between reduced phase range and the intrinsic overhead introduced by the subtraction architecture, and show that for sufficiently lossy phase shifters the reduced phase range can compensate for this penalty. These results identify perturbative programming as a conditional but potentially useful route toward more scalable programmable photonic matrix processors.
arXiv:2606.02481v1 Announce Type: new
Abstract: Large image datasets have accelerated progress in cognitive neuroscience and computer vision. However, most datasets are low-resolution, internet-sourced JPEGs with unknown capture conditions and limited spatial context. Places in the Wild is a dataset of 67,574 high-resolution photographs collected in situ across 810 physical locations spanning 260 basic-level scene categories, including indoor, urban, and natural environments. At each location, a 45-megapixel Canon EOS R5 mounted on a panoramic tripod captured 72 images at 5-degree horizontal intervals plus 12 images at varying elevations, yielding dense 360-degree viewpoint sampling. All images were recorded simultaneously as 14-bit RAW (CR3) files and compressed JPEGs, preserving sensor-level detail for analyses of luminance, contrast, color, and other image statistics. The dataset is accompanied by complete EXIF metadata and a suite of image-quality metrics. Places in the Wild supports research on viewpoint-dependent recognition in humans and models, training and evaluation of scene-understanding systems under realistic conditions, characterization of natural scene statistics, and experiments requiring near-full-field visual displays.
arXiv:2606.02484v1 Announce Type: new
Abstract: Recent advances in large language models and agentic AI systems have enabled significant progress in mathematical discovery, from solving competition problems to tackling research-level conjectures. However, open problems in computational mathematics have received comparatively less attention: research in this area often requires not only proofs but also numerical experimentation, adversarial constructions, and algorithm design. In this paper, we introduce an agentic research system, Iteris, designed for open problems in computational mathematics. We apply Iteris to two open problems from a recent Simons Workshop collection (arXiv:2602.05394). In these case studies, Iteris generated numerical evidence, constructions, and proof drafts that led, after expert review and correction, to verified results. The first result is a phase diagram for the asymptotic comparison between conjugate gradient and randomized coordinate descent on power-law spectra; the second is a counterexample showing that QR factorization with column pivoting can fail to select well-conditioned submatrices even under low coherence. These case studies suggest that agentic AI systems can participate meaningfully in research workflows for open problems in computational mathematics, while human validation remains essential.
arXiv:2510.06028v3 Announce Type: replace
Abstract: This paper provides data-dependent bounds on the expected error of the Gibbs algorithm in the overparameterized interpolation regime, where low training errors are also obtained for impossible data, such as random labels in classification. The results show that generalization in the low-temperature regime is already signaled by small training errors in the noisier high-temperature regime. The bounds are stable under approximation with Langevin Monte Carlo algorithms. The analysis motivates the design of an algorithm to compute bounds, which on the MNIST, CIFAR-10, and SVHN datasets yield nontrivial, close predictions on the test error for true labeled data, while maintaining a correct upper bound on the test error for random labels.
arXiv:2606.02424v1 Announce Type: new
Abstract: Histology-based single-cell spatial transcriptomics (ST) estimation aims to predict gene expression for individual cells from histopathological images and cell locations, reducing the need for costly single-cell ST measurements. Unlike existing histology-to-ST methods that mainly predict spot-level profiles for local regions containing multiple cells, this task requires modeling cell-to-cell expression variability, which is strongly structured by cell type. We propose Genomics-Guided Cell-Type-Specific Mixture-of-Experts (GC-MoE), which estimates cell-type probabilities with a routing network and softly combines cell-type-specific experts for gene expression prediction. To further encode cell-type-dependent gene programs, we introduce the Cell-Type-Specific Co-Expression-Aware Predictor (CAP), together with a lightweight Cell-to-Cell Interaction Attention (C2CA) module for neighboring-cell context. Experiments and ablations on public single-cell ST datasets show consistent improvements over existing single-cell and adapted spot-level baselines.
arXiv:2604.10788v2 Announce Type: replace
Abstract: Tool-Integrated Reasoning (TIR) has emerged as a promising direction by extending Large Language Models' (LLMs) capabilities with external tools during reasoning. Existing TIR methods typically rely on external tool documentation during reasoning. However, this leads to tool mastery difficulty, tool size constraints, and inference inefficiency. To mitigate these issues, we explore Tool-Internalized Reasoning (TInR), aiming at facilitating reasoning with tool knowledge internalized into LLMs. Achieving this goal presents notable requirements, including tool internalization and tool-reasoning coordination. To address them, we propose TInR-U, a tool-internalized reasoning framework for unified reasoning and tool usage. TInR-U is trained through a three-phase pipeline: 1) tool internalization with a bidirectional knowledge alignment strategy; 2) supervised fine-tuning warm-up using high-quality reasoning annotations, and 3) reinforcement learning with TInR-specific rewards. We comprehensively evaluate our method across in-domain and out-of-domain settings. Experiment results show that TInR-U achieves superior performance in both settings, highlighting its effectiveness and efficiency.