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01.
arXiv (CS.CV) 2026-06-15

S$^2$COPE: Self-Supervised Concept Discovery via Preference Learning

Current representation learning paradigms force a fundamental compromise: self-supervised methods scale to massive datasets but yield opaque features, whereas interpretable models remain bottlenecked by the need for dense human annotation. We introduce Self-Supervised Concept discOvery via Preference lEarning (\model), a label-free framework that resolves this dilemma. Instead of treating Vision-Large-Language Models (VLLMs) as static feature extractors, \model leverages them as active participants in a self-supervised preference optimization loop. By autonomously hypothesizing, validating, and reinforcing candidate visual attributes directly from raw imagery, our framework discovers novel, structured concepts without a single label. Extensive experiments across natural, medical, and physics domains demonstrate that \model successfully extracts domain-specific concepts where standard VLLMs often fail to generate. By amortizing concept discovery directly into the VLLM backbone through our self-supervised preference objective – rather than relying on static generation and disjoint filtering – we achieve up to a 24-point absolute improvement in downstream top-1 classification accuracy on unseen data. Our work suggest that interpretability can emerge through a model's autonomous interaction with incidental visual structures, without any human supervision.

02.
arXiv (CS.CL) 2026-06-18

ScholaWrite: A Dataset of End-to-End Scholarly Writing Process

Writing is a cognitively demanding activity that requires constant decision-making, heavy reliance on working memory, and frequent shifts between tasks of different goals. To build writing assistants that truly align with writers' cognition, we must capture and decode the complete thought process behind how writers transform ideas into final texts. We present ScholaWrite, the first dataset of end-to-end scholarly writing, tracing the multi-month journey from initial drafts to final manuscripts. We contribute three key advances: (1) a Chrome extension that unobtrusively records keystrokes on Overleaf, enabling the collection of realistic, in-situ writing data; (2) a novel corpus of full scholarly manuscripts, enriched with fine-grained annotations of cognitive writing intentions. The dataset includes \LaTeX-based edits from five computer science preprints, capturing nearly 62K text changes over four months; and (3) analyses and insights into the micro-dynamics of scholarly writing, highlighting gaps between human writing processes and the current capabilities of large language models (LLMs) in providing meaningful assistance. ScholaWrite underscores the value of capturing end-to-end writing data to develop future writing assistants that support, not replace, the cognitive work of scientists.

03.
arXiv (CS.AI) 2026-06-19

AURA: Adaptive Uncertainty-aware Refinement for LLM-as-a-Judge Auditing

arXiv:2606.19714v1 Announce Type: cross Abstract: Large language models (LLMs) are increasingly used as judges for open-ended generation, as large-scale human evaluation is often expensive and difficult to scale, yet their preferences remain imperfect proxies for human judgment. Existing auditing pipelines often assume that a reliable subset of examples or clean supervision signals are available beforehand, for example from human annotation, heuristic filtering, or the outputs of strong judges. In LLM evaluation, this assumption is fragile: the initial split may inherit judge bias, while human verification is typically too scarce to define stable groups at scale. We propose AURA, an adaptive uncertainty–aware refinement framework for auditing pairwise LLM–as–a–judge decisions under selected human verification. AURA iteratively learns a human-consistency signal, propagates reliable evidence, and prioritizes uncertain comparisons for human review. The key idea is to treat trust in a judge as a latent quantity that is progressively refined as evidence accumulates. We provide a compact formulation, a stable refinement procedure, and a comprehensive evaluation on both synthetic and real pairwise LLM-answer data.

04.
arXiv (math.PR) 2026-06-17

Decay of correlations and zeros for the hard-core model

arXiv:2603.17858v2 Announce Type: replace Abstract: In a recent paper the last author proved that absence of complex zeros of the partition function of the hard-core model near a parameter $\lambda>0$ implies a form of correlation decay called strong spacial mixing. In this paper we investigate the reverse implication. We introduce a strengthening of strong spatial mixing that we call very strong spatial mixing (VSSM). Our main result is that if VSSM holds at a parameter $\lambda>0$ for a family of graphs, this implies that the partition function has no zeros near that parameter for each graph in the family. We also demonstrate that a closely related variant of very strong spatial mixing does not imply zero-freeness. As a consequence of our main result, we moreover obtain that VSSM implies spectral independence. Our proof relies on transforming the problem to the analysis of an induced non-autonomous dynamical system given by Möbius transformations.

05.
arXiv (CS.CV) 2026-06-11

ReMoT: Reinforcement Learning with Motion Contrast Triplets

We present ReMoT, a unified training paradigm to systematically address the fundamental shortcomings of VLMs in spatio-temporal consistency – a critical failure point in navigation, robotics, and autonomous driving. ReMoT integrates two core components: (1) A rule-based automatic framework that generates ReMoT-16K, a large-scale (16.5K triplets) motion-contrast dataset derived from video meta-annotations, surpassing costly manual or model-based generation. (2) Group Relative Policy Optimization, which we empirically validate yields optimal performance and data efficiency for learning this contrastive reasoning, far exceeding standard Supervised Fine-Tuning. We also construct the first benchmark for fine-grained motion contrast triplets to measure a VLM's discrimination of subtle motion attributes (e.g., opposing directions). The resulting model achieves state-of-the-art performance on our new benchmark and multiple standard VLM benchmarks, culminating in a remarkable 25.1% performance leap on spatio-temporal reasoning tasks.

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

SpecAlign: Efficient Specification-Grounded Alignment of Large Language Models via Synthetic Data

arXiv:2606.16276v1 Announce Type: new Abstract: As large language models (LLMs) are increasingly deployed in real-world applications, alignment is no longer governed by a single universal notion of safety or helpfulness, but instead by provider- or application-specific model specifications. These specifications are typically long, structured, and frequently updated, yet existing alignment pipelines lack a systematic mechanism to operationalize them as training signals. In this paper, we propose specification-grounded alignment, a new alignment paradigm that treats provider-authored model specifications as the primary alignment target rather than abstract principles or static benchmarks. To instantiate this paradigm, we introduce SpecAlign, a framework that synthesizes alignment data directly from specification documents. SpecAlign combines structured rule annotation, controllable specification instantiation, and multi-agent adversarial data synthesis to generate fine-grained, boundary-aware preference pairs that capture both compliant behaviors and meaningful specification violations. Experiments across multiple model specifications and backbone models demonstrate that training with SpecAlign consistently improves rule compliance while preserving general capabilities and avoiding over-conservative behavior. These results suggest that grounding alignment in explicit model specifications enables rapid, precise, and scalable adaptation of LLM behavior to evolving policy requirements.

07.
arXiv (CS.CV) 2026-06-17

Does the Data Processing Inequality Reflect Practice? On the Utility of Low-Level Tasks

The data processing inequality is an information-theoretic principle stating that the information content of a signal cannot be increased by processing the observations. In particular, it suggests that there is no benefit in enhancing the signal or encoding it before addressing a classification problem. This assertion can be proven to be true for the case of the optimal Bayes classifier. However, in practice, it is common to perform "low-level" tasks before "high-level" downstream tasks despite the overwhelming capabilities of modern deep neural networks. In this paper, we aim to understand when and why low-level processing can be beneficial for classification. We present a comprehensive theoretical study of a binary classification setup, where we consider a classifier that is tightly connected to the optimal Bayes classifier and converges to it as the number of training samples increases. We prove that for any finite number of training samples, there exists a pre-classification processing that improves the classification accuracy. We also explore the effect of class separation, training set size, and class balance on the relative gain from this procedure. We support our theory with an empirical investigation of the theoretical setup. Finally, we conduct an empirical study where we investigate the effect of denoising and encoding on the performance of practical deep classifiers on benchmark datasets. Specifically, we vary the size and class distribution of the training set, and the noise level, and demonstrate trends that are consistent with our theoretical results.

08.
arXiv (CS.CL) 2026-06-18

ScholarSum: Student-Teacher Abstractive Summarization via Knowledge Graph Reasoning and Reflective Refinement

Abstractive summarization plays a crucial role in enabling efficient understanding of scientific literature, yet it inherently demands both linguistic fluency and factual faithfulness. Existing approaches often fail to reconcile these two requirements. Extractive methods rely on rigid sentence splicing that disrupts macro-level logical coherence, while large language model (LLM)-based generative approaches, despite mastering linguistic fluency, exhibit limited factual consistency. In this work, we propose ScholarSum, a hierarchical reflective graph-based framework that emulates a student-teacher writing process for fluent and faithful scientific summarization. ScholarSum first organizes the document into a hierarchical knowledge graph by segmenting it into semantically coherent units, whose multi-layered community structure captures global logic and macro-level themes. Guided by this global structure, the student generates an initial draft, which is subsequently refined through fine-grained evidence retrieval. To ensure factual consistency, a teacher-like reviewer then iteratively examines the draft, identifies unsupported content, and prompts targeted re-retrieval and rewriting until the summary meets rigorous quality standards. Extensive experiments demonstrate that ScholarSum significantly outperforms previous baselines in terms of both completeness and faithfulness. Our code is available at https://github.com/Xiaoyu-Tao/ScholarSum.

09.
arXiv (CS.AI) 2026-06-18

Externalizing Research Synthesis and Validation in AI Scientists through a Research Harness

arXiv:2606.18874v1 Announce Type: new Abstract: AI systems can increasingly automate scientific workflows, but the reasoning that links prior evidence, generated ideas, experiments and final claims often remains implicit inside model inference. Here we introduce Xcientist, a research harness that externalizes research synthesis and experimental validation into inspectable, contract-governed processes. Xcientist organizes literature evidence, idea states, implementation plans, ablation records and repair traces as persistent research artifacts, so that generated mechanisms can be grounded, executed, tested and revised without losing their evidential basis. We identify claim drift as a failure mode of automated research, where runnable artifacts no longer support the mechanism originally claimed. Across training-free memory systems, graph-structured traffic forecasting and multi-scale physics-informed neural networks, Xcientist preserves traceable trajectories from problem formulation to mechanism design, validation and bounded revision. These results suggest that AI scientists should be evaluated not only by their final artifacts, but by whether their synthesis and validation processes remain attributable, inspectable and scientifically accountable.

10.
arXiv (CS.CL) 2026-06-16

SAAS: Self-Aware Reinforcement Learning for Over-Search Mitigation in Agentic Search

Agentic search enables LLMs to solve complex multi-hop questions through iterative reasoning and external search. Despite the effectiveness, these systems often suffer from a critical limitation in practice: agents fail to recognize their own knowledge boundaries, blindly triggering searches when internal knowledge suffices and failing to terminate search even when adequate evidence has been collected. The lack of self-awareness leads to severe over-search, incurring substantial inference latency and prohibitive computational cost. To this end, we propose SAAS, a novel RL framework designed to cultivate dynamic self-awareness that precisely regulates search behavior without compromising accuracy. SAAS introduces three key components: (i) a search boundary modeling mechanism, which identifies the search boundary under the evolving policy by contrasting search-disabled and search-enabled rollouts; (ii) a boundary-aware reward module, which translates this boundary awareness into trajectory-level penalties, suppressing unnecessary and redundant searches; and (iii) a stage-wise optimization strategy, which leverages a sequential curriculum to prioritize reasoning over search regularization, thereby avoiding reward hacking. Extensive experiments demonstrate that SAAS substantially reduces over-search, while maintaining accuracy. Our code and implementation details are released at https://github.com/XMUDeepLIT/SAAS.

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

Active Learning with Low-Rank Structure for Data Selection

arXiv:2606.16045v1 Announce Type: new Abstract: In the data selection problem, the objective is to choose a small, representative subset of data that can be used to efficiently train a machine learning model. Sener and Savarese [ICLR 2018] showed that, given an embedding representation of the data and suitable geometric assumptions, heuristics based on $k$-center clustering can be used to perform data selection. This perspective was further explored by Axiotis et. al. [ICML 2024], who proposed a data selection approach based on $k$-means clustering and sensitivity sampling. However, these methods rely on the assumption that the dataset exhibits intrinsic geometric structure that can be effectively captured by clustering, whereas many modern datasets instead possess global algebraic structure that is better exploited by low-rank approximation or principal component analysis. In this paper, we introduce a new data selection framework based on low-rank approximation and residual-based sampling, formulated through the lens of row subset selection and loss-preserving coreset construction. Given an embedding representation of the data satisfying mild regularity conditions, which can be interpreted as algebraic or angular notions of Lipschitz continuity, we show that it is possible to select a weighted subset of $\tilde{O}\left(k + \frac{1}{\varepsilon^2}\right)$ data points whose average loss approximates the average loss over the full dataset within a $(1+\varepsilon)$ relative error, up to an additive $\varepsilon \Phi_k$ term, where $\Phi_k$ denotes the optimal rank-$k$ approximation cost of the embedding matrix. We complement these theoretical guarantees with empirical evaluations, demonstrating that on a range of real-world datasets, our data selection approach achieves improved performance over prior strategies based on uniform sampling or clustering-based sensitivity sampling.

12.
arXiv (CS.LG) 2026-06-16

SILAGE: Memory-Efficient, Full-Gradient-Free Nonconvex Optimization for Nested Finite Sums

arXiv:2606.15832v1 Announce Type: new Abstract: Empirical risk minimization on massive datasets naturally exhibits a nested double finite-sum structure, where $N=nm$ total samples are logically or physically partitioned into $n$ blocks of size $m$ (e.g., in pooled data silos, out-of-core learning, or deliberate stratification). While variance-reduced methods achieve optimal oracle complexities for nonconvex objectives, they suffer from severe scaling bottlenecks in this centralized regime. Recursive estimators, such as PAGE, require periodic global full-gradient refreshes over all $nm$ samples, which are computationally expensive. Conversely, single-loop methods, such as SILVER, avoid such refreshes but require an impractical $\mathcal{O}(nm)$ memory footprint to store a control variate for every sample. In this paper, we propose SILAGE, a variance-reduced algorithm that addresses this trade-off. By actively exploiting the double-sum structure, SILAGE eliminates periodic global full-gradient refreshes over all $nm$ components (evaluating at most one local group gradient per iteration) while requiring only $\mathcal{O}(n)$ memory. Furthermore, we provide a tight convergence analysis that avoids pessimistic worst-case Lipschitz constants. Instead, SILAGE's complexity natively adapts to the underlying data geometry via nested functional similarities: across-group ($\delta_1$) and within-group ($\delta_2$) heterogeneity. Our results improve existing state-of-the-art bounds in several practically relevant regimes.

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

CASHEW: Stabilizing Multimodal Reasoning via Iterative Trajectory Aggregation

Vision-language models achieve strong performance across a wide range of multimodal understanding and reasoning tasks, yet their multi-step reasoning remains unstable. Repeated sampling over the same input often produces divergent reasoning trajectories and inconsistent final predictions. To address this, we introduce two complementary approaches inspired by test-time scaling: (1) CASHEW, an inference-time framework that stabilizes reasoning by iteratively aggregating multiple candidate trajectories into higher-quality reasoning traces, with explicit visual verification filtering hallucinated steps and grounding reasoning in visual evidence, and (2) CASHEW-RL, a learned variant that internalizes this aggregation behavior within a single model. CASHEW-RL is trained using Group Sequence Policy Optimization (GSPO) with a composite reward that encourages correct answers grounded in minimal yet sufficient visual evidence, while adaptively allocating reasoning effort based on task difficulty. This training objective enables robust self-aggregation at inference. Extensive experiments on 13 image understanding, video understanding, and video reasoning benchmarks show significant performance improvements, including gains of up to +26.2 percentage points on ScienceQA and +9.1 percentage points on EgoSchema.

14.
arXiv (CS.AI) 2026-06-11

On the Geometry of On-Policy Distillation

arXiv:2606.07082v2 Announce Type: replace-cross Abstract: On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

15.
arXiv (CS.AI) 2026-06-18

Large-Scale OD Matrix Estimation with A Deep Learning Method

arXiv:2310.05753v2 Announce Type: replace Abstract: The estimation of origin-destination (OD) matrices is a crucial aspect of Intelligent Transport Systems (ITS). It involves adjusting an initial OD matrix by regressing the current observations like traffic counts of road sections (e.g., using least squares). However, the OD estimation problem lacks sufficient constraints and is mathematically underdetermined. To alleviate this problem, some researchers incorporate a prior OD matrix as a target in the regression to provide more structural constraints. However, this approach is highly dependent on the existing prior matrix, which may be outdated. Others add structural constraints through sensor data, such as vehicle trajectory and speed, which can reflect more current structural constraints in real-time. Our proposed method integrates deep learning and numerical optimization algorithms to infer matrix structure and guide numerical optimization. This approach combines the advantages of both deep learning and numerical optimization algorithms. The neural network(NN) learns to infer structural constraints from probe traffic flows, eliminating dependence on prior information and providing real-time performance. Additionally, due to the generalization capability of NN, this method is economical in engineering. We conducted tests to demonstrate the good generalization performance of our method on a large-scale synthetic dataset. Subsequently, we verified the stability of our method on real traffic data. Our experiments provided confirmation of the benefits of combining NN and numerical optimization.

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

Understanding LLM Reasoning for Abstractive Summarization

Reasoning has substantially improved Large Language Models (LLMs) on analytical tasks such as mathematics and code generation, but its value for abstractive summarization remains unclear. To address this gap, we adapt general reasoning strategies to the summarization setting and conduct a large-scale comparative study of 8 reasoning strategies and 3 Large Reasoning Models (LRMs) across 8 diverse datasets, evaluating both summary quality and factual faithfulness. Our results show that reasoning is not a universal solution and its effectiveness depends strongly on the strategy and the summarization setting. In particular, we find a trade-off between summary quality and factual faithfulness. Explicit reasoning strategies often improve reference-based quality, but may weaken factual grounding, whereas implicit reasoning in LRMs shows the opposite tendency. We further find that increasing an LRM's internal reasoning budget does not reliably improve summarization and can even reduce factual consistency. These findings suggest that, for summarization, more reasoning is not always better. Effective reasoning should preserve faithful compression rather than induce over-elaboration. Our source code is publicly available.

17.
arXiv (CS.LG) 2026-06-18

Acceleration of an algebraic multigrid pressure solver using graph neural networks

arXiv:2606.19251v1 Announce Type: cross Abstract: Solving the pressure-Poisson equation remains the primary computational bottleneck in incompressible unstructured flow solvers primarily due to the inherent sensitivity of traditional linear solvers to mesh irregularities. This work introduces a data-driven algebraic multigrid (AMG) smoother that uses a modified graph convolutional isomorphism network (GCIN). The graph neural network predicts optimal polynomial coefficients to construct a sparse pseudo-inverse operator across diverse grid topologies. The coefficients are optimized to reduce the residual after each V-cycle iteration. By directly capturing the algebraic structure of the system from the sparse coefficient matrix, the proposed method maintains the solver's linearity while adapting to local anisotropies in unstructured grids. Our framework demonstrates significant performance gains by reducing the number of V-cycles required for a given tolerance and delivering wall-clock speedups from 4% to 37% across diverse benchmarks. Notably, the model exhibits robust generalization by maintaining efficiency on meshes up to 128 times larger than those seen in training, and by accelerating the solver's convergence on unseen industry-relevant problems such as the AirfRANS dataset.

18.
arXiv (CS.CV) 2026-06-18

Moebius: 0.2B Lightweight Image Inpainting Framework with 10B-Level Performance

While 10B-level industrial foundation models have pushed the boundaries of image inpainting, their prohibitive computational costs severely hinder practical deployment. Constructing a highly optimized task-specific specialist offers a promising solution; however, extreme structural compression inevitably triggers a severe representation bottleneck. To conquer this, we propose Moebius, a highly efficient lightweight inpainting framework. We systematically reconstruct the diffusion backbone by introducing the Local-$\lambda$ Mix Interaction ($L\lambda MI$) block. Comprising Local-$\lambda$ and Interactive-$\lambda$ modules, it elegantly summarizes spatial contexts and global semantic priors into fixed-size linear matrices, preserving complex latent interactions while drastically shedding parameters. Furthermore, to unlock the full representational capacity of this highly compact architecture, we synergistically pair it with an adaptive multi-granularity distillation strategy. Operating strictly within the latent space to avoid expensive pixel-space decoding, this strategy dynamically balances multiple gradient-based losses to achieve high-fidelity alignment. Extensive experiments across natural and portrait benchmarks demonstrate that this optimal synergy enables Moebius to rival or even surpass the generation quality of the 10B-level industrial generalist FLUX.1-Fill-Dev. Remarkably, Moebius achieves this using less than 2\% of the parameters (0.22B vs. 11.9B) while delivering a $>15\times$ acceleration in total inference time, setting a new efficiency standard for high-fidelity inpainting. Project page at https://hustvl.github.io/Moebius.

19.
medRxiv (Medicine) 2026-06-10

Assessment of the accuracy of lung lesions diagnosis in adolescents with osteosarcoma using artificial intelligence

Background. Lung metastases in osteosarcoma (OS) are the main cause of the death. The accuracy of the diagnosis of nodules by computed tomography (CT) of the lungs is critically important for determining the disseminated stage of the disease and planning surgical treatment. The use of artificial intelligence (AI) in the search for lung nodules increases the accuracy of diagnosis and reduces the chance of missing metastases. Objective: to evaluate the accuracy of lung nodules diagnosis in adolescents with OS using AI. Methods. A retrospective assessment of CT scans of adolescents with OS was performed. A pathological nodule with an average size of [≥]4 mm was considered a target finding. The diagnostic accuracy of an AI algorithm previously trained on an adult dataset was evaluated, and the number of false positives (FP) and false negatives (FN) was determined. Sensitivity, specificity, accuracy, area under the ROC curve (AUC), positive predictive value, negative predictive value, and F1-measure were calculated. Based on the obtained results, the effectiveness of the algorithm was assessed. Results. 248 CT scans of adolescents with OS were evaluated. The following results were obtained: in 5 cases, the AI algorithm showed a FP result (2.02%), in 34 cases, it showed a FN result (13.71%), and in 209 cases, a correct result (both true positive and true negative) (84.27%). The diagnostic accuracy of the algorithm was 0.843 (95% CI 0.794-0.887). The application of the AI algorithm in the practice of an X-ray doctor in a specific clinical task would allow to increase the sensitivity from 0.805 to 0.891, while ensuring an absolute decrease in the number of FN results by 8.59% and a relative decrease by 44%. Conclusion. The obtained results confirm the practical value of the application of the AI algorithm and justify the implementation of AI-assisted systems in the diagnostic protocols for lung metastases in adolescents with OS.

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

A Neuro-Symbolic Approach to Strategy Synthesis for Strategic Logics

arXiv:2606.17962v1 Announce Type: cross Abstract: Reasoning about what agents can achieve through strategic interaction is a core challenge in Multi-Agent Systems (MAS). Logics for strategic ability, such as ATL, provide rigorous methods, but their adoption is often hindered by the computational cost of strategy synthesis. We introduce a neuro-symbolic framework that integrates large language models (LLMs) into the model-checking pipeline for MAS. The LLM acts as a strategy-generation oracle, proposing candidate strategies that are then formally validated by a standard MAS model checker. This generate-and-certify architecture uses LLM guidance to navigate large combinatorial strategy spaces while preserving formal soundness: generated strategies are accepted only when certified by the verifier. We instantiate the framework for bounded strategic reasoning in NatATL and introduce the first NatATL strategy-synthesis dataset, consisting of 4211 instances. Experiments with an open-weight Qwen3-32B model show that our certified pipeline achieves 92\% accuracy on strategy-synthesis outcomes.

21.
arXiv (math.PR) 2026-06-15

Longest weakly increasing subsequences of discrete random walks on the integers with heavy tailed distribution of increments

arXiv:2603.29047v2 Announce Type: replace-cross Abstract: We investigate the behavior of the length of the longest weakly increasing subsequences (weak LIS) of $n$-step random walks with nonzero integer increments $k = \pm 1, \pm 2, \dots$ given by a symmetric heavy tailed mass distribution proportional to $|k|^{-1-\alpha}$ for several values of the real parameter $\alpha > 0$ together with that of the simple random walk ($k=\pm 1$), to which the $n$-step heavy tailed walks reduce when $\alpha$ grows large enough that step jumps beyond $\pm 1$ become essentially absent on the scale of $n$. By means of exploratory fits, weighted nonlinear least squares, and nested-model comparisons, we found that the sample average length $\langle{L_{n}}\rangle$ scales like $\langle{L_{n}}\rangle \sim \sqrt{n}\log{n}$ when the distribution of increments has finite variance ($\alpha > 2$) and $\langle{L_{n}}\rangle \sim n^{\theta}$ with a varying exponent $\theta > 0.5$ when the variance is infinite ($\alpha \leq 2$). Distributional diagnostics indicate that the bulk of the $L_{n}$ distribution is very well-approximated by a lognormal model, though systematic deviations are observed in the tails. Our results corroborate and expand upon previous results for the LIS of other types of heavy-tailed random walks and raise a conjecture as to whether the distribution of $L_{n}$ is given, or can be effectively described, by a lognormal distribution.

22.
arXiv (CS.LG) 2026-06-18

Exponentially many initializations to avoid barren plateaus

arXiv:2606.18515v1 Announce Type: cross Abstract: Barren plateaus are stated as an average-case phenomenon: pick an ansatz, initialize it naively, and concentration follows. This has led to the common view that a potential cure for barren plateaus is simply to initialize the parameters more carefully. Here we show that the situation is subtler. We introduce a first-moment framework that gives a simple operator-level diagnostic for when an initialization may escape the fully concentrated barren-plateau fixed point, and for comparing the biases induced by different initialization strategies. Our framework recovers several known initialization schemes such as identity and Gaussian initialization, but also shows that barren-plateau avoidance is highly non-unique. Indeed, many shifted, biased, and non-symmetric parameter distributions can avoid concentration, and these choices need not be equivalent. In fact, our results show that one can generate exponentially many families of inequivalent initialization strategies. Then, our numerics indicate that different first-moment-distinct initializations can lead to different attained minima, suggesting that avoiding barren plateaus via smart initializations can trade the exponential concentration problem for the challenge of selecting the right trainable pocket amongst many options.

23.
arXiv (CS.CL) 2026-06-16

Encode Errors: Representational Retrieval of In-Context Demonstrations for Multilingual Grammatical Error Correction

Grammatical Error Correction (GEC) involves detecting and correcting the wrong usage of grammar. While large language models (LLMs) with in-context learning (ICL) capabilities have shown significant progress on various natural language processing (NLP) tasks, their few-shot performance on GEC remains suboptimal. This is mainly due to the challenge of retrieving suitable in-context demonstrations that capture error patterns instead of semantic similarity. In this paper, we demonstrate that LLMs can inherently capture information related to grammatical errors through their internal states. From these states, we extract the Grammatical Error Representation (GER), an informative and semantically neutral encoding of grammatical errors. Our novel GER-based retrieval method significantly boosts performance in ICL settings on multilingual GEC datasets, improving the precision of correction. For high-resource languages, our results on 8B-sized open-source models match those of closed-source models such as Deepseek2.5 and GPT-4o-mini. For low-resource languages, our $F_{0.5}$ scores surpass the baseline by up to a factor of 1.20. This method provides a more precise and resource-efficient solution for multilingual GEC, offering a promising direction for interpretable GEC research.

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

AIGS-Net: Compact Illumination Field Modeling via 2D Gaussian Splatting for Fast Low-Light Image Enhancement

Existing low-light image enhancement methods often face a bottleneck between the representation capacity of illumination-field modeling and computational complexity. To address this issue, this paper proposes an Adaptive Illumination Gaussian Splatting Network (AIGS-Net), an ultra-lightweight architecture for fast low-light enhancement. Unlike conventional static priors, AIGS-Net constructs an input-adaptive 2D Gaussian Splatting illumination field. The opacity of Gaussian basis functions is dynamically modulated by relative luminance statistics of the input image, and spatially varying illumination compensation is rendered through ordered alpha compositing. To guide adaptive illumination compensation efficiently, a zero-parameter nonlinear multiscale contextual encoding module is introduced to extract low-frequency structures and local contrast cues without additional convolutional weights. To suppress noise amplification and sensor-induced color bias, AIGS-Net integrates noise-mask estimation, locked single-channel Gamma mapping, cross-channel consistency regularization, and target color-alignment constraints. Experiments on LOL and LSRW benchmarks show that AIGS-Net improves detail recovery and color fidelity while requiring only approximately 40 learnable parameters, achieving an effective trade-off between enhancement quality and extreme inference efficiency.

25.
arXiv (math.PR) 2026-06-11

Percolation on hierarchical lattices

arXiv:2606.11503v1 Announce Type: new Abstract: We consider independent Bernoulli percolation on top of sequences of hierarchical graphs. Given a graph $G_{1}$ with two distinguished vertices $a_{1}$ and $b_{1}$, the hierarchical graph with seed $G_{1}$ is the sequence $\big( G_{k} \big)_{k \geq 1}$ resulting from the inductive procedure, where the graph $G_{k+1}$ is obtained from $G_{k}$ by replacing each of its edges with a copy of $G_{1}$, attached by the vertices $a_{1}$ and $b_{1}$. We prove that, under sharp hypotheses, percolation on these graphs presents a unique phase transition. Second, we establish the existence of several critical exponents in this context, such as the critical exponents for the correlation length $\nu$, the surface tension $\mu$, the one-arm exponent $\alpha_{1}$. Several results are also obtained for their infinite counterpart $G_\infty$, which is the Benjamini-Schramm limit of $G_k$: uniqueness of the infinite cluster, continuity of $\theta(p)$, existence of the percolation-probability exponent $\beta$ and scaling relations for the critical exponents $\alpha_1$, $\nu$ and $\beta$. Furthermore, we analyze noise sensitivity for crossing functions in $G_{k}$ and establish sharp noise sensitivity in this setting. Finally, we propose a setup where it is possible to verify the locality hypothesis, stating that the critical threshold for percolation is a local property, while critical exponents are determined by the global geometry of the graph. As a consequence of the techniques developed here, we also provide a necessary and sufficient condition for the existence of a unique fixed point for the map $p \mapsto \mathbb{E}_p[g]$ in $(0,1)$, where $g:\{0,1\}^n \to \{0,1\}$ is a nontrivial monotone Boolean function.