Proof-Number Search is a best-first search algorithm with many successful applications, especially in game solving. As large-scale computing clusters become increasingly accessible, parallelization is a natural way to accelerate computation. However, existing parallel versions of Proof-Number Search are known to scale poorly on many CPU cores. Using two parallelized levels and shared information among workers, we present the first massively parallel version of Proof-Number Search that scales efficiently even on a large number of CPUs. We apply our solver, enhanced with Grundy numbers for reducing game trees of impartial games, to the Sprouts game, a case study motivated by the long-standing Sprouts Conjecture. Our algorithm achieves 332.9$\times$ speedup on 1024 cores, significantly improving previous parallelizations and outperforming the state-of-the-art Sprouts solver GLOP by four orders of magnitude in runtime while generating proofs 1,000$\times$ more complex. Despite exponential growth in game tree size, our solver verified the Sprouts Conjecture for 42 new positions, nearly doubling the number of known outcomes.

Can language models (LMs) learn to faithfully describe their internal computations? Are they better able to describe themselves than other models? We study the extent to which LMs' privileged access to their own internals can be leveraged to produce new techniques for explaining their behavior. Using existing interpretability techniques as a source of ground truth, we fine-tune LMs to generate natural language descriptions of (1) the information encoded by LM features, (2) the causal structure of LMs' internal activations, and (3) the influence of specific input tokens on LM outputs. When trained with only tens of thousands of example explanations, explainer models exhibit non-trivial generalization to new queries. This generalization appears partly attributable to explainer models' privileged access to their own internals: using a model to explain its own computations generally works better than using a *different* model to explain its computations (even if the explainer model is significantly more capable than the target). Our results suggest not only that LMs can learn to reliably explain their internal computations, but that such explanations offer a scalable complement to existing interpretability methods. Code and data at https://github.com/TransluceAI/introspective-interp

We introduce a novel Mutual Information (MI) estimator that fundamentally reframes the discriminative approach. Instead of training a classifier to discriminate between joint and marginal distributions, we learn a normalizing flow that transforms one into the other. This technique produces a computationally efficient and precise MI estimate that scales well to high dimensions and across a wide range of ground-truth MI values.

With the growing demand for high-quality image generation on resource-constrained devices, efficient diffusion models have received increasing attention. However, such models suffer from approximation errors introduced by efficiency techniques, which significantly degrade generation quality. Once deployed, these errors are difficult to correct, as modifying the model is typically infeasible in deployment environments. Through an analysis of error propagation across diffusion timesteps, we reveal that these approximation errors can accumulate exponentially, severely impairing output quality. Motivated by this insight, we propose Iterative Error Correction (IEC), a novel test-time method that mitigates inference-time errors by iteratively refining the model's output. IEC is theoretically proven to reduce error propagation from exponential to linear growth, without requiring any retraining or architectural changes. IEC can seamlessly integrate into the inference process of existing diffusion models, enabling a flexible trade-off between performance and efficiency. Extensive experiments show that IEC consistently improves generation quality across various datasets, efficiency techniques, and model architectures, establishing it as a practical and generalizable solution for test-time enhancement of efficient diffusion models. The code is available in https://github.com/zysxmu/IEC.

The ability to grasp objects, signal with gestures, and share emotion through touch all stem from the unique capabilities of human hands. Yet creating high-quality personalized hand avatars from images remains challenging due to complex geometry, appearance, and articulation, particularly under unconstrained lighting and limited views. Progress has also been limited by the lack of datasets that jointly provide accurate 3D geometry, high-resolution multiview imagery, and a diverse population of subjects. To address this, we present PALM, a large-scale dataset comprising 13k high-quality hand scans from 263 subjects and 90k multi-view images, capturing rich variation in skin tone, age, and geometry. To show its utility, we present a baseline PALM-Net, a multi-subject prior over hand geometry and material properties learned via physically based inverse rendering, enabling realistic, relightable single-image hand avatar personalization. PALM's scale and diversity make it a valuable real-world resource for hand modeling and related research.

This study introduces the Korean Tax Avoidance Panel (KoTaP), a long-term panel dataset of non-financial firms listed on KOSPI and KOSDAQ between 2011 and 2024. After excluding financial firms, firms with non-December fiscal year ends, capital impairment, and negative pre-tax income, the final dataset consists of 12,653 firm-year observations from 1,754 firms. KoTaP is designed to treat corporate tax avoidance as a predictor variable and link it to multiple domains, including earnings management (accrual- and activity-based), profitability (ROA, ROE, CFO, LOSS), stability (LEV, CUR, SIZE, PPE, AGE, INVREC), growth (GRW, MB, TQ), and governance (BIG4, FORN, OWN). Tax avoidance itself is measured using complementary indicators cash effective tax rate (CETR), GAAP effective tax rate (GETR), and book-tax difference measures (TSTA, TSDA) with adjustments to ensure interpretability. A key strength of KoTaP is its balanced panel structure with standardized variables and its consistency with international literature on the distribution and correlation of core indicators. At the same time, it reflects distinctive institutional features of Korean firms, such as concentrated ownership, high foreign shareholding, and elevated liquidity ratios, providing both international comparability and contextual uniqueness. KoTaP enables applications in benchmarking econometric and deep learning models, external validity checks, and explainable AI analyses. It further supports policy evaluation, audit planning, and investment analysis, making it a critical open resource for accounting, finance, and interdisciplinary research.

Vision language models (VLMs) have advanced graphical user interface (GUI) task automation but still lag behind humans. We hypothesize this gap stems from missing core GUI knowledge, which existing training schemes (such as supervised fine tuning and reinforcement learning) alone cannot fully address. By analyzing common failure patterns in GUI task execution, we distill GUI knowledge into three dimensions: (1) interface knowledge about widget functions, layout semantics, and system states; (2) interaction knowledge about GUI interaction types and effects; and (3) procedure knowledge of task objectives and workflow sequences. We further introduce GUI Knowledge Bench, a benchmark with multiple-choice and yes/no questions across six platforms (Web, Android, MacOS, Windows, Linux, IOS) and 292 applications. Our evaluation indicates that current VLMs are generally aware of the functions of individual widgets, but lack the GUI-specific knowledge required to track system states, adhere to GUI interaction conventions, and assess task completion progress. Experiments on real-world GUI tasks further validate the close link between GUI knowledge and task success. By providing a structured framework for assessing GUI knowledge, our work supports the selection of VLMs with greater potential prior to downstream training and provides insights for building more capable GUI agents.

In this paper, we introduce PSI-LinUCB, a scalable variant of LinUCB that enables efficient training, inference, and memory usage by representing the inverse regularized design matrix as a sum of a diagonal matrix and low-rank correction. We derive numerically stable rank-1 and batched updates that maintain the inverse without explicitly forming the matrix. To control memory growth, we employ a projector-splitting integrator for dynamical low-rank approximation, yielding an average per-step update cost and memory usage of $O(dr)$ for approximation rank $r$. The inference complexity of the proposed algorithm is $O(dr)$ per action evaluation. Experiments on recommender system datasets demonstrate the effectiveness of our algorithm.

Swarm trajectory optimization problems are a well-recognized class of multi-agent optimal control problems with strong nonlinearity. However, the heuristic nature of needing to set the final time for agents beforehand and the time-consuming limitation of the significant number of iterations prohibit the application of existing methods to large-scale swarm of Unmanned Aerial Vehicles (UAVs) in practice. In this paper, we propose a spatial-temporal trajectory optimization framework that accomplishes multi-UAV consensus based on the Alternating Direction Multiplier Method (ADMM) and uses Differential Dynamic Programming (DDP) for fast local planning of individual UAVs. The introduced framework is a two-level architecture that employs Parameterized DDP (PDDP) as the trajectory optimizer for each UAV, and ADMM to satisfy the local constraints and accomplish the spatial-temporal parameter consensus among all UAVs. This results in a fully distributed algorithm called Distributed Parameterized DDP (D-PDDP). In addition, an adaptive tuning criterion based on the spectral gradient method for the penalty parameter is proposed to reduce the number of algorithmic iterations. Several simulation examples are presented to verify the effectiveness of the proposed algorithm.

Structured reporting (SR) and artificial intelligence (AI) may transform how radiologists interact with imaging studies. This prospective study (July to December 2024) evaluated the impact of three reporting modes: free-text (FT), structured reporting (SR), and AI-assisted structured reporting (AI-SR), on image analysis behavior, diagnostic accuracy, efficiency, and user experience. Four novice and four non-novice readers (radiologists and medical students) each analyzed 35 bedside chest radiographs per session using a customized viewer and an eye-tracking system. Outcomes included diagnostic accuracy (compared with expert consensus using Cohen's $κ$), reporting time per radiograph, eye-tracking metrics, and questionnaire-based user experience. Statistical analysis used generalized linear mixed models with Bonferroni post-hoc tests with a significance level of ($P \le .01$). Diagnostic accuracy was similar in FT ($κ= 0.58$) and SR ($κ= 0.60$) but higher in AI-SR ($κ= 0.71$, $P < .001$). Reporting times decreased from $88 \pm 38$ s (FT) to $37 \pm 18$ s (SR) and $25 \pm 9$ s (AI-SR) ($P < .001$). Saccade counts for the radiograph field ($205 \pm 135$ (FT), $123 \pm 88$ (SR), $97 \pm 58$ (AI-SR)) and total fixation duration for the report field ($11 \pm 5$ s (FT), $5 \pm 3$ s (SR), $4 \pm 1$ s (AI-SR)) were lower with SR and AI-SR ($P < .001$ each). Novice readers shifted gaze towards the radiograph in SR, while non-novice readers maintained their focus on the radiograph. AI-SR was the preferred mode. In conclusion, SR improves efficiency by guiding visual attention toward the image, and AI-prefilled SR further enhances diagnostic accuracy and user satisfaction.

The rapid growth of AI conferences is straining an already fragile peer-review system, leading to heavy reviewer workloads, expertise mismatches, inconsistent evaluation standards, superficial or templated reviews, and limited accountability under compressed timelines. In response, conference organizers have introduced new policies and interventions to preserve review standards. Yet these ad-hoc changes often create further concerns and confusion about the review process, leaving how papers are ultimately accepted - and how practices evolve across years - largely opaque. We present Paper Copilot, a system that creates durable digital archives of peer reviews across a wide range of computer-science venues, an open dataset that enables researchers to study peer review at scale, and a large-scale empirical analysis of ICLR reviews spanning multiple years. By releasing both the infrastructure and the dataset, Paper Copilot supports reproducible research on the evolution of peer review. We hope these resources help the community track changes, diagnose failure modes, and inform evidence-based improvements toward a more robust, transparent, and reliable peer-review system.

General SVG modeling remains challenging due to fragmented datasets, limited transferability of methods across tasks, and the difficulty of handling structural complexity. In response, we leverage the strong transfer and generalization capabilities of multimodal large language models (MLLMs) to achieve unified modeling for SVG understanding, editing, and generation. We present the InternSVG family, an integrated data-benchmark-model suite. At its core is SAgoge, the largest and most comprehensive multimodal dataset for SVG tasks, encompassing both static graphics and dynamic animations. It covers icons, long-sequence illustrations, scientific diagrams, and dynamic animations, supporting tasks of varied difficulty levels and providing deeper hierarchies with richer attributes compared to previous datasets. Based on this resource, we introduce SArena, a companion benchmark with comprehensive task definitions and standardized evaluation that aligns with the domains and difficulty spectrum covered by SAgoge. Building on these foundations, we propose InternSVG, a unified MLLM for SVG understanding, editing, and generation with SVG-specific special tokens, subword-based embedding initialization, and a two-stage training strategy that progresses from short static SVGs to long-sequence illustrations and complex animations. This unified formulation induces positive transfer and improves overall performance. Experiments on SArena and prior benchmark confirm that InternSVG achieves substantial gains and consistently outperforms leading open and proprietary counterparts.

Recent advances in large audio language models (LALMs) have greatly enhanced multimodal conversational systems. However, existing benchmarks remain limited -- they are mainly English-centric, rely on synthetic speech, and lack comprehensive, discriminative evaluation across multiple dimensions. To address these gaps, we present Voice Chat Bot Bench (VCB Bench) -- a high-quality Chinese benchmark built entirely on real human speech. VCB Bench evaluates LALMs from three complementary perspectives: instruction following (including speech-level control beyond text commands), knowledge understanding (general knowledge, reasoning, and daily dialogue), and robustness (stability under perturbations in content, environment, and speaker traits). Experiments on representative LALMs reveal notable performance gaps and highlight future directions for improvement. VCB Bench provides a reproducible and fine-grained evaluation framework, offering standardized methodology and practical insights for advancing Chinese voice conversational models.

Understanding how deep neural networks make decisions is crucial for analyzing their behavior and diagnosing failure cases. In computer vision, a common approach to improve interpretability is to assign importance to individual pixels using post-hoc methods. Although they are widely used to explain black-box models, their fidelity to the model's actual reasoning is uncertain due to the lack of reliable evaluation metrics. This limitation motivates an alternative approach, which is to design models whose decision processes are inherently interpretable. To this end, we propose a face similarity metric that breaks down global similarity into contributions from restricted receptive fields. Our method defines the similarity between two face images as the sum of patch-level similarity scores, providing a locally additive explanation without relying on post-hoc analysis. We show that the proposed approach achieves competitive verification performance even with patches as small as 28x28 within 112x112 face images, and surpasses state-of-the-art methods when using 56x56 patches.

Large Language Models (LLMs) have become foundational tools in natural language processing, powering a wide range of applications and research. Many studies have shown that LLMs share significant similarities with the human brain. Recent neuroscience research has found that a small subset of biological neurons in the human brain are crucial for core cognitive functions, which raises a fundamental question: do LLMs also contain a small subset of critical neurons? In this paper, we investigate this question by proposing a Perturbation-based Causal Identification of Critical Neurons method to systematically locate such critical neurons in LLMs. Our findings reveal three key insights: (1) LLMs contain ultra-sparse critical neuron sets. Disrupting these critical neurons can cause a 72B-parameter model with over 1.1 billion neurons to completely collapse, with perplexity increasing by up to 20 orders of magnitude; (2) These critical neurons are not uniformly distributed, but tend to concentrate in the outer layers, particularly within the MLP down\_proj components; (3) Performance degradation exhibits sharp phase transitions, rather than a gradual decline, when these critical neurons are disrupted. Through comprehensive experiments across diverse model architectures and scales, we provide deeper analysis of these phenomena and their implications for LLM robustness and interpretability. These findings can offer guidance for developing more robust model architectures and improving deployment security in safety-critical applications. Our code is available at https://github.com/qqqqqqqzx/The-Achilles-Heel-of-LLMs.

In this work, we present Color3D, a highly adaptable framework for colorizing both static and dynamic 3D scenes from monochromatic inputs, delivering visually diverse and chromatically vibrant reconstructions with flexible user-guided control. In contrast to existing methods that focus solely on static scenarios and enforce multi-view consistency by averaging color variations which inevitably sacrifice both chromatic richness and controllability, our approach is able to preserve color diversity and steerability while ensuring cross-view and cross-time consistency. In particular, the core insight of our method is to colorize only a single key view and then fine-tune a personalized colorizer to propagate its color to novel views and time steps. Through personalization, the colorizer learns a scene-specific deterministic color mapping underlying the reference view, enabling it to consistently project corresponding colors to the content in novel views and video frames via its inherent inductive bias. Once trained, the personalized colorizer can be applied to infer consistent chrominance for all other images, enabling direct reconstruction of colorful 3D scenes with a dedicated Lab color space Gaussian splatting representation. The proposed framework ingeniously recasts complicated 3D colorization as a more tractable single image paradigm, allowing seamless integration of arbitrary image colorization models with enhanced flexibility and controllability. Extensive experiments across diverse static and dynamic 3D colorization benchmarks substantiate that our method can deliver more consistent and chromatically rich renderings with precise user control. Project Page https://yecongwan.github.io/Color3D/.

The extensive application of unmanned aerial vehicles (UAVs) in military reconnaissance, environmental monitoring, and related domains has created an urgent need for accurate and efficient multi-object tracking (MOT) technologies, which are also essential for UAV situational awareness. However, complex backgrounds, small-scale targets, and frequent occlusions and interactions continue to challenge existing methods in terms of detection accuracy and trajectory continuity. To address these issues, this paper proposes the Global-Local Detection and Tracking (GL-DT) framework. It employs a Spatio-Temporal Feature Fusion (STFF) module to jointly model motion and appearance features, combined with a global-local collaborative detection strategy, effectively enhancing small-target detection. Building upon this, the JPTrack tracking algorithm is introduced to mitigate common issues such as ID switches and trajectory fragmentation. Experimental results demonstrate that the proposed approach significantly improves the continuity and stability of MOT while maintaining real-time performance, providing strong support for the advancement of UAV detection and tracking technologies.

Self-evolution is a central research topic in enabling large language model (LLM)-based agents to continually improve their capabilities after pretraining. Recent research has witnessed a transition from reinforcement learning (RL)-free to RL-based methods. Current RL-based methods either rely on dense external reward signals or extract intrinsic reward signals from LLMs themselves. However, these approaches diverge from the self-evolution mechanisms observed in human intelligence, where individuals learn and improve through mutual discussion and collaboration. In this work, we introduce Co-Evolving Multi-Agent Systems (CoMAS), a novel framework that enables agents to improve autonomously by learning from inter-agent interactions without external supervision. CoMAS generates intrinsic rewards from rich discussion dynamics, employs an LLM-as-a-judge mechanism to formulate these rewards, and optimizes each agent's policy through RL, thereby enabling decentralized and scalable co-evolution. Experimental results demonstrate that CoMAS consistently outperforms untrained agents and achieves state-of-the-art performance across most evaluation settings. Ablation studies confirm the necessity of interaction-based reward signals and reveal promising scalability as the number and diversity of agents increase. These findings establish CoMAS as a novel and effective paradigm for self-evolution in LLM-based agents.

The rapid progress of large language models (LLMs) has laid the foundation for multimodal models. However, visual language models (VLMs) still face heavy computational costs when extended from images to videos due to high frame rates and long durations. Token compression is a promising solution, yet most existing training-free methods cause information loss and performance degradation. To overcome this, we propose \textbf{Memory-Augmented Reinforcement Learning-based Token Compression (MARC)}, which integrates structured retrieval and RL-based distillation. MARC adopts a \textit{retrieve-then-compress} strategy using a \textbf{Visual Memory Retriever (VMR)} to select key clips and a \textbf{Compression Group Relative Policy Optimization (C-GRPO)} framework to distil reasoning ability from a teacher to a student model. Experiments on six video benchmarks show that MARC achieves near-baseline accuracy using only one frame's tokens -- reducing visual tokens by \textbf{95\%}, GPU memory by \textbf{72\%}, and latency by \textbf{23.9\%}. This demonstrates its potential for efficient, real-time video understanding in resource-constrained settings such as video QA, surveillance, and autonomous driving.

Generative auto-bidding has demonstrated strong performance in online advertising, yet it often suffers from data scarcity in small-scale settings with limited advertiser participation. While cross-task data sharing is a natural remedy to mitigate this issue, naive approaches often introduce gradient bias due to distribution shifts across different tasks, and existing methods are not readily applicable to generative auto-bidding. In this paper, we propose Validation-Aligned Optimization (VAO), a principled data-sharing method that adaptively reweights cross-task data contributions based on validation performance feedback. Notably, VAO aligns training dynamics to prioritize updates that improve generalization on the target task, effectively leveraging auxiliary data and mitigating gradient bias. Building on VAO, we introduce a unified generative autobidding framework that generalizes across multiple tasks using a single model and all available task data. Extensive experiments on standard auto-bidding benchmarks validate the effectiveness of our approach.

Accurate semantic segmentation of terrestrial laser scanning (TLS) point clouds is limited by costly manual annotation. We propose a semi-automated, uncertainty-aware pipeline that integrates spherical projection, feature enrichment, ensemble learning, and targeted annotation to reduce labeling effort, while sustaining high accuracy. Our approach projects 3D points to a 2D spherical grid, enriches pixels with multi-source features, and trains an ensemble of segmentation networks to produce pseudo-labels and uncertainty maps, the latter guiding annotation of ambiguous regions. The 2D outputs are back-projected to 3D, yielding densely annotated point clouds supported by a three-tier visualization suite (2D feature maps, 3D colorized point clouds, and compact virtual spheres) for rapid triage and reviewer guidance. Using this pipeline, we build Mangrove3D, a semantic segmentation TLS dataset for mangrove forests. We further evaluate data efficiency and feature importance to address two key questions: (1) how much annotated data are needed and (2) which features matter most. Results show that performance saturates after ~12 annotated scans, geometric features contribute the most, and compact nine-channel stacks capture nearly all discriminative power, with the mean Intersection over Union (mIoU) plateauing at around 0.76. Finally, we confirm the generalization of our feature-enrichment strategy through cross-dataset tests on ForestSemantic and Semantic3D. Our contributions include: (i) a robust, uncertainty-aware TLS annotation pipeline with visualization tools; (ii) the Mangrove3D dataset; and (iii) empirical guidance on data efficiency and feature importance, thus enabling scalable, high-quality segmentation of TLS point clouds for ecological monitoring and beyond. The dataset and processing scripts are publicly available at https://fz-rit.github.io/through-the-lidars-eye/.

The landscape of Large Language Models remains predominantly English-centric, resulting in a significant performance gap for other major languages, such as French, especially in the context of Small Language Models (SLMs). Existing multilingual models demonstrate considerably lower performance in French compared to English, and research on efficient adaptation methods for French remains limited. To address this, we introduce \textbf{Luth}, a family of French-specialized SLMs: through targeted post-training on curated, high-quality French data, our models outperform all open-source counterparts of comparable size on multiple French benchmarks while retaining their original English capabilities. We further show that strategic model merging enhances performance in both languages, establishing Luth as a new state of the art for French SLMs and a robust baseline for future French-language research.

Natural Language Processing (NLP) for low-resource languages remains fundamentally constrained by the lack of textual corpora, standardized orthographies, and scalable annotation pipelines. While recent advances in large language models have improved cross-lingual transfer, they remain inaccessible to underrepresented communities due to their reliance on massive, pre-collected data and centralized infrastructure. In this position paper, we argue for a paradigm shift toward open-ended, interactive language discovery, where AI systems learn new languages dynamically through dialogue rather than static datasets. We contend that the future of language technology, particularly for low-resource and under-documented languages, must move beyond static data collection pipelines toward interactive, uncertainty-driven discovery, where learning emerges dynamically from human-machine collaboration instead of being limited to pre-existing datasets. We propose a framework grounded in joint human-machine uncertainty, combining epistemic uncertainty from the model with hesitation cues and confidence signals from human speakers to guide interaction, query selection, and memory retention. This paper is a call to action: we advocate a rethinking of how AI engages with human knowledge in under-documented languages, moving from extractive data collection toward participatory, co-adaptive learning processes that respect and empower communities while discovering and preserving the world's linguistic diversity. This vision aligns with principles of human-centered AI, emphasizing interactive, cooperative model building between AI systems and speakers.

Manual annotation of anatomical landmarks on 3D facial scans is a time-consuming and expertise-dependent task, yet it remains critical for clinical assessments, morphometric analysis, and craniofacial research. While several deep learning methods have been proposed for facial landmark localization, most focus on pseudo-landmarks or require complex input representations, limiting their clinical applicability. This study presents a fully automated deep learning pipeline (PAL-Net) for localizing 50 anatomical landmarks on stereo-photogrammetry facial models. The method combines coarse alignment, region-of-interest filtering, and an initial approximation of landmarks with a patch-based pointwise CNN enhanced by attention mechanisms. Trained and evaluated on 214 annotated scans from healthy adults, PAL-Net achieved a mean localization error of 3.686 mm and preserves relevant anatomical distances with a 2.822 mm average error, comparable to intra-observer variability. To assess generalization, the model was further evaluated on 700 subjects from the FaceScape dataset, achieving a point-wise error of 0.41\,mm and a distance-wise error of 0.38\,mm. Compared to existing methods, PAL-Net offers a favorable trade-off between accuracy and computational cost. While performance degrades in regions with poor mesh quality (e.g., ears, hairline), the method demonstrates consistent accuracy across most anatomical regions. PAL-Net generalizes effectively across datasets and facial regions, outperforming existing methods in both point-wise and structural evaluations. It provides a lightweight, scalable solution for high-throughput 3D anthropometric analysis, with potential to support clinical workflows and reduce reliance on manual annotation. Source code can be found at https://github.com/Ali5hadman/PAL-Net-A-Point-Wise-CNN-with-Patch-Attention

In certain real-world optimization scenarios, practitioners are not interested in solving multiple problems but rather in finding the best solution to a single, specific problem. When the computational budget is large relative to the cost of evaluating a candidate solution, multiple heuristic alternatives can be tried to solve the same given problem, each possibly with a different algorithm, parameter configuration, initialization, or stopping criterion. In this practically relevant setting, the sequential selection of which alternative to try next is crucial for efficiently identifying the best possible solution across multiple attempts. However, suitable sequential alternative selection strategies have traditionally been studied separately across different research topics and have not been the exclusive focus of any existing review. As a result, the state-of-the-art remains fragmented for practitioners interested in this setting, with surveys either covering only subsets of relevant strategies or including approaches that rely on assumptions that are not feasible for the single-problem case. This work addresses the identified gap by providing a focused review of single-problem multi-attempt heuristic optimization. It brings together suitable strategies for this setting that have been studied separately through algorithm selection, parameter tuning, multi-start, and resource allocation. These strategies are described using a unified terminology within a common framework, which supports the construction of a taxonomy for systematically organizing and classifying them. The resulting comprehensive review facilitates both the identification and the development of strategies for the single-problem multi-attempt setting in practice.

We examine gradient descent in matrix factorization and show that under large step sizes the parameter space develops a fractal structure. We derive the exact critical step size for convergence in scalar-vector factorization and show that near criticality the selected minimizer depends sensitively on the initialization. Moreover, we show that adding regularization amplifies this sensitivity, generating a fractal boundary between initializations that converge and those that diverge. The analysis extends to general matrix factorization with orthogonal initialization. Our findings reveal that near-critical step sizes induce a chaotic regime of gradient descent where the training outcome is unpredictable and there are no simple implicit biases, such as towards balancedness, minimum norm, or flatness.

Transformers have proven highly effective across modalities, but standard softmax attention scales quadratically with sequence length, limiting long context modeling. Linear attention mitigates this by approximating attention with kernel feature maps, yet most attention mechanisms remain row normalized and can over concentrate mass on a few tokens, harming robustness and information flow. Doubly stochastic attention counteracts this by balancing token participation across both rows and columns, but existing approaches often add significant overhead. We propose LOTFormer, a linear time doubly stochastic attention mechanism derived from an optimal transport view of attention as a coupling between query and key measures. LOTFormer enforces a low rank transport plan by conditioning on a learnable pivot measure with small support. We solve two entropic transport problems, queries to pivot and pivot to keys, and compose them into a conditional coupling that is provably doubly stochastic, has rank at most $r \ll n$, and applies to values in $O(nr)$ time without forming the full $n \times n$ matrix. The pivot locations and masses are learned end-to-end. Across vision and text benchmarks, LOTFormer delivers strong accuracy efficiency tradeoffs when plugged into standard backbones including Swin, DeiT, and BERT.

Despite significant strides in statement autoformalization, a critical gap remains in the development of automated evaluation metrics capable of assessing formal translation quality. Existing metrics often fail to balance semantic and structural information: string-based methods neglect semantics, whereas proof-based approaches offer no graded similarity when proofs fail. To address these issues, we introduce ASSESS (A Semantic and Structural Evaluation Framework for Statement Similarity), which captures syntactic structure by transforming formal statements into operator trees and computes a real-valued similarity score using our novel TransTED (Transformation Tree Edit Distance) Similarity metric by incorporating semantic transformations. For rigorous validation, we present EPLA (Evaluating Provability and Likeness for Autoformalization), a benchmark comprising 1,247 expert-annotated formal statement pairs derived from miniF2F and ProofNet, distinctively labeled for both semantic provability and structural likeness. Experiments on the EPLA benchmark demonstrate that TransTED Similarity surpasses existing methods, achieving state-of-the-art accuracy and Kappa score. The benchmark dataset, code, and detailed experimental results are available at https://github.com/XiaoyangLiu-sjtu/ASSESS.

We propose a modular, data-driven framework for jointly learning unknown functional mappings and discovering the underlying one-parameter symmetry subgroup governing the data. Unlike conventional geometric deep learning methods that assume known symmetries, our approach identifies the relevant continuous subgroup directly from data. We consider the broad class of one-parameter subgroups, which admit a canonical geometric classification into three regimes: elliptical, hyperbolic, and parabolic. Given an assumed regime, our framework instantiates a corresponding symmetry discovery architecture with invariant and equivariant representation layers structured according to the Lie algebra of the subgroup, and learns the exact generator parameters end-to-end from data. This yields models whose invariance or equivariance is guaranteed by construction and admits formal proofs, enabling symmetry to be explicitly traced to identifiable components of the architecture. The approach is applicable to one-parameter subgroups of a wide range of matrix Lie groups, including $SO(n)$, $SL(n)$, and the Lorentz group. Experiments on synthetic and real-world systems, including moment of inertia prediction, double-pendulum dynamics, and high-energy \textit{Top Quark Tagging}, demonstrate accurate subgroup recovery and strong predictive performance across both compact and non-compact regimes.

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful framework for improving the reasoning abilities of Large Language Models (LLMs). However, current methods such as GRPO rely only on problems where the model responses to the same input differ in correctness, while ignoring those where all responses receive the same reward -- so-called zero-variance prompts. In this work, we argue that such prompts are not useless but can, in fact, provide meaningful feedback for policy optimization. To this end, we introduce Reinforcement Learning with Zero-Variance Prompts (RL-ZVP), a novel algorithm that extract learning signals from zero-variance prompts. RL-ZVP directly rewards correctness and penalizes errors even without contrasting responses, modulating feedback with token-level characteristics to preserve informative, nuanced signals. Across six math reasoning benchmarks, RL-ZVP achieves significant improvements of up to 8.61 points in accuracy and 7.77 points in pass rate over GRPO, while consistently outperforming other baselines that filter out zero-variance prompts. These results highlight the untapped potential of learning from zero-variance prompts in RLVR. The project page is available at https://bltnynk.github.io/publications/rl-zvp/.