Consider the task of locating an unknown target point using approximate distance queries: in each round, a reconstructor selects a reference point and receives a noisy version of its distance to the target. This problem arises naturally in various contexts--ranging from localization in GPS and sensor networks to privacy-aware data access--and spans a wide variety of metric spaces. It is relevant from the perspective of both the reconstructor (seeking accurate recovery) and the responder (aiming to limit information disclosure, e.g., for privacy or security reasons). We study this reconstruction game through a learning-theoretic lens, focusing on the rate and limits of the best possible reconstruction error. Our first result provides a tight geometric characterization of the optimal error in terms of the Chebyshev radius, a classical concept from geometry. This characterization applies to all compact metric spaces (in fact, even to all totally bounded spaces) and yields explicit formulas for natural metric spaces. Our second result addresses the asymptotic behavior of reconstruction, distinguishing between pseudo-finite spaces--where the optimal error is attained after finitely many queries--and spaces where the approximation curve exhibits a nontrivial decay. We characterize pseudo-finiteness for convex Euclidean spaces.

UAV tracking can be widely applied in scenarios such as disaster rescue, environmental monitoring, and logistics transportation. However, existing UAV tracking methods predominantly emphasize speed and lack exploration in semantic awareness, which hinders the search region from extracting accurate localization information from the template.

Spiking Neural Networks (SNNs) are distinguished from Artificial Neural Networks (ANNs) for their complex neuronal dynamics and sparse binary activations (spikes) inspired by the biological neural system. Traditional neuron models use iterative step-by-step dynamics, resulting in serial computation and slow training speed of SNNs. Recently, parallelizable spiking neuron models have been proposed to fully utilize the massive parallel computing ability of graphics processing units to accelerate the training of SNNs. However, existing parallelizable spiking neuron models involve dense floating operations and can only achieve high long-term dependencies learning ability with a large order at the cost of huge computational and memory costs. To solve the dilemma of performance and costs, we propose the mul-free channel-wise Parallel Spiking Neuron, which is hardware-friendly and suitable for SNNs' resource-restricted application scenarios.

Deep Neural Networks (DNN) have emerged as an effective approach to implementing challenging subproblems. They are increasingly being used as components in critical transportation, medical, and military systems. However, like human-written software, DNNs may have flaws that can lead to unsafe system performance. To confidently deploy DNNs in such systems, strong evidence is needed that they do not contain such flaws. This has led researchers to explore the adaptation and customization of software verification approaches to the problem of neural network verification (NNV). Many dozens of NNV tools have been developed in recent years and as a field these techniques have matured to the point where realistic networks can be analyzed to detect flaws and to prove conformance with specifications. NNV tools are highly-engineered and complex may harbor flaws that cause them to produce unsound results. We identify commonalities in algorithmic approaches taken by NNV tools to define a verifier independent proof format--activation pattern tree proofs (APTP)--and design an algorithm for checking those proofs that is proven correct and optimized to enable scalable checking. We demonstrate that existing verifiers can efficiently generate APTP proofs, and that an APTPcheckersignificantly outperforms prior work on a benchmark of 16 neural networks and 400 NNV problems, and that it is robust to variation in APTP proof structure arising from different NNV tools.

A.1 Details of Dimension Design We argue that multi-dimensional evaluation is significant to visual caption evaluation and is more comprehensive than previous work. So how to choose proper dimensions? We refer to existing VQA benchmarks [62, 63, 64, 65] and visual generation benchmarks [31, 32, 33]. VQA benchmarks usually design various types of questions to include multi-dimensional evaluation and analysis of MLLMs. For instance, MMBench [64] defines 20 ability dimensions, including attribute recognition, attribute comparison, action recognition, spatial relationship, physical property, OCR, object localization, image style, image scene, identity reasoning, etc. MVBench [64] covers 20 challenging video tasks including action, object, position, count, scene, pose, attribute, character, cognition, etc. Due to the flexible design of questions, VQA benchmarks can be naturally built with comprehensive dimensions. Different from the VQA task, the visual caption task does not require specific questions, but inspects the alignment of visual and textual information. Visual generation is the inverse task of visual captioning, as it requires models to generate specific visual content based on detailed textual descriptions. GenEval [31] designs 6 different tasks to evaluate text-to-image alignment, including single object, two object, counting, colors, position, and attribute binding. VBench [32] comprises 16 dimensions, including subject consistency, background consistency, object class, human action, color, spatial relationship, scene, style, etc. We follow their explored dimensions to design proper dimensions for visual captioning. Finally, we design 6 views, covering object, global, text, camera, temporal, and knowledge. The object-related view includes object category, object color, object 1 number, and spatial relation, the global-related view includes scene and style, the text-related view evaluates the OCR capability of captions, the camera-related view covers the camera angle and movement, the temporal-related view contains action and event, and we also design a view to evaluate the knowledge of MLLMs, i.e., character identification. We believe these dimensions contribute to a comprehensive visual caption benchmarking.

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We study the noise-free Gaussian Process (GP) bandit problem, in which a learner seeks to minimize regret through noise-free observations of a black-box objective function that lies in a known reproducing kernel Hilbert space (RKHS). The Gaussian Process Upper Confidence Bound (GP-UCB) algorithm is a well-known approach for GP bandits, where query points are adaptively selected based on the GP-based upper confidence bound score. While several existing works have reported the practical success of GP-UCB, its theoretical performance remains suboptimal. However, GP-UCB often empirically outperforms other nearly-optimal noise-free algorithms that use non-adaptive sampling schemes. This paper resolves the gap between theoretical and empirical performance by establishing a nearly-optimal regret upper bound for noise-free GP-UCB. Specifically, our analysis provides the first constant cumulative regret bounds in the noise-free setting for both the squared exponential kernel and the Mat ern kernel with some degree of smoothness.

Recent work suggests that large language models (LLMs) can perform multi-hop reasoning implicitly--producing correct answers without explicitly verbalizing intermediate steps--but the underlying mechanisms remain poorly understood. In this paper, we study how such implicit reasoning emerges by training transformers from scratch in a controlled symbolic environment. Our analysis reveals a threestage developmental trajectory: early memorization, followed by in-distribution generalization, and eventually cross-distribution generalization. We find that training with atomic triples is not necessary but accelerates learning, and that second-hop generalization relies on query-level exposure to specific compositional structures. To interpret these behaviors, we introduce two diagnostic tools: cross-query semantic patching, which identifies semantically reusable intermediate representations, and a cosine-based representational lens, which reveals that successful reasoning correlates with the cosine-base clustering in hidden space. This clustering phenomenon in turn provides a coherent explanation for the behavioral dynamics observed across training, linking representational structure to reasoning capability. These findings provide new insights into the interpretability of implicit multi-hop reasoning in LLMs, helping to clarify how complex reasoning processes unfold internally and offering pathways to enhance the transparency of such models.

Yet, training still treats these logits in isolation--either supervising only the final, highest-resolution logits or applying deep supervision with identical loss weights at every scale--without exploring mixed-scale combinations. Consequently, the decoder output misses the complementary cues that arise only when coarse and fine predictions are fused. To address this issue, we introduce LoMix (Logits Mixing), a Neural Architecture Search (NAS)-inspired, differentiable plug-and-play module that generates new mixed-scale outputs and learns how exactly each of them should guide the training process. More precisely, LoMix mixes the multi-scale decoder logits with four lightweight fusion operators: addition, multiplication, concatenation, and attentionbased weighted fusion, yielding a rich set of synthetic "mutant" maps. Every original or mutant map is given a softplus loss weight that is co-optimized with network parameters, mimicking a one-step architecture search that automatically discovers the most useful scales, mixtures, and operators. Plugging LoMix into recent U-shaped architectures (i.e., PVT-V2-B2 backbone with EMCAD decoder) on Synapse 8-organ dataset improves DICE by +4.2% over single-output supervision, +2.2% over deep supervision, and +1.5% over equally weighted additive fusion, all with zero inference overhead. When training data are scarce (e.g., one or two labeled scans, 5% of the trainset), the advantage grows to +9.23%, underscoring LoMix's data efficiency. Across four benchmarks and diverse U-shaped networks, LoMiX improves DICE by up to +13.5% over single-output supervision, confirming that learnable weighted mixed-scale fusion generalizes broadly while remaining data efficient, fully interpretable, and overhead-free at inference. Our implementation is available at https://github.com/SLDGroup/LoMix.

Vision-Language Models (VLMs) excel at visual understanding but often suffer from visual hallucinations, where they generate descriptions of nonexistent objects, actions, or concepts, posing significant risks in safety-critical applications. Existing hallucination mitigation methods typically follow one of two paradigms: generation adjustment, which modifies decoding behavior to align text with visual inputs, and post-hoc verification, where external models assess and correct outputs. While effective, generation adjustment methods often rely on heuristics and lack correction mechanisms, while post-hoc verification is complicated, typically requiring multiple models and tending to reject outputs rather than refine them. In this work, we introduce REVERSE, a unified framework that integrates hallucination-aware training with on-the-fly self-verification. By leveraging a new hallucination-verification dataset containing over 1.3M semi-synthetic samples, along with a novel inference-time retrospective resampling technique, our approach enables VLMs to both detect hallucinations during generation and dynamically revise those hallucinations. Our evaluations show that REVERSE achieves state-of-the-art hallucination reduction, outperforming the best existing methods by up to 12% on CHAIR-MSCOCO and 34% on HaloQuest.