arXiv subjects

Chao Wang

Publications and source records attributed to Chao Wang.

At least 145 records · Page 8Linked to original sources

arXiv2026

Analytic Proof of a Quartic Continued Fraction Identity for $8/π^2$ via Operator Decoupling

We present a rigorous analytic proof of a generalized continued fraction (GCF) identity for the transcendental constant $8/π^2$, a result recently conjectured via the algorithmic framework of the Ramanujan Machine. Distinct from canonical GCFs derived from classical hypergeometric series, the identity at hand features a complex polynomial architecture characterized by quartic partial numerators. Our approach utilizes an algebraic decomposition of the second-order shift operator $\mathcal{L} = \mathcal{T}^2 - b_n \mathcal{T} - a_n$ into a coupled first-order system. This decomposition enables an exact mapping of the higher-order recurrence to a cascaded system, from which the continued fraction is identified as the reciprocal of a binomial series for $(\arcsin)^2$ involving central binomial coefficients. The convergence is established through Pincherle's Theorem: the true minimal solution of the associated difference equation is $f_n = A_n - (8/π^2)\,B_n$, which satisfies $f_n/B_n \to 0$, confirming absolute convergence of the continued fraction. This work provides a systematic operator-theoretic methodology for verifying automated conjectures of transcendental constants with high-degree polynomial coefficients.

math.GM↗

arXiv2026

Locatability-Guided Adaptive Reasoning for Image Geo-Localization with Vision-Language Models

The emergence of Vision-Language Models (VLMs) has introduced new paradigms for global image geo-localization through retrieval-augmented generation (RAG) and reasoning-driven inference. However, RAG methods are constrained by retrieval database quality, while reasoning-driven approaches fail to internalize image locatability, relying on inefficient, fixed-depth reasoning paths that increase hallucinations and degrade accuracy. To overcome these limitations, we introduce an Optimized Locatability Score that quantifies an image's suitability for deep reasoning in geo-localization. Using this metric, we curate Geo-ADAPT-51K, a locatability-stratified reasoning dataset enriched with augmented reasoning trajectories for complex visual scenes. Building on this foundation, we propose a two-stage Group Relative Policy Optimization (GRPO) curriculum with customized reward functions that regulate adaptive reasoning depth, visual grounding, and hierarchical geographical accuracy. Our framework, Geo-ADAPT, learns an adaptive reasoning policy, achieves state-of-the-art performance across multiple geo-localization benchmarks, and substantially reduces hallucinations by reasoning both adaptively and efficiently.

cs.CV↗

arXiv2026

VERDICT: Verifiable Evolving Reasoning with Directive-Informed Collegial Teams for Legal Judgment Prediction

Legal Judgment Prediction (LJP) predicts applicable law articles, charges, and penalty terms from case facts. Beyond accuracy, LJP calls for intrinsically interpretable and legally grounded reasoning that can reconcile statutory rules with precedent-informed standards. However, existing methods often behave as static, one-shot predictors, providing limited procedural support for verifiable reasoning and little capability to adapt as jurisprudential practice evolves. We propose VERDICT, a self-refining collaborative multi-agent framework that simulates a virtual collegial panel. VERDICT assigns specialized agents to complementary roles (e.g., fact structuring, legal retrieval, opinion drafting, and supervisory verification) and coordinates them in a traceable draft--verify--revise workflow with explicit Pass/Reject feedback, producing verifiable reasoning traces and revision rationales. To capture evolving case experience, we further introduce a Hybrid Jurisprudential Memory (HJM) grounded in the Micro-Directive Paradigm, which stores precedent standards and continually distills validated multi-agent verification trajectories into updated Micro-Directives for continual learning across cases. We evaluate VERDICT on CAIL2018 and a newly constructed CJO2025 dataset with a strict future time-split for temporal generalization. VERDICT achieves state-of-the-art performance on CAIL2018 and demonstrates strong generalization on CJO2025. To facilitate reproducibility and further research, we release our code and the dataset at https://anonymous.4open.science/r/ARR-4437.

cs.IR↗

arXiv2026

FVG-PT: Adaptive Foreground View-Guided Prompt Tuning for Vision-Language Models

CLIP-based prompt tuning enables pretrained Vision-Language Models (VLMs) to efficiently adapt to downstream tasks. Although existing studies have made significant progress, they pay limited attention to changes in the internal attention representations of VLMs during the tuning process. In this paper, we attribute the failure modes of prompt tuning predictions to shifts in foreground attention of the visual encoder, and propose Foreground View-Guided Prompt Tuning (FVG-PT), an adaptive plug-and-play foreground attention guidance module, to alleviate the shifts. Concretely, FVG-PT introduces a learnable Foreground Reliability Gate to automatically enhance the foreground view quality, applies a Foreground Distillation Compensation module to guide visual attention toward the foreground, and further introduces a Prior Calibration module to mitigate generalization degradation caused by excessive focus on the foreground. Experiments on multiple backbone models and datasets show the effectiveness and compatibility of FVG-PT. Codes are available at: https://github.com/JREion/FVG-PT

cs.CV↗

arXiv2026

Reparameterized Tensor Ring Functional Decomposition for Multi-Dimensional Data Recovery

Tensor Ring (TR) decomposition is a powerful tool for high-order data modeling, but is inherently restricted to discrete forms defined on fixed meshgrids. In this work, we propose a TR functional decomposition for both meshgrid and non-meshgrid data, where factors are parameterized by Implicit Neural Representations (INRs). However, optimizing this continuous framework to capture fine-scale details is intrinsically difficult. Through a frequency-domain analysis, we demonstrate that the spectral structure of TR factors determines the frequency composition of the reconstructed tensor and limits the high-frequency modeling capacity. To mitigate this, we propose a reparameterized TR functional decomposition, in which each TR factor is a structured combination of a learnable latent tensor and a fixed basis. This reparameterization is theoretically shown to improve the training dynamics of TR factor learning. We further derive a principled initialization scheme for the fixed basis and prove the Lipschitz continuity of our proposed model. Extensive experiments on image inpainting, denoising, super-resolution, and point cloud recovery demonstrate that our method achieves consistently superior performance over existing approaches. Code is available at https://github.com/YangyangXu2002/RepTRFD.

cs.CV↗

arXiv2026

Local Stability and Quantitative Bounds for the Betke-Henk-Wills Conjecture

The Betke-Henk-Wills conjecture provides an upper bound for the lattice point enumerator $G(K, Λ)$ of a convex body in terms of its successive minima. While the conjecture is established for orthogonal parallelotopes, its validity for general convex bodies in dimensions $d \ge 5$ remains open. In this paper, we examine the stability of the conjecture under metric perturbations. Specifically, we demonstrate that the inequality is strictly maintained for integer boxes subjected to rotations within a calculated radius, a consequence of the discrete nature of the lattice point enumerator. We derive explicit, geometry-invariant quantitative bounds on the perturbation radius using the operator norm. Furthermore, we extend the analysis to $L_p$-balls for sufficiently large $p$, identifying a sharp threshold $p_0$ for the invariance of the integer hull.

math.MG↗

arXiv2026

Content-Aware Frequency Encoding for Implicit Neural Representations with Fourier-Chebyshev Features

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for various signal processing tasks, but their inherent spectral bias limits the ability to capture high-frequency details. Existing methods partially mitigate this issue by using Fourier-based features, which usually rely on fixed frequency bases. This forces multi-layer perceptrons (MLPs) to inefficiently compose the required frequencies, thereby constraining their representational capacity. To address this limitation, we propose Content-Aware Frequency Encoding (CAFE), which builds upon Fourier features through multiple parallel linear layers combined via a Hadamard product. CAFE can explicitly and efficiently synthesize a broader range of frequency bases, while the learned weights enable the selection of task-relevant frequencies. Furthermore, we extend this framework to CAFE+, which incorporates Chebyshev features as a complementary component to Fourier bases. This combination provides a stronger and more stable frequency representation. Extensive experiments across multiple benchmarks validate the effectiveness and efficiency of our approach, consistently achieving superior performance over existing methods. Our code is available at https://github.com/JunboKe0619/CAFE.

cs.CV↗

arXiv2026

RUMAD: Reinforcement-Unifying Multi-Agent Debate

Multi-agent debate (MAD) systems leverage collective intelligence to enhance reasoning capabilities, yet existing approaches struggle to simultaneously optimize accuracy, consensus formation, and computational efficiency. Static topology methods lack adaptability to task complexity variations, while external LLM-based coordination risks introducing privileged knowledge that compromises debate neutrality. This work presents RUMAD (Reinforcement-Unifying Multi-Agent Debate), a novel framework that formulates dynamic communication topology control in MAD as a reinforcement learning (RL) problem. RUMAD employs a content-agnostic observation scheme that captures high-level debate dynamics avoiding access to raw agent reasoning content. RUMAD uses a multi-objective reward to model solution quality, cohesion and efficiency. A PPO-trained controller dynamically adjusts edge weights in the communication graph, while a dual-threshold mechanism enables fine-grained control over both agent activation and information visibility. Experimental evaluation across MMLU, GSM8K, and GPQA benchmarks demonstrates that RUMAD achieves substantial efficiency gains, reducing token costs by over 80\%, while still improving reasoning accuracy compared to single LLM model and multiple MAD baselines. Notably, RUMAD trained exclusively on MMLU exhibits robust zero-shot generalization to out-of-domain (OOD) tasks, indicating that the learned communication strategies capture task-independent principles of effective multi-agent coordination. These results establish RUMAD as a efficient and robust approach for deploying multi-agent reasoning application with practical resource constraints.

cs.AI↗

arXiv2026

On the classical solution for the steady triple-deck equations

This paper establishes the existence and uniqueness of classical solutions to the steady Triple-Deck equations, which describe incompressible boundary layer flow over localized roughness at high Reynolds numbers. The triple-deck theory was developed to overcome the Goldstein singularity in classical Prandtl boundary layer theory, capturing the interaction between the viscous sublayer, main layer, and upper layer when surface roughness of height $O({\rm Re}^{-\frac58})$ is present. The key ingredients of this paper include: (1) A decomposition separating roughness effects from nonlinear difficulties; (2) A novel Green's function using Airy functions that overcomes low-frequency singularities via the non-vanishing property of $\sqrt{3}Ai(z)+Bi(z)$; (3) The introduction of weighted Sobolev norms $\norm{|\p_x|^{\frac{1}{18}}y^{\frac16}ω}_{L^2}$ of the vorticity yielding $M$-independent estimates for displacement $A$. As a byproduct, local uniqueness of Couette flow is established when $F=0$.

math.AP↗

arXiv2026

Turning Semantics into Topology: LLM-Driven Attribute Augmentation for Collaborative Filtering

Large Language Models (LLMs) have shown great potential for enhancing recommender systems through their extensive world knowledge and reasoning capabilities. However, effectively translating these semantic signals into traditional collaborative embeddings remains an open challenge. Existing approaches typically fall into two extremes: direct inference methods are computationally prohibitive for large-scale retrieval, while embedding-based methods primarily focus on unilateral feature augmentation rather than holistic collaborative signal enhancement. To bridge this gap, we propose Topology-Augmented Graph Collaborative Filtering (TAGCF), a novel framework that transforms semantic knowledge into topological connectivity. Unlike existing approaches that depend on textual features or direct interaction synthesis, TAGCF employs LLMs to infer interaction intents and underlying causal relationships from user-item pairs, representing these insights as intermediate attribute nodes within an enriched User-Attribute-Item (U-A-I) graph. Furthermore, to effectively model the heterogeneous relations in this augmented structure, we propose Adaptive Relation-weighted Graph Convolution (ARGC), which employs relation-specific prediction networks to dynamically estimate the importance of each relation type. Extensive experiments across multiple benchmark datasets and CF backbones demonstrate consistent improvements, with comprehensive evaluations including cold-start scenarios validating the effectiveness and robustness of our framework. All code will be made publicly available. For anonymous review, our code is available at the following anonymous link: https://anonymous.4open.science/r/AGCF-2441353190/.

cs.IR↗

arXiv2026

Epitaxial Growth and Anomalous Hall Effect in High-Quality Altermagnetic $α$-MnTe Thin Films

The recent identification of $α$-MnTe as a candidate altermagnet has attracted considerable interest, particularly for its potential application in magnetic random-access memory. However, the development of high-quality thin films - essential for practical implementation - has remained limited. Here, we report the epitaxial growth of centimeter-scale $α$-MnTe thin films on InP(111) substrates via molecular beam epitaxy (MBE). Through X-ray diffraction (XRD) analysis, we construct a MnTe phase diagram that provides clear guidance for stabilizing the pure $α$-MnTe phase, revealing that it is favored under high Te/Mn flux ratios and elevated growth temperatures. Cross-sectional electron microscopy confirms an atomically sharp film-substrate interface, consistent with a layer-by-layer epitaxial growth mode. Remarkably, these high-quality $α$-MnTe films exhibit a pronounced anomalous Hall effect (AHE) originating from Berry curvature, despite a net magnetic moment approaching zero - a signature of robust altermagnetic character. Our work establishes a viable route for synthesizing wafer-scale $α$-MnTe thin films and highlights their promise for altermagnet-based spintronics and magnetic sensing.

cond-mat.mtrl-sci↗

arXiv2026

Scaling Embeddings Outperforms Scaling Experts in Language Models

While Mixture-of-Experts (MoE) architectures have become the standard for sparsity scaling in large language models, they increasingly face diminishing returns and system-level bottlenecks. In this work, we explore embedding scaling as a potent, orthogonal dimension for scaling sparsity. Through a comprehensive analysis and experiments, we identify specific regimes where embedding scaling achieves a superior Pareto frontier compared to expert scaling. We systematically characterize the critical architectural factors governing this efficacy -- ranging from parameter budgeting to the interplay with model width and depth. Moreover, by integrating tailored system optimizations and speculative decoding, we effectively convert this sparsity into tangible inference speedups. Guided by these insights, we introduce LongCat-Flash-Lite, a 68.5B parameter model with ~3B activated trained from scratch. Despite allocating over 30B parameters to embeddings, LongCat-Flash-Lite not only surpasses parameter-equivalent MoE baselines but also exhibits exceptional competitiveness against existing models of comparable scale, particularly in agentic and coding domains.

cs.CL↗

arXiv2026

Quantitative Stability of the Betke-Henk-Wills Conjecture

The Betke-Henk-Wills conjecture proposes a sharp upper bound for the lattice point enumerator $G(K, Λ)$ of a convex body in terms of its successive minima. While the conjecture remains open for general convex bodies in dimensions $d \ge 5$, it is known to hold for orthogonal parallelotopes (boxes). In this paper, we establish the \textit{local stability} of the conjecture under small perturbations of the metric. Specifically, we prove that the inequality is strictly stable for integer boxes subjected to small rotations, owing to the discrete nature of the lattice point counting function. We derive explicit, geometry-invariant quantitative bounds on the permissible perturbation radius using the operator norm. Furthermore, we extend the validity of the conjecture to a class of $L_p$-balls for sufficiently large $p$, deriving a sharp threshold $p_0$ for the stability of the integer hull.

math.GM↗

arXiv2026

Analyzing Fairness of Neural Network Prediction via Counterfactual Dataset Generation

Interpreting the inference-time behavior of deep neural networks remains a challenging problem. Existing approaches to counterfactual explanation typically ask: What is the closest alternative input that would alter the model's prediction in a desired way? In contrast, we explore counterfactual datasets. Rather than perturbing the input, our method efficiently finds the closest alternative training dataset, one that differs from the original dataset by changing a few labels. Training a new model on this altered dataset can then lead to a different prediction of a given test instance. This perspective provides a new way to assess fairness by directly analyzing the influence of label bias on training and inference. Our approach can be characterized as probing whether a given prediction depends on biased labels. Since exhaustively enumerating all possible alternate datasets is infeasible, we develop analysis techniques that trace how bias in the training data may propagate through the learning algorithm to the trained network. Our method heuristically ranks and modifies the labels of a bounded number of training examples to construct a counterfactual dataset, retrains the model, and checks whether its prediction on a chosen test case changes. We evaluate our approach on feedforward neural networks across over 1100 test cases from 7 widely-used fairness datasets. Results show that it modifies only a small subset of training labels, highlighting its ability to pinpoint the critical training examples that drive prediction changes. Finally, we demonstrate how our counterfactual datasets reveal connections between training examples and test cases, offering an interpretable way to probe dataset bias.

cs.LG↗

arXiv2026

VFGS-Net: Frequency-Guided State-Space Learning for Topology-Preserving Retinal Vessel Segmentation

Accurate retinal vessel segmentation is a critical prerequisite for quantitative analysis of retinal images and computer-aided diagnosis of vascular diseases such as diabetic retinopathy. However, the elongated morphology, wide scale variation, and low contrast of retinal vessels pose significant challenges for existing methods, making it difficult to simultaneously preserve fine capillaries and maintain global topological continuity. To address these challenges, we propose the Vessel-aware Frequency-domain and Global Spatial modeling Network (VFGS-Net), an end-to-end segmentation framework that seamlessly integrates frequency-aware feature enhancement, dual-path convolutional representation learning, and bidirectional asymmetric spatial state-space modeling within a unified architecture. Specifically, VFGS-Net employs a dual-path feature convolution module to jointly capture fine-grained local textures and multi-scale contextual semantics. A novel vessel-aware frequency-domain channel attention mechanism is introduced to adaptively reweight spectral components, thereby enhancing vessel-relevant responses in high-level features. Furthermore, at the network bottleneck, we propose a bidirectional asymmetric Mamba2-based spatial modeling block to efficiently capture long-range spatial dependencies and strengthen the global continuity of vascular structures. Extensive experiments on four publicly available retinal vessel datasets demonstrate that VFGS-Net achieves competitive or superior performance compared to state-of-the-art methods. Notably, our model consistently improves segmentation accuracy for fine vessels, complex branching patterns, and low-contrast regions, highlighting its robustness and clinical potential.

cs.CV↗

arXiv2026

UniARM: Towards a Unified Autoregressive Reward Model for Multi-Objective Test-Time Alignment

Multi-objective alignment aims to align LLM responses with multiple human preference objectives. Among existing methods, guiding the generation of frozen LLMs through autoregressive reward models (ARMs) to accomplish multi-objective test-time alignment is a low-cost solution. However, these methods typically rely on independent parameters for each preference objective, either by training ARMs independently across preference dimensions, which neglects interactions among preference features, or by training a single ARM with separate feature extraction modules for each preference, which can cause feature entanglement. Both strategies can result in misalignment between generated outputs and user preferences. To address this limitation, we propose Preference-Modulated \& Shared Low-Rank Adaptation (MoSLoRA) for ARM training, which first extracts shared features via a preference-agnostic module and then applies affine transformations to shared features via a preference modulation module conditioned on mixed preference vectors. This design mitigates feature entanglement and enables precise control over preference trade-offs during inference. Building on this, we introduce the Unified Autoregressive Reward Model (UniARM), a novel framework for multi-objective test-time alignment. UniARM jointly models all preference dimensions in a single parameter space, eliminating the need for independent parameters for each preference objective. es on larger-scale LLMs, enhancing its practical usability.

cs.CL↗

arXiv2026

Task-free Adaptive Meta Black-box Optimization

Handcrafted optimizers become prohibitively inefficient for complex black-box optimization (BBO) tasks. MetaBBO addresses this challenge by meta-learning to automatically configure optimizers for low-level BBO tasks, thereby eliminating heuristic dependencies. However, existing methods typically require extensive handcrafted training tasks to learn meta-strategies that generalize to target tasks, which poses a critical limitation for realistic applications with unknown task distributions. To overcome the issue, we propose the Adaptive meta Black-box Optimization Model (ABOM), which performs online parameter adaptation using solely optimization data from the target task, obviating the need for predefined task distributions. Unlike conventional metaBBO frameworks that decouple meta-training and optimization phases, ABOM introduces a closed-loop adaptive parameter learning mechanism, where parameterized evolutionary operators continuously self-update by leveraging generated populations during optimization. This paradigm shift enables zero-shot optimization: ABOM achieves competitive performance on synthetic BBO benchmarks and realistic unmanned aerial vehicle path planning problems without any handcrafted training tasks. Visualization studies reveal that parameterized evolutionary operators exhibit statistically significant search patterns, including natural selection and genetic recombination.

cs.NE↗

arXiv2026

PRPO: Aligning Process Reward with Outcome Reward in Policy Optimization

Policy optimization for large language models often suffers from sparse reward signals in multi-step reasoning tasks. Critic-free methods like GRPO assign a single normalized outcome reward to all tokens, providing limited guidance for intermediate reasoning . While Process Reward Models (PRMs) offer dense feedback, they risk premature collapse when used alone, as early low-reward tokens can drive policies toward truncated outputs. We introduce Process Relative Policy Optimization (PRPO), which combines outcome reliability with process-level guidance in a critic-free framework. PRPO segments reasoning sequences based on semantic clues, normalizes PRM scores into token-level advantages, and aligns their distribution with outcome advantages through location-parameter shift. On MATH500, PRPO improves Qwen2.5-Math-1.5B accuracy from 61.2% to 64.4% over GRPO using only eight rollouts and no value network, demonstrating efficient fine-grained credit assignment within critic-free optimization. Code is available at: https://github.com/SchumiDing/srpocode

cs.LG↗