arXiv subjects

Yicheng Zhou

Publications and source records attributed to Yicheng Zhou.

4 recordsLinked to original sources

arXiv2026

Representability of continuous K-theory in rigid analytic motivic $\mathbb{A}^1$-homotopy theory

We prove that both continuous K-theory and analytic K-theory of rigid analytic spaces (à la Kerz--Saito--Tamme) satisfiy descent with respect to the Nisnevich topology. Together with the fact that it is $\mathbb{A}^1$-invariant assuming resolutions of singularities, we deduce that it is representable in the $\mathbb{A}^{1}$-homotopy category of rigid spaces (à la Dahlhausen--Yaylali). We identifiy the representing object with both $\mathbb{Z}\times\mathrm{BGL}$ and the analytification of algebraic K-theory. As a consequence, we get a representability statement for coefficients in light condensed spectra. Moreover, we show Weibel vanishing and that continuous K-theory is $\mathbb{A}^1$-invariant on local Tate pairs (without any regularity assumption).

math.KT↗

arXiv2025

Extracting Conceptual Knowledge to Locate Software Issues

Issue localization, which identifies faulty code elements such as files or functions, is critical for effective bug fixing. While recent LLM-based and LLM-agent-based approaches improve accuracy, they struggle in large-scale repositories due to concern tangling, where relevant logic is buried in large functions, and concern scattering, where related logic is dispersed across files. To address these challenges, we propose RepoLens, a novel approach that abstracts and leverages conceptual knowledge from code repositories. RepoLens decomposes fine-grained functionalities and recomposes them into high-level concerns, semantically coherent clusters of functionalities that guide LLMs. It operates in two stages: an offline stage that extracts and enriches conceptual knowledge into a repository-wide knowledge base, and an online stage that retrieves issue-specific terms, clusters and ranks concerns by relevance, and integrates them into localization workflows via minimally intrusive prompt enhancements. We evaluate RepoLens on SWE-Lancer-Loc, a benchmark of 216 tasks derived from SWE-Lancer. RepoLens consistently improves three state-of-the-art tools, namely AgentLess, OpenHands, and mini-SWE-agent, achieving average gains of over 22% in Hit@k and 46% in Recall@k for file- and function-level localization. It generalizes across models (GPT-4o, GPT-4o-mini, GPT-4.1) with Hit@1 and Recall@10 gains up to 504% and 376%, respectively. Ablation studies and manual evaluation confirm the effectiveness and reliability of the constructed concerns.

cs.SE↗

arXiv2024

Make Graph Neural Networks Great Again: A Generic Integration Paradigm of Topology-Free Patterns for Traffic Speed Prediction

Urban traffic speed prediction aims to estimate the future traffic speed for improving urban transportation services. Enormous efforts have been made to exploit Graph Neural Networks (GNNs) for modeling spatial correlations and temporal dependencies of traffic speed evolving patterns, regularized by graph topology.While achieving promising results, current traffic speed prediction methods still suffer from ignoring topology-free patterns, which cannot be captured by GNNs. To tackle this challenge, we propose a generic model for enabling the current GNN-based methods to preserve topology-free patterns. Specifically, we first develop a Dual Cross-Scale Transformer (DCST) architecture, including a Spatial Transformer and a Temporal Transformer, to preserve the cross-scale topology-free patterns and associated dynamics, respectively. Then, to further integrate both topology-regularized/-free patterns, we propose a distillation-style learning framework, in which the existing GNN-based methods are considered as the teacher model, and the proposed DCST architecture is considered as the student model. The teacher model would inject the learned topology-regularized patterns into the student model for integrating topology-free patterns. The extensive experimental results demonstrated the effectiveness of our methods.

cs.LG↗

arXiv2019

On algebraic integers all conjugates of which belong to a given compact subset of the complex plane

The study of Frobenius endomorphism provides numerous information about its corresponding Abelian variety. To understand the action of the Frobenius endomorphism, one may be interested in its eigenvalues. According to Weil's third conjecture ("Riemann hypothesis over finite fields"), they all have absolute value less than or equal to $2g\sqrt{p}$. Thus, the eigenvalues of the Frobenius endomorphism all belong to the same compact subset of the complex plane, and are roots of the same monic polynomial with integer coefficients (the characteristic polynomial of the Frobenius endomorphism). Such complex numbers are called algebraic integers "totally" in a compact subset, which means algebraic integers all conjugates of which belong to a same given compact subset of the complex plane. The study of such algebraic integers helps to understand the eigenvalues of the Frobenius endomorphism, especially their distribution. In this paper, we will study the following question : under which conditions a compact subset of the complex plane has a finite or infinite number of algebraic integers "totally" in it ? The problem can be studied in light of the notion of capacity of a compact subset, which comes from potential theory. In this paper, we will present the theory of capacity and some theorems (Fekete, Szegö, Robinson) derived from it that partially answer the question: in the case of a union of real segments, when the capacity is smaller (resp. larger) than 1, it contains a finite (resp. infinite) number of algebraic integers totally in it. For instance, for real line segments, the limit length is 4. This paper is written as part of a collective project conducted in École Polytechnique (France). It is aimed towards undergraduate audience in mathematics, with basic knowledge in algebra, topology, analysis, and dwells into a modern topic of research.

math.NT↗