arXiv subjects

Haowei Yuan

Publications and source records attributed to Haowei Yuan.

4 recordsLinked to original sources

arXiv2026

Exact Closed-Form Formulae for Linear and Circular Continuous Scan Statistics: $P_c(N - 1; N, w)$, $P_c(3; N, w)$, and $P(3; N, w)$

The continuous linear $P(k; N, w)$ and circular scan statistics $P_c(k; N, w)$ are fundamental tools in probability and spatial statistics, frequently used to detect clustering in uniform data. Let $X_1, X_2, \dots, X_N$ be independently and uniformly distributed random variables on a unit interval or unit ring. The exact distribution of these scan statistics relies on the minimum window width required to capture exactly $k$ points. Furthermore, the survival function $1 - P_c(k; N, w)$ directly corresponds to the geometric probability that if $N$ arcs of length $1 - w$ are uniformly and randomly placed on a unit circle, every point on the circle is covered at least $N + 1 - k$ times. Historically, evaluating the exact cumulative distribution functions, $P(k; N, w)$ and $P_c(k; N, w)$, relies heavily on complex recursive approximations. In this paper, we bypass these traditional recursive methods to derive direct, generalized closed-form expressions for some linear and circular continuous scan statistics. Specifically, we present the exact analytical solutions for $P_c(N - 1; N, w)$, $P_c(3; N, w)$, and $P(3; N, w)$ for arbitrary values of $N$ and window width $w$. These newly derived closed-form expressions not only provide exact baseline distributions for extreme spacings but also significantly simplify computational complexity compared to existing iterative approaches.

math.PR↗

arXiv2025

DebugTA: An LLM-Based Agent for Simplifying Debugging and Teaching in Programming Education

In programming education, Debugging and Teaching (DT) task is a common scenario where students receive assistance in correcting their erroneous code. The task involves multiple inputs, including erroneous code, error messages, reference solutions, and the question description, with the goal of generating modification suggestions to the erroneous code. However, two key challenges hinder the effectiveness of existing approaches. Firstly, the complexity and heterogeneity of inputs inherent in DT tasks significantly elevate the reasoning challenges faced by LLMs. Second, existing approaches often fail to fully leverage the availability of standard code in DT tasks, forcing models to rely solely on complex multi-step reasoning, which limits the potential of LLMs in addressing DT tasks effectively. To address these challenges, we propose DebugTA, a novel LLM-based debugging and teaching agent with specialized tools for standard code retrieval, variable substitution to align reference code, and an external compiler for real-time code analysis. Guided by explicit pedagogical and debugging principles, DebugTA acts as an agent that decomposes a complex task into sequential LLM interactions, each utilizing distinct tools for specific subtasks, thereby simplifying the logical reasoning at each step and reducing overall reasoning complexity. Furthermore, DebugTA utilizes tool calls to align the standard code with the erroneous code as much as possible, allowing the LLM to focus on logic errors within the erroneous code and improving the accuracy of the generated suggestions. To rigorously assess the quality of modification suggestions, we introduce a student simulator-teacher interaction paradigm. Experimental results on three real-world code datasets demonstrate that DebugTA consistently improves teaching effectiveness while significantly reducing computational costs.

cs.SE↗

arXiv2025

CoreCodeBench: Decoupling Code Intelligence via Fine-Grained Repository-Level Tasks

The evaluation of Large Language Models (LLMs) for software engineering has shifted towards complex, repository-level tasks. However, existing benchmarks predominantly rely on coarse-grained pass rates that treat programming proficiency as a monolithic capability, obscuring specific cognitive bottlenecks. Furthermore, the static nature of these benchmarks renders them vulnerable to data contamination and performance saturation. To address these limitations, we introduce CoreCodeBench, a configurable repository-level benchmark designed to dissect coding capabilities through atomized tasks. Leveraging our automated framework, CorePipe, we extract and transform Python repositories into a comprehensive suite of tasks that isolate distinct cognitive demands within identical code contexts. Unlike static evaluations, CoreCodeBench supports controllable difficulty scaling to prevent saturation and ensures superior data quality. It achieves a 78.55% validity yield, significantly surpassing the 31.7% retention rate of SWE-bench-Verified. Extensive experiments with state-of-the-art LLMs reveal a significant capability misalignment, evidenced by distinct ranking shifts across cognitive dimensions. This indicates that coding proficiency is non-monolithic, as strength in one aspect does not necessarily translate to others. These findings underscore the necessity of our fine-grained taxonomy in diagnosing model deficiencies and offer a sustainable, rigorous framework for evolving code intelligence. The code for CorePipe is available at https://github.com/AGI-Eval-Official/CoreCodeBench, and the data for CoreCodeBench can be accessed at https://huggingface.co/collections/tubehhh/corecodebench-68256d2faabf4b1610a08caa.

cs.SE↗

arXiv2024

pEBR: A Probabilistic Approach to Embedding Based Retrieval

Embedding-based retrieval aims to learn a shared semantic representation space for both queries and items, enabling efficient and effective item retrieval through approximate nearest neighbor (ANN) algorithms. In current industrial practice, retrieval systems typically retrieve a fixed number of items for each query. However, this fixed-size retrieval often results in insufficient recall for head queries and low precision for tail queries. This limitation largely stems from the dominance of frequentist approaches in loss function design, which fail to address this challenge in industry. In this paper, we propose a novel \textbf{p}robabilistic \textbf{E}mbedding-\textbf{B}ased \textbf{R}etrieval (\textbf{pEBR}) framework. Our method models the item distribution conditioned on each query, enabling the use of a dynamic cosine similarity threshold derived from the cumulative distribution function (CDF) of the probabilistic model. Experimental results demonstrate that pEBR significantly improves both retrieval precision and recall. Furthermore, ablation studies reveal that the probabilistic formulation effectively captures the inherent differences between head-to-tail queries.

cs.IR↗