arXiv subjects

Linghao Zhang

Publications and source records attributed to Linghao Zhang.

29 records · Page 2Linked to original sources

arXiv2025

Learning Polynomial Activation Functions for Deep Neural Networks

Activation functions are crucial for deep neural networks. This novel work frames the problem of training neural network with learnable polynomial activation functions as a polynomial optimization problem, which is solvable by the Moment-SOS hierarchy. This work represents a fundamental departure from the conventional paradigm of training deep neural networks, which relies on local optimization methods like backpropagation and gradient descent. Numerical experiments are presented to demonstrate the accuracy and robustness of optimum parameter recovery in presence of noises.

math.OC↗

arXiv2025

Sparse Polynomial Optimization with Matrix Constraints

This paper studies the hierarchy of sparse matrix Moment-SOS relaxations for solving sparse polynomial optimization problems with matrix constraints. First, we prove a sufficient and necessary condition for the sparse hierarchy to be tight. Second, we discuss how to detect the tightness and extract minimizers. Third, for the convex case, we show that the hierarchy of the sparse matrix Moment-SOS relaxations is tight, under some general assumptions. In particular, we show that the sparse matrix Moment-SOS relaxation is tight for every order when the problem is SOS-convex. Numerical experiments are provided to show the efficiency of the sparse relaxations.

math.OC↗

arXiv2025

Solving the Min-Max Multiple Traveling Salesmen Problem via Learning-Based Path Generation and Optimal Splitting

This study addresses the Min-Max Multiple Traveling Salesmen Problem ($m^3$-TSP), which aims to coordinate tours for multiple salesmen such that the length of the longest tour is minimized. Due to its NP-hard nature, exact solvers become impractical under the assumption that $P \ne NP$. As a result, learning-based approaches have gained traction for their ability to rapidly generate high-quality approximate solutions. Among these, two-stage methods combine learning-based components with classical solvers, simplifying the learning objective. However, this decoupling often disrupts consistent optimization, potentially degrading solution quality. To address this issue, we propose a novel two-stage framework named \textbf{Generate-and-Split} (GaS), which integrates reinforcement learning (RL) with an optimal splitting algorithm in a joint training process. The splitting algorithm offers near-linear scalability with respect to the number of cities and guarantees optimal splitting in Euclidean space for any given path. To facilitate the joint optimization of the RL component with the algorithm, we adopt an LSTM-enhanced model architecture to address partial observability. Extensive experiments show that the proposed GaS framework significantly outperforms existing learning-based approaches in both solution quality and transferability.

cs.AI↗

arXiv2025

Contextual Code Retrieval for Commit Message Generation: A Preliminary Study

A commit message describes the main code changes in a commit and plays a crucial role in software maintenance. Existing commit message generation (CMG) approaches typically frame it as a direct mapping which inputs a code diff and produces a brief descriptive sentence as output. However, we argue that relying solely on the code diff is insufficient, as raw code diff fails to capture the full context needed for generating high-quality and informative commit messages. In this paper, we propose a contextual code retrieval-based method called C3Gen to enhance CMG by retrieving commit-relevant code snippets from the repository and incorporating them into the model input to provide richer contextual information at the repository scope. In the experiments, we evaluated the effectiveness of C3Gen across various models using four objective and three subjective metrics. Meanwhile, we design and conduct a human evaluation to investigate how C3Gen-generated commit messages are perceived by human developers. The results show that by incorporating contextual code into the input, C3Gen enables models to effectively leverage additional information to generate more comprehensive and informative commit messages with greater practical value in real-world development scenarios. Further analysis underscores concerns about the reliability of similaritybased metrics and provides empirical insights for CMG.

cs.SE↗

arXiv2025

SWE-bench Goes Live!

The issue-resolving task, where a model generates patches to fix real-world bugs, has emerged as a critical benchmark for evaluating the capabilities of large language models (LLMs). While SWE-bench and its variants have become standard in this domain, they suffer from key limitations: they have not been updated since their initial releases, cover a narrow set of repositories, and depend heavily on manual effort for instance construction and environment setup. These factors hinder scalability and introduce risks of overfitting and data contamination. In this work, we present SWE-bench-Live, a live-updatable benchmark designed to overcome these challenges. Our initial release consists of 1,319 tasks derived from real GitHub issues created since 2024, spanning 93 repositories. Each task is accompanied by a dedicated Docker image to ensure reproducible execution. Central to our benchmark is \method, an automated curation pipeline that streamlines the entire process from instance creation to environment setup, removing manual bottlenecks and enabling scalability and continuous updates. We evaluate a range of state-of-the-art agent frameworks and LLMs on SWE-bench-Live, revealing a substantial performance gap compared to static benchmarks like SWE-bench, even under controlled evaluation conditions. To better understand this discrepancy, we perform detailed analyses across repository origin, issue recency, and task difficulty. By providing a fresh, diverse, and executable benchmark grounded in live repository activity, SWE-bench-Live facilitates rigorous, contamination-resistant evaluation of LLMs and agents in dynamic, real-world software development settings.

cs.SE↗

arXiv2025

A Characterization for Tightness of the Sparse Moment-SOS Hierarchy

This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if the objective can be written as a sum of sparse nonnegative polynomials, each of which belongs to the sum of the ideal and quadratic module generated by the corresponding sparse constraints. Based on this characterization, we give several sufficient conditions for the sparse Moment-SOS hierarchy to be tight. In particular, we show that this sparse hierarchy is tight under some assumptions such as convexity, optimality conditions or finiteness of constraining sets.

math.OC↗

arXiv2025

DI-BENCH: Benchmarking Large Language Models on Dependency Inference with Testable Repositories at Scale

Large Language Models have advanced automated software development, however, it remains a challenge to correctly infer dependencies, namely, identifying the internal components and external packages required for a repository to successfully run. Existing studies highlight that dependency-related issues cause over 40\% of observed runtime errors on the generated repository. To address this, we introduce DI-BENCH, a large-scale benchmark and evaluation framework specifically designed to assess LLMs' capability on dependency inference. The benchmark features 581 repositories with testing environments across Python, C#, Rust, and JavaScript. Extensive experiments with textual and execution-based metrics reveal that the current best-performing model achieves only a 42.9% execution pass rate, indicating significant room for improvement. DI-BENCH establishes a new viewpoint for evaluating LLM performance on repositories, paving the way for more robust end-to-end software synthesis.

cs.CL↗

arXiv2024

RAG-Enhanced Commit Message Generation

Commit message is one of the most important textual information in software development and maintenance. However, it is time-consuming to write commit messages manually. Commit Message Generation (CMG) has become a research hotspot. Recently, several pre-trained language models (PLMs) and large language models (LLMs) with code capabilities have been introduced, demonstrating impressive performance on code-related tasks. Meanwhile, prior studies have explored the utilization of retrieval techniques for CMG, but it is still unclear what effects would emerge from combining advanced retrieval techniques with various generation models. This paper proposed REACT, a REtrieval-Augmented framework for CommiT message generation. It integrates advanced retrieval techniques with different PLMs and LLMs, to enhance the performance of these models on the CMG task. Specifically, a hybrid retriever is designed and used to retrieve the most relevant code diff and commit message pair as an exemplar. Then, the retrieved pair is utilized to guide and enhance the CMG task by PLMs and LLMs through fine-tuning and in-context learning. The experimental results show that REACT significantly enhances these models' performance on the CMG task, improving the BLEU score of CodeT5 by up to 55%, boosting Llama 3's BLEU score by 102%, and substantially surpassing all baselines.

cs.SE↗

arXiv2024

Polynomial Optimization Over Unions of Sets

This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove the asymptotic or finite convergence of the unified hierarchy. Special properties for the univariate case are discussed.The application for computing $(p,q)$-norms of matrices is also presented.

math.OC↗

arXiv2024

Using Large Language Models for Commit Message Generation: A Preliminary Study

A commit message is a textual description of the code changes in a commit, which is a key part of the Git version control system (VCS). It captures the essence of software updating. Therefore, it can help developers understand code evolution and facilitate efficient collaboration between developers. However, it is time-consuming and labor-intensive to write good and valuable commit messages. Some researchers have conducted extensive studies on the automatic generation of commit messages and proposed several methods for this purpose, such as generationbased and retrieval-based models. However, seldom studies explored whether large language models (LLMs) can be used to generate commit messages automatically and effectively. To this end, this paper designed and conducted a series of experiments to comprehensively evaluate the performance of popular open-source and closed-source LLMs, i.e., Llama 2 and ChatGPT, in commit message generation. The results indicate that considering the BLEU and Rouge-L metrics, LLMs surpass the existing methods in certain indicators but lag behind in others. After human evaluations, however, LLMs show a distinct advantage over all these existing methods. Especially, in 78% of the 366 samples, the commit messages generated by LLMs were evaluated by humans as the best. This work not only reveals the promising potential of using LLMs to generate commit messages, but also explores the limitations of commonly used metrics in evaluating the quality of auto-generated commit messages.

cs.SE↗

arXiv2018

Question Relevance in Visual Question Answering

Free-form and open-ended Visual Question Answering systems solve the problem of providing an accurate natural language answer to a question pertaining to an image. Current VQA systems do not evaluate if the posed question is relevant to the input image and hence provide nonsensical answers when posed with irrelevant questions to an image. In this paper, we solve the problem of identifying the relevance of the posed question to an image. We address the problem as two sub-problems. We first identify if the question is visual or not. If the question is visual, we then determine if it's relevant to the image or not. For the second problem, we generate a large dataset from existing visual question answering datasets in order to enable the training of complex architectures and model the relevance of a visual question to an image. We also compare the results of our Long Short-Term Memory Recurrent Neural Network based models to Logistic Regression, XGBoost and multi-layer perceptron based approaches to the problem.

cs.CV↗