arXiv subjects

Lin Mu

Publications and source records attributed to Lin Mu.

At least 19 recordsLinked to original sources

arXiv2026

Fully discrete analysis of pressure-robust enriched Galerkin methods for the time-dependent Stokes equations

This paper presents a fully discrete analysis of pressure-robust enriched Galerkin (EG) methods for the time-dependent Stokes equations. The spatial discretization employs a velocity reconstruction operator that preserves the continuous component of the EG space while mapping its enriched discontinuous component into the lowest-order Raviart-Thomas ($\mathcal{R}T_0$) subspace of $H(\mathrm{div})$, ensuring strict local mass conservation and pressure-robustness. Fully discrete schemes are constructed using the backward Euler and Crank-Nicolson methods, with the reconstruction incorporated into both the forcing and discrete time-derivative terms. We prove unconditional stability and derive optimal-order, parameter-explicit \textit{a priori} error estimates for both the velocity and pressure. In particular, the velocity estimates are independent of the continuous pressure and the irrotational component of the forcing term, contain no inverse-viscosity factors, and explicitly track the spatial mesh size, time-step size, and viscosity. Numerical experiments in two and three dimensions verify the predicted convergence rates, strict local mass conservation, and robustness with respect to the viscosity, while comparisons with non-pressure-robust variants demonstrate the importance of incorporating the reconstruction into the discrete time-derivative term.

math.NA↗

arXiv2026

Coloring for dispersion: A polynomial-time algorithm for cardinality-constrained 2-anticlustering

The $k$-Maximum Dispersion Problem with Cardinality Constraints ($k$-MDCC) asks for a partition of a given item set with pairwise dissimilarities into $k$ cardinality-constrained groups such that the minimum pairwise intra-group dissimilarity, which is also known as the dispersion, is maximized. The problem arises in the context of anticlustering, where the goal is to create maximally heterogeneous groups of items with applications in psychological research, bioinformatics, and data science. It is known that $k$-MDCC is NP-hard for $k \geq 3$ but it has been an open question whether it can be solved in polynomial time for $k = 2$. We give a positive answer to this question by showing that $2$-MDCC can be solved by a quadratic number of cardinality-constrained 2-coloring problem instances ($2$-COLCC). We solve these instances by transforming them into a restricted class of subset sum instances. Although subset sum is NP-complete in general, for this restricted class the input values are bounded, ensuring that the pseudopolynomial dynamic programming algorithm runs in polynomial time. As a consequence, we obtain a polynomial-time algorithm for $2$-MDCC. We demonstrate that a publicly available open-source implementation of our new algorithm outperforms the previous integer linear programming solution by several orders of magnitude so that even large datasets ($n = 10{,}000$) can be processed in less than a second.

cs.DS↗

arXiv2026

GraphLoRA: Structure-Aware Low-Rank Adaptation for Large Language Model Recommendation

Large Language Models (LLMs) have shown strong potential for recommendation (LLMRec) due to their powerful reasoning and generalization abilities. However, effectively aligning the textual semantics modeled by LLMs with the collaborative signals remains a key challenge. Existing methods either translate collaborative information into textual prompts or inject pre-trained embeddings into the LLM, both of which treat structural information as static input and fail to capture high-order relational dependencies. To bridge this gap, we propose GraphLoRA, a novel framework that generalizes low-rank adaptation from independent to structure-aware propagation. GraphLoRA embeds a trainable graph message-passing network within the low-rank adaptation pathway, enabling structural signals to propagate through the parameter space. This design allows collaborative topology to explicitly guide parameter updates, fostering deep integration between graph-structured and textual semantic information. Extensive experiments on multiple benchmarks demonstrate that GraphLoRA not only outperforms state-of-the-art LLM-based recommendation methods but also achieves superior generalization, effectively balancing structural reasoning capability with computational efficiency. Code is available at \href{https://github.com/wgj15965/GraphLoRA}{https://github.com/wgj15965/GraphLoRA}.

cs.CL↗

arXiv2026

Polynomial Expansion Rank Adaptation: Enhancing Low-Rank Fine-Tuning with High-Order Interactions

Low-rank adaptation (LoRA) is a widely used strategy for efficient fine-tuning of large language models (LLMs), but its strictly linear structure fundamentally limits expressive capacity. The bilinear formulation of weight updates captures only first-order dependencies between low-rank factors, restricting the modeling of nonlinear and higher-order parameter interactions. In this paper, we propose Polynomial Expansion Rank Adaptation (PERA), a novel method that introduces structured polynomial expansion directly into the low-rank factor space. By expanding each low-rank factor to synthesize high-order interaction terms before composition, PERA transforms the adaptation space into a polynomial manifold capable of modeling richer nonlinear coupling without increasing rank or inference cost. We provide theoretical analysis demonstrating that PERA offers enhanced expressive capacity and more effective feature utilization compare to existing linear adaptation approaches. Empirically, PERA consistently outperforms state-of-the-art methods across diverse benchmarks. Notably, our experiments show that incorporating high-order nonlinear components particularly square terms is crucial for enhancing expressive capacity and maintaining strong and robust performance under various rank settings. Our code is available at https://github.com/zhangwenhao6/PERA

cs.LG↗

arXiv2026

From Clues to Generation: Language-Guided Conditional Diffusion for Cross-Domain Recommendation

Cross-domain Recommendation (CDR) exploits multi-domain correlations to alleviate data sparsity. As a core task within this field, inter-domain recommendation focuses on predicting preferences for users who interact in a source domain but lack behavioral records in a target domain. Existing approaches predominantly rely on overlapping users as anchors for knowledge transfer. In real-world scenarios, overlapping users are often scarce, leaving the vast majority of users with only single-domain interactions. For these users, the absence of explicit alignment signals makes fine-grained preference transfer intrinsically difficult. To address this challenge, this paper proposes Language-Guided Conditional Diffusion for CDR (LGCD), a novel framework that integrates Large Language Models (LLMs) and diffusion models for inter-domain sequential recommendation. Specifically, we leverage LLM reasoning to bridge the domain gap by inferring potential target preferences for single-domain users and mapping them to real items, thereby constructing pseudo-overlapping data. We distinguish between real and pseudo-interaction pathways and introduce additional supervision constraints to mitigate the semantic noise brought by pseudo-interaction. Furthermore, we design a conditional diffusion architecture to precisely guide the generation of target user representations based on source-domain patterns. Extensive experiments demonstrate that LGCD significantly outperforms state-of-the-art methods in inter-domain recommendation tasks.

cs.IR↗

arXiv2026

TalkLoRA: Communication-Aware Mixture of Low-Rank Adaptation for Large Language Models

Low-Rank Adaptation (LoRA) enables parameter-efficient fine-tuning of Large Language Models (LLMs), and recent Mixture-of-Experts (MoE) extensions further enhance flexibility by dynamically combining multiple LoRA experts. However, existing MoE-augmented LoRA methods assume that experts operate independently, often leading to unstable routing, expert dominance. In this paper, we propose \textbf{TalkLoRA}, a communication-aware MoELoRA framework that relaxes this independence assumption by introducing expert-level communication prior to routing. TalkLoRA equips low-rank experts with a lightweight Talking Module that enables controlled information exchange across expert subspaces, producing a more robust global signal for routing. Theoretically, we show that expert communication smooths routing dynamics by mitigating perturbation amplification while strictly generalizing existing MoELoRA architectures. Empirically, TalkLoRA consistently outperforms vanilla LoRA and MoELoRA across diverse language understanding and generation tasks, achieving higher parameter efficiency and more balanced expert routing under comparable parameter budgets. These results highlight structured expert communication as a principled and effective enhancement for MoE-based parameter-efficient adaptation. Code is available at https://github.com/why0129/TalkLoRA.

cs.LG↗

arXiv2026

L-UNet: An LSTM Network for Remote Sensing Image Change Detection

Change detection of high-resolution remote sensing images is an important task in earth observation and was extensively investigated. Recently, deep learning has shown to be very successful in plenty of remote sensing tasks. The current deep learning-based change detection method is mainly based on conventional long short-term memory (Conv-LSTM), which does not have spatial characteristics. Since change detection is a process with both spatiality and temporality, it is necessary to propose an end-to-end spatiotemporal network. To achieve this, Conv-LSTM, an extension of the Conv-LSTM structure, is introduced. Since it shares similar spatial characteristics with the convolutional layer, L-UNet, which substitutes partial convolution layers of UNet-to-Conv-LSTM and Atrous L-UNet (AL-UNet), which further using Atrous structure to multiscale spatial information is proposed. Experiments on two data sets are conducted and the proposed methods show the advantages both in quantity and quality when compared with some other methods.

eess.IV↗

arXiv2026

From Representation to Clusters: A Contrastive Learning Approach for Attributed Hypergraph Clustering

Contrastive learning has demonstrated strong performance in attributed hypergraph clustering. Typically, existing methods based on contrastive learning first learn node embeddings and then apply clustering algorithms, such as k-means, to these embeddings to obtain the clustering results.However, these methods lack direct clustering supervision, risking the inclusion of clustering-irrelevant information in the learned graph.To this end, we propose a Contrastive learning approach for Attributed Hypergraph Clustering (CAHC), an end-to-end method that simultaneously learns node embeddings and obtains clustering results. CAHC consists of two main steps: representation learning and cluster assignment learning. The former employs a novel contrastive learning approach that incorporates both node-level and hyperedge-level objectives to generate node embeddings.The latter joint embedding and clustering optimization to refine these embeddings by clustering-oriented guidance and obtains clustering results simultaneously.Extensive experimental results demonstrate that CAHC outperforms baselines on eight datasets.

cs.LG↗

arXiv2025

Pressure-robust enriched Galerkin finite element methods for coupled Navier-Stokes and heat equations

We propose a pressure-robust enriched Galerkin (EG) finite element method for the incompressible Navier-Stokes and heat equations in the Boussinesq regime. For the Navier-Stokes equations, the EG formulation combines continuous Lagrange elements with a discontinuous enrichment vector per element in the velocity space and a piecewise constant pressure space, and it can be implemented efficiently within standard finite element frameworks. To enforce pressure robustness, we construct velocity reconstruction operators that map the discrete EG velocity field into exactly divergence-free, H(div)-conforming fields. In particular, we develop reconstructions based on Arbogast-Correa (AC) mixed finite element spaces on quadrilateral meshes and demonstrate that the resulting schemes remain stable and accurate even on highly distorted grids. The nonlinearity of the coupled Navier-Stokes-Boussinesq system is treated with several iterative strategies, including Picard iterations and Anderson-accelerated iterations; our numerical study shows that Anderson acceleration yields robust and efficient convergence for high Rayleigh number flows within the proposed framework. The performance of the method is assessed on a set of benchmark problems and application-driven test cases. These numerical experiments highlight the potential of pressure-robust EG methods as flexible and accurate tools for coupled flow and heat transport in complex geometries.

cs.CE↗

arXiv2025

Weakly Supervised Fine-grained Span-Level Framework for Chinese Radiology Report Quality Assurance

Quality Assurance (QA) for radiology reports refers to judging whether the junior reports (written by junior doctors) are qualified. The QA scores of one junior report are given by the senior doctor(s) after reviewing the image and junior report. This process requires intensive labor costs for senior doctors. Additionally, the QA scores may be inaccurate for reasons like diagnosis bias, the ability of senior doctors, and so on. To address this issue, we propose a Span-level Quality Assurance EvaluaTOR (Sqator) to mark QA scores automatically. Unlike the common document-level semantic comparison method, we try to analyze the semantic difference by exploring more fine-grained text spans. Specifically, Sqator measures QA scores by measuring the importance of revised spans between junior and senior reports, and outputs the final QA scores by merging all revised span scores. We evaluate Sqator using a collection of 12,013 radiology reports. Experimental results show that Sqator can achieve competitive QA scores. Moreover, the importance scores of revised spans can be also consistent with the judgments of senior doctors.

cs.CL↗

arXiv2025

Robustness of Prompting: Enhancing Robustness of Large Language Models Against Prompting Attacks

Large Language Models (LLMs) have demonstrated remarkable performance across various tasks by effectively utilizing a prompting strategy. However, they are highly sensitive to input perturbations, such as typographical errors or slight character order errors, which can significantly impair their performance. Despite advances in prompting techniques such as Chain-of-Thought and automatic prompt generation, developing a prompting strategy that explicitly mitigates the negative impact of such perturbations remains an open challenge. To bridge this gap, we propose Robustness of Prompting (RoP), a novel prompting strategy aimed at enhancing the robustness of LLMs. RoP consists of two stages: Error Correction and Guidance. In the Error Correction stage, RoP applies diverse perturbation methods to generate adversarial examples, which are used to generate prompts that correct input errors automatically. In the Guidance stage, RoP generates an optimal guidance prompt based on the corrected input, guiding the model to generate more robust and accurate inferences. Through comprehensive experiments spanning arithmetic, commonsense, and logical reasoning tasks, we demonstrate that RoP significantly improves LLMs' robustness against adversarial perturbations. Crucially, it preserves model accuracy with only minimal degradation compared to clean input scenarios, thereby establishing RoP as a practical and effective approach for enhancing LLM robustness in real-world applications.

cs.CL↗

arXiv2025

DenseLoRA: Dense Low-Rank Adaptation of Large Language Models

Low-rank adaptation (LoRA) has been developed as an efficient approach for adapting large language models (LLMs) by fine-tuning two low-rank matrices, thereby reducing the number of trainable parameters. However, prior research indicates that many of the weights in these matrices are redundant, leading to inefficiencies in parameter utilization. To address this limitation, we introduce Dense Low-Rank Adaptation (DenseLoRA), a novel approach that enhances parameter efficiency while achieving superior performance compared to LoRA. DenseLoRA builds upon the concept of representation fine-tuning, incorporating a single Encoder-Decoder to refine and compress hidden representations across all adaptation layers before applying adaptation. Instead of relying on two redundant low-rank matrices as in LoRA, DenseLoRA adapts LLMs through a dense low-rank matrix, improving parameter utilization and adaptation efficiency. We evaluate DenseLoRA on various benchmarks, showing that it achieves 83.8% accuracy with only 0.01% of trainable parameters, compared to LoRA's 80.8% accuracy with 0.70% of trainable parameters on LLaMA3-8B. Additionally, we conduct extensive experiments to systematically assess the impact of DenseLoRA's components on overall model performance. Code is available at https://github.com/mulin-ahu/DenseLoRA.

cs.CL↗

arXiv2025

Pre-trained Prompt-driven Semi-supervised Local Community Detection

Semi-supervised local community detection aims to leverage known communities to detect the community containing a given node. Although existing semi-supervised local community detection studies yield promising results, they suffer from time-consuming issues, highlighting the need for more efficient algorithms. Therefore, we apply the "pre-train, prompt" paradigm to semi-supervised local community detection and propose the Pre-trained Prompt-driven Semi-supervised Local community detection method (PPSL). PPSL consists of three main components: node encoding, sample generation, and prompt-driven fine-tuning. Specifically, the node encoding component employs graph neural networks to learn the representations of nodes and communities. Based on representations of nodes and communities, the sample generation component selects known communities that are structurally similar to the local structure of the given node as training samples. Finally, the prompt-driven fine-tuning component leverages these training samples as prompts to guide the final community prediction. Experimental results on five real-world datasets demonstrate that PPSL outperforms baselines in both community quality and efficiency.

cs.SI↗

arXiv2025

Community Search in Time-dependent Road-social Attributed Networks

Real-world networks often involve both keywords and locations, along with travel time variations between locations due to traffic conditions. However, most existing cohesive subgraph-based community search studies utilize a single attribute, either keywords or locations, to identify communities. They do not simultaneously consider both keywords and locations, which results in low semantic or spatial cohesiveness of the detected communities, and they fail to account for variations in travel time. Additionally, these studies traverse the entire network to build efficient indexes, but the detected community only involves nodes around the query node, leading to the traversal of nodes that are not relevant to the community. Therefore, we propose the problem of discovering semantic-spatial aware k-core, which refers to a k-core with high semantic and time-dependent spatial cohesiveness containing the query node. To address this problem, we propose an exact and a greedy algorithm, both of which gradually expand outward from the query node. They are local methods that only access the local part of the attributed network near the query node rather than the entire network. Moreover, we design a method to calculate the semantic similarity between two keywords using large language models. This method alleviates the disadvantages of keyword-matching methods used in existing community search studies, such as mismatches caused by differently expressed synonyms and the presence of irrelevant words. Experimental results show that the greedy algorithm outperforms baselines in terms of structural, semantic, and time-dependent spatial cohesiveness.

cs.SI↗

arXiv2025

Community and hyperedge inference in multiple hypergraphs

Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding relationship between genes and their protein products, drive the establishment of interconnections between multiple hypergraphs. Here, we demonstrate how to utilize those interconnections between multiple hypergraphs to synthesize integrated information from multiple higher-order systems, thereby enhancing understanding of underlying structures. We propose a model based on the stochastic block model, which integrates information from multiple hypergraphs to reveal latent high-order structures. Real-world hyperedges exhibit preferential attachment, where certain nodes dominate hyperedge formation. To characterize this phenomenon, our model introduces hyperedge internal degree to quantify nodes' contributions to hyperedge formation. This model is capable of mining communities, predicting missing hyperedges of arbitrary sizes within hypergraphs, and inferring inter-hypergraph edges between hypergraphs. We apply our model to high-order datasets to evaluate its performance. Experimental results demonstrate strong performance of our model in community detection, hyperedge prediction, and inter-hypergraph edge prediction tasks. Moreover, we show that our model enables analysis of multiple hypergraphs of different types and supports the analysis of a single hypergraph in the absence of inter-hypergraph edges. Our work provides a practical and flexible tool for analyzing multiple hypergraphs, greatly advancing the understanding of the organization in real-world high-order systems.

cs.SI↗

arXiv2025

A function space approach to the shape optimization of the Boussinesq system

We investigate a shape optimization problem for a heat-conducting fluid governed by a Boussinesq system. The main goal is to determine an optimal domain shape that yields a temperature distribution as uniform as possible. Initially, we analyze the state problem, prove its well-posedness and establish a local boundary regularity result for the weak solution. We then demonstrate the existence of an optimal shape and derive a first-order optimality condition. This requires the derivation and analysis of the adjoint system associated with the Boussinesq model, as well as a rigorous treatment of the directional derivatives of the objective functional under appropriate domain perturbations. Finally, we present numerical experiments that illustrate and support the theoretical findings.

math.AP↗

arXiv2024

ComGPT: Detecting Local Community Structure with Large Language Models

Large Language Models (LLMs), like GPT-3.5-turbo, have demonstrated the ability to understand graph structures and have achieved excellent performance in various graph reasoning tasks, such as node classification. Despite their strong abilities in graph reasoning tasks, they lack specific domain knowledge and have a weaker understanding of community-related graph information, which hinders their capabilities in the community detection task. Moreover, local community detection algorithms based on seed expansion, referred to as seed expansion algorithms, often face several shortcomings, including the seed-dependent problem, community diffusion, and free rider effect. To use LLMs to overcome the above shortcomings, we explore a GPT-guided seed expansion algorithm named ComGPT. ComGPT iteratively selects potential nodes by local modularity from the detected community's neighbors, and subsequently employs LLMs to choose the node from these selected potential nodes to join the detected community. To improve LLMs' understanding of community-related graph information, we propose ComIncident, a graph encoding method that incorporates community knowledge and is designed for the community detection task. Additionally, we design the Node Selection Guide (NSG) prompt to enhance LLMs' understanding of community characteristics. Experimental results demonstrate that ComGPT outperforms the baselines, thereby confirming the effectiveness of the ComIncident and the NSG prompt.

cs.SI↗

arXiv2024

Tree-based Ensemble Learning for Out-of-distribution Detection

Being able to successfully determine whether the testing samples has similar distribution as the training samples is a fundamental question to address before we can safely deploy most of the machine learning models into practice. In this paper, we propose TOOD detection, a simple yet effective tree-based out-of-distribution (TOOD) detection mechanism to determine if a set of unseen samples will have similar distribution as of the training samples. The TOOD detection mechanism is based on computing pairwise hamming distance of testing samples' tree embeddings, which are obtained by fitting a tree-based ensemble model through in-distribution training samples. Our approach is interpretable and robust for its tree-based nature. Furthermore, our approach is efficient, flexible to various machine learning tasks, and can be easily generalized to unsupervised setting. Extensive experiments are conducted to show the proposed method outperforms other state-of-the-art out-of-distribution detection methods in distinguishing the in-distribution from out-of-distribution on various tabular, image, and text data.

cs.LG↗