arXiv subjects

Xianlin Zeng

Publications and source records attributed to Xianlin Zeng.

At least 19 recordsLinked to original sources

arXiv2026

A unified framework for imitation dynamics on higher-order networks

Cooperation is central to human societies and often unfolds within groups. Higher-order networks, such as hypergraphs, naturally represent these groups as hyperedges. Network structures and update rules, by which individuals revise their strategies, are the two fundamental components that shape the evolution of cooperation in structured populations. Yet while the effects of network structure have been studied extensively, update rules have been examined mostly through isolated models, leaving their relationships and the origins of their differing evolutionary outcomes poorly understood. Here we develop a unified framework for imitation dynamics on higher-order networks, parameterizing imitation-based update rules by the number of groups an individual samples and the number of peers consulted within each group. Under weak selection, we derive a closed-form condition for the success of cooperation in any multiplayer social dilemma on homogeneous hypergraphs, encompassing games with both linear and nonlinear payoff structures. The framework places previously disconnected update rules within a single family and reduces their effects on cooperation to one interpretable quantity, which we term information diversity. Update rules inducing higher information diversity promote cooperation more effectively, and we prove that this ordering holds strictly across the entire space of multiplayer social dilemmas. Simulations extend this principle to heterogeneous hypergraphs constructed both synthetically and from empirical data. Our framework provides a systematic way to represent, analyze, and compare update rules on higher-order networks, turning a fragmented collection of microscopic updating mechanisms into a tractable and interpretable theory.

physics.soc-ph↗

arXiv2026

ERAlign: Energy-based Representation Alignment of GNNs and LLMs on Text-attributed Graphs

Text-attributed Graphs (TAGs) incorporate textual node attributes with graph structures to describe rich relational semantics. Recent efforts to integrate Graph Neural Networks (GNNs) and Large Language Models (LLMs) have shown promise for learning on TAGs, yet achieving well-aligned representations remains challenging. Prior studies largely rely on heuristics that perform coarse-grained matching. They lack sufficient constraints and ignore distributional alignment, leading to representation drift and limited generalization. Building on Energy-based Models (EBMs), we propose an Energy-based Representation Alignment (ERAlign) framework that projects GNN-encoded graph structure and LLM-derived text embeddings in a shared latent space to achieve distribution consistency. Concretely, layer-wise alignment is quantified by a distance metric and optimized via an EBM objective. By decreasing energy values, our framework yields well-aligned representations for downstream tasks. During training, we introduce Energy Discrepancy (ED) to avoid high sampling costs associated with intractable normalization. ED also carries theoretical guarantees of higher training efficiency and reduced energy landscape distortion. Empirical evaluations on eight TAG datasets demonstrate that ERAlign obtains state-of-the-art performance across varying levels of supervision and cross-task transfer scenarios.

cs.LG↗

arXiv2025

Graph Structure Refinement with Energy-based Contrastive Learning

Graph Neural Networks (GNNs) have recently gained widespread attention as a successful tool for analyzing graph-structured data. However, imperfect graph structure with noisy links lacks enough robustness and may damage graph representations, therefore limiting the GNNs' performance in practical tasks. Moreover, existing generative architectures fail to fit discriminative graph-related tasks. To tackle these issues, we introduce an unsupervised method based on a joint of generative training and discriminative training to learn graph structure and representation, aiming to improve the discriminative performance of generative models. We propose an Energy-based Contrastive Learning (ECL) guided Graph Structure Refinement (GSR) framework, denoted as ECL-GSR. To our knowledge, this is the first work to combine energy-based models with contrastive learning for GSR. Specifically, we leverage ECL to approximate the joint distribution of sample pairs, which increases the similarity between representations of positive pairs while reducing the similarity between negative ones. Refined structure is produced by augmenting and removing edges according to the similarity metrics among node representations. Extensive experiments demonstrate that ECL-GSR outperforms the state-of-the-art on eight benchmark datasets in node classification. ECL-GSR achieves faster training with fewer samples and memories against the leading baseline, highlighting its simplicity and efficiency in downstream tasks.

cs.LG↗

arXiv2024

Primal-dual Accelerated Mirror-Descent Method for Constrained Bilinear Saddle-Point Problems

We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent dynamics. It deals with constraints such as simplices and convex set constraints effectively, and converges with a rate of $O(1/t^2)$. Furthermore, we employ the acceleration scheme to constrained distributed optimization and bilinear zero-sum games, and obtain two variants of distributed accelerated algorithms.

math.OC↗

arXiv2024

BiPFT: Binary Pre-trained Foundation Transformer with Low-rank Estimation of Binarization Residual Polynomials

Pretrained foundation models offer substantial benefits for a wide range of downstream tasks, which can be one of the most potential techniques to access artificial general intelligence. However, scaling up foundation transformers for maximal task-agnostic knowledge has brought about computational challenges, especially on resource-limited devices such as mobiles. This work proposes the first Binary Pretrained Foundation Transformer (BiPFT) for natural language understanding (NLU) tasks, which remarkably saves 56 times operations and 28 times memory. In contrast to previous task-specific binary transformers, BiPFT exhibits a substantial enhancement in the learning capabilities of binary neural networks (BNNs), promoting BNNs into the era of pre-training. Benefiting from extensive pretraining data, we further propose a data-driven binarization method. Specifically, we first analyze the binarization error in self-attention operations and derive the polynomials of binarization error. To simulate full-precision self-attention, we define binarization error as binarization residual polynomials, and then introduce low-rank estimators to model these polynomials. Extensive experiments validate the effectiveness of BiPFTs, surpassing task-specific baseline by 15.4% average performance on the GLUE benchmark. BiPFT also demonstrates improved robustness to hyperparameter changes, improved optimization efficiency, and reduced reliance on downstream distillation, which consequently generalize on various NLU tasks and simplify the downstream pipeline of BNNs. Our code and pretrained models are publicly available at https://github.com/Xingrun-Xing/BiPFT.

cs.LG↗

arXiv2023

An Approach for Multi-Object Tracking with Two-Stage Min-Cost Flow

The minimum network flow algorithm is widely used in multi-target tracking. However, the majority of the present methods concentrate exclusively on minimizing cost functions whose values may not indicate accurate solutions under occlusions. In this paper, by exploiting the properties of tracklets intersections and low-confidence detections, we develop a two-stage tracking pipeline with an intersection mask that can accurately locate inaccurate tracklets which are corrected in the second stage. Specifically, we employ the minimum network flow algorithm with high-confidence detections as input in the first stage to obtain the candidate tracklets that need correction. Then we leverage the intersection mask to accurately locate the inaccurate parts of candidate tracklets. The second stage utilizes low-confidence detections that may be attributed to occlusions for correcting inaccurate tracklets. This process constructs a graph of nodes in inaccurate tracklets and low-confidence nodes and uses it for the second round of minimum network flow calculation. We perform sufficient experiments on popular MOT benchmark datasets and achieve 78.4 MOTA on the test set of MOT16, 79.2 on MOT17, and 76.4 on MOT20, which shows that the proposed method is effective.

cs.CV↗

arXiv2022

Distributed Event-Triggered Algorithm for Convex Optimization with Coupled Constraints

This paper develops a distributed primal-dual algorithm via event-triggered mechanism to solve a class of convex optimization problems subject to local set constraints, coupled equality and inequality constraints. Different from some existing distributed algorithms with the diminishing step-sizes, our algorithm uses the constant step-sizes, and is shown to achieve an exact convergence to an optimal solution with an $O(1/k)$ convergence rate for general convex objective functions, where $k>0$ is the iteration number. Moreover, by applying event-triggered communication mechanism, the proposed algorithm can effectively reduce the communication cost without sacrificing the convergence rate. Finally, a numerical example is presented to verify the effectiveness of the proposed algorithm.

math.OC↗

arXiv2022

Distributed stochastic proximal algorithm with random reshuffling for non-smooth finite-sum optimization

The non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying multi-agent networks. The objective function is a sum of differentiable convex functions and non-smooth regularization. Each agent in the network updates local variables with a constant step-size by local information and cooperates to seek an optimal solution. We prove that local variable estimates generated by the proposed algorithm achieve consensus and are attracted to a neighborhood of the optimal solution in expectation with an $\mathcal{O}(\frac{1}{T}+\frac{1}{\sqrt{T}})$ convergence rate, where $T$ is the total number of iterations. Finally, some comparative simulations are provided to verify the convergence performance of the proposed algorithm.

math.OC↗

arXiv2022

Distributed Momentum-based Frank-Wolfe Algorithm for Stochastic Optimization

This paper considers distributed stochastic optimization, in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network. Stochastic optimization problems are usually tackled by variants of projected stochastic gradient descent. However, projecting a point onto a feasible set is often expensive. The Frank-Wolfe (FW) method has well-documented merits in handling convex constraints, but existing stochastic FW algorithms are basically developed for centralized settings. In this context, the present work puts forth a distributed stochastic Frank-Wolfe solver, by judiciously combining Nesterov's momentum and gradient tracking techniques for stochastic convex and nonconvex optimization over networks. It is shown that the convergence rate of the proposed algorithm is $\mathcal{O}(k^{-\frac{1}{2}})$ for convex optimization, and $\mathcal{O}(1/\mathrm{log}_2(k))$ for nonconvex optimization. The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.

math.OC↗

arXiv2022

Distributed stochastic projection-free solver for constrained optimization

This paper proposes a distributed stochastic projection-free algorithm for large-scale constrained finite-sum optimization whose constraint set is complicated such that the projection onto the constraint set can be expensive. The global cost function is allocated to multiple agents, each of which computes its local stochastic gradients and communicates with its neighbors to solve the global problem. Stochastic gradient methods enable low computational cost, while they are hard and slow to converge due to the variance caused by random sampling. To construct a convergent distributed stochastic projection-free algorithm, this paper incorporates a variance reduction technique and gradient tracking technique in the Frank-Wolfe update. We develop a sampling rule for the variance reduction technique to reduce the variance introduced by stochastic gradients. Complete and rigorous proofs show that the proposed distributed projection-free algorithm converges with a sublinear convergence rate and enjoys superior complexity guarantees for both convex and non-convex objective functions. By comparative simulations, we demonstrate the convergence and computational efficiency of the proposed algorithm.

math.OC↗

arXiv2022

Dynamical Primal-Dual Accelerated Method with Applications to Network Optimization

This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in the proposed method and prove that the rate of convergence in terms of the duality gap function is $O(\tfrac{1}{t^2})$ by choosing suitable parameters. As far as we know, this is the first continuous-time primal-dual accelerated method that can obtain the optimal rate. Then this work applies the proposed method to two network optimization problems, a distributed optimization problem with consensus constraints and a distributed extended monotropic optimization problem, and obtains two variant distributed algorithms. Finally, numerical simulations are given to demonstrate the efficacy of the proposed method.

math.OC↗

arXiv2021

A Hierarchical Spatio-Temporal Graph Convolutional Neural Network for Anomaly Detection in Videos

Deep learning models have been widely used for anomaly detection in surveillance videos. Typical models are equipped with the capability to reconstruct normal videos and evaluate the reconstruction errors on anomalous videos to indicate the extent of abnormalities. However, existing approaches suffer from two disadvantages. Firstly, they can only encode the movements of each identity independently, without considering the interactions among identities which may also indicate anomalies. Secondly, they leverage inflexible models whose structures are fixed under different scenes, this configuration disables the understanding of scenes. In this paper, we propose a Hierarchical Spatio-Temporal Graph Convolutional Neural Network (HSTGCNN) to address these problems, the HSTGCNN is composed of multiple branches that correspond to different levels of graph representations. High-level graph representations encode the trajectories of people and the interactions among multiple identities while low-level graph representations encode the local body postures of each person. Furthermore, we propose to weightedly combine multiple branches that are better at different scenes. An improvement over single-level graph representations is achieved in this way. An understanding of scenes is achieved and serves anomaly detection. High-level graph representations are assigned higher weights to encode moving speed and directions of people in low-resolution videos while low-level graph representations are assigned higher weights to encode human skeletons in high-resolution videos. Experimental results show that the proposed HSTGCNN significantly outperforms current state-of-the-art models on four benchmark datasets (UCSD Pedestrian, ShanghaiTech, CUHK Avenue and IITB-Corridor) by using much less learnable parameters.

cs.CV↗

arXiv2021

Distributed stochastic gradient tracking algorithm with variance reduction for non-convex optimization

This paper proposes a distributed stochastic algorithm with variance reduction for general smooth non-convex finite-sum optimization, which has wide applications in signal processing and machine learning communities. In distributed setting, large number of samples are allocated to multiple agents in the network. Each agent computes local stochastic gradient and communicates with its neighbors to seek for the global optimum. In this paper, we develop a modified variance reduction technique to deal with the variance introduced by stochastic gradients. Combining gradient tracking and variance reduction techniques, this paper proposes a distributed stochastic algorithm, GT-VR, to solve large-scale non-convex finite-sum optimization over multi-agent networks. A complete and rigorous proof shows that the GT-VR algorithm converges to first-order stationary points with $O(\frac{1}{k})$ convergence rate. In addition, we provide the complexity analysis of the proposed algorithm. Compared with some existing first-order methods, the proposed algorithm has a lower $\mathcal{O}(PMε^{-1})$ gradient complexity under some mild condition. By comparing state-of-the-art algorithms and GT-VR in experimental simulations, we verify the efficiency of the proposed algorithm.

math.OC↗

arXiv2021

Distributed synchronous and asynchronous algorithms for semi-definite programming with diagonal constraints

This paper develops distributed synchronous and asynchronous algorithms for the large-scale semi-definite programming with diagonal constraints, which has wide applications in combination optimization, image processing and community detection. The information of the semi-definite programming is allocated to multiple interconnected agents such that each agent aims to find a solution by communicating to its neighbors. Based on low-rank property of solutions and the Burer-Monteiro factorization, we transform the original problem into a distributed optimization problem over unit spheres to reduce variable dimensions and ensure positive semi-definiteness without involving semi-definite projections, which are computationally expensive. For the distributed optimization problem, we propose distributed synchronous and asynchronous algorithms, both of which reduce computational burden and storage space compared with existing centralized algorithms. Specifically, the distributed synchronous algorithm almost surely escapes strict saddle points and converges to the set of optimal solutions to the optimization problem. In addition, the proposed distributed asynchronous algorithm allows communication delays and converges to the set of critical points to the optimization problem under mild conditions. By applying proposed algorithms to image segmentation applications, we illustrate the efficiency and convergence performance of the two proposed algorithms.

math.OC↗

arXiv2021

Distributed proximal gradient algorithm for non-smooth non-convex optimization over time-varying networks

This note studies the distributed non-convex optimization problem with non-smooth regularization, which has wide applications in decentralized learning, estimation and control. The objective function is the sum of different local objective functions, which consist of differentiable (possibly non-convex) cost functions and non-smooth convex functions. This paper presents a distributed proximal gradient algorithm for the non-smooth non-convex optimization problem over time-varying multi-agent networks. Each agent updates local variable estimate by the multi-step consensus operator and the proximal operator. We prove that the generated local variables achieve consensus and converge to the set of critical points with convergence rate $O(1/T)$. Finally, we verify the efficacy of proposed algorithm by numerical simulations.

math.OC↗

arXiv2020

Solving A Class of Nonsmooth Resource Allocation Problems with Directed Graphs though Distributed Smooth Multi-Proximal Algorithms

In this paper, two distributed multi-proximal primal-dual algorithms are proposed to deal with a class of distributed nonsmooth resource allocation problems. In these problems, the global cost function is the summation of local convex and nonsmooth cost functions, each of which consists of one twice differentiable function and multiple nonsmooth functions. Communication graphs of underling multi-agent systems are directed and strongly connected but not necessarily weighted-balanced. The multi-proximal splitting is designed to deal with the difficulty caused by the unproximable property of the summation of those nonsmooth functions. Moreover, it can also guarantee the smoothness of proposed algorithms. Auxiliary variables in the multi-proximal splitting are introduced to estimate subgradients of nonsmooth functions. Theoretically, the convergence analysis is conducted by employing Lyapunov stability theory and integral input-to-state stability (iISS) theory with respect to set. It shows that proposed algorithms can make states converge to the optimal point that satisfies resource allocation conditions.

math.OC↗

arXiv2020

Distributed sub-optimal resource allocation via a projected form of singular perturbation

Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is applicable to weight-balanced graphs. Moreover, it can deal with both local set constraints and coupled inequality constraints, and remove the requirement of twice differentiability of the cost function in comparison with the existing sub-optimal algorithm. However, this algorithm is not easy to be analyzed since it involves singular perturbation type dynamics with projected non-differentiable right-hand side. We overcome the encountered difficulties and obtain results including the existence of an equilibrium, the sub-optimality, and the convergence of the algorithm.

math.OC↗

arXiv2020

Exponentially Convergent Algorithm Design for Constrained Distributed Optimization via Non-smooth Approach

We consider minimizing a sum of non-smooth objective functions with set constraints in a distributed manner. As to this problem, we propose a distributed algorithm with an exponential convergence rate for the first time. By the exact penalty method, we reformulate the problem equivalently as a standard distributed one without consensus constraints. Then we design a distributed projected subgradient algorithm with the help of differential inclusions. Furthermore, we show that the algorithm converges to the optimal solution exponentially for strongly convex objective functions.

math.OC↗