Linyuan Lü

Yiming Huang, Yujie Zeng, Qiang Wu et al.

Despite the recent successes of vanilla Graph Neural Networks (GNNs) on various tasks, their foundation on pairwise networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs. Codes and datasets are available at https://github.com/Yiminghh/HiGCN.

Min Tang, Fanqi Kong, Linyuan Lü et al.

Mixed-motive scenarios are ubiquitous in real-world multi-agent interactions, where self-interested agents often defect for immediate rewards, overlooking the potential of altruistic cooperation to improve long-term gains and collective welfare. Peer punishment can deter defection, but as costly second-order altruism, its persistent imposition may undermine the punisher's interests. Existing approaches often struggle to effectively implement punishment to promote cooperation. To balance the efficacy and cost of punishment, we propose Adaptive Punishment for Cooperation (APC), a distributed method that determines punishment intensity based on both a dynamic punishment probability and the severity of defection. This dynamic probability substantially reduces costly and ineffective punishment while also promotes cooperation. To accurately assess defection and its severity, we use a defection awareness module, whose learning is guided by game reward. Theoretical analysis and empirical results show APC performs effectively in iterated public goods game. Empirically, APC also significantly outperforms existing baselines across sequential social dilemmas, learning rational and effective punishment policies that foster cooperation by strategically deterring defection.

Yujie Zeng, Yiming Huang, Qiang Wu et al.

Simplicial complexes have recently been in the limelight of higher-order network analysis, where a minority of simplices play crucial roles in structures and functions due to network heterogeneity. We find a significant inconsistency between identifying influential nodes and simplices. Therefore, it remains elusive how to characterize simplices' influence and identify influential simplices, despite the relative maturity of research on influential nodes (0-simplices) identification. Meanwhile, graph neural networks (GNNs) are potent tools that can exploit network topology and node features simultaneously, but they struggle to tackle higher-order tasks. In this paper, we propose a higher-order graph learning model, named influential simplices mining neural network (ISMnet), to identify vital h-simplices in simplicial complexes. It can tackle higher-order tasks by leveraging novel higher-order presentations: hierarchical bipartite graphs and higher-order hierarchical (HoH) Laplacians, where targeted simplices are grouped into a hub set and can interact with other simplices. Furthermore, ISMnet employs learnable graph convolutional operators in each HoH Laplacian domain to capture interactions among simplices, and it can identify influential simplices of arbitrary order by changing the hub set. Empirical results demonstrate that ISMnet significantly outperforms existing methods in ranking 0-simplices (nodes) and 2-simplices. In general, this novel framework excels in identifying influential simplices and promises to serve as a potent tool in higher-order network analysis.

Rui Sun, Jie Ding, Chenghua Gong et al.

Optimizing communication topology in LLM-based multi-agent system is critical for enabling collective intelligence. Existing methods mainly rely on spatio-temporal interaction paradigms, where the sequential execution of multi-round dialogues incurs high latency and computation. Motivated by the recent insights that evaluation and debate mechanisms can improve problem-solving in multi-agent systems, we propose TopoDIM, a framework for one-shot Topology generation with Diverse Interaction Modes. Designed for decentralized execution to enhance adaptability and privacy, TopoDIM enables agents to autonomously construct heterogeneous communication without iterative coordination, achieving token efficiency and improved task performance. Experiments demonstrate that TopoDIM reduces total token consumption by 46.41% while improving average performance by 1.50% over state-of-the-art methods. Moreover, the framework exhibits strong adaptability in organizing communication among heterogeneous agents. Code is available at: https://anonymous.4open.science/r/TopoDIM-8D35/

Rui Sun, Chenghua Gong, Tianjun Gu et al.

Advancing epidemic dynamics forecasting is vital for targeted interventions and safeguarding public health. Current approaches mainly fall into two categories: mechanism-based and data-driven models. Mechanism-based models are constrained by predefined compartmental structures and oversimplified system assumptions, limiting their ability to model complex real-world dynamics, while data-driven models focus solely on intrinsic data dependencies without physical or epidemiological constraints, risking biased or misleading representations. Although recent studies have attempted to integrate epidemiological knowledge into neural architectures, most of them fail to reconcile explicit physical priors with neural representations. To overcome these obstacles, we introduce Epi$^2$-Net, a Epidemic Forecasting Framework built upon Physics-Inspired Neural Networks. Specifically, we propose reconceptualizing epidemic transmission from the physical transport perspective, introducing the concept of neural epidemic transport. Further, we present a physic-inspired deep learning framework, and integrate physical constraints with neural modules to model spatio-temporal patterns of epidemic dynamics. Experiments on real-world datasets have demonstrated that Epi$^2$-Net outperforms state-of-the-art methods in epidemic forecasting, providing a promising solution for future epidemic containment. The code is available at: https://anonymous.4open.science/r/Epi-2-Net-48CE.

Qiang Wu, Yiming Huang, Yujie Zeng et al.

Graph research, the systematic study of interconnected data points represented as graphs, plays a vital role in capturing intricate relationships within networked systems. However, in the real world, as graphs scale up, concerns about data security among different data-owning agencies arise, hindering information sharing and, ultimately, the utilization of graph data. Therefore, establishing a mutual trust mechanism among graph agencies is crucial for unlocking the full potential of graphs. Here, we introduce a Cooperative Network Learning (CNL) framework to ensure secure graph computing for various graph tasks. Essentially, this CNL framework unifies the local and global perspectives of GNN computing with distributed data for an agency by virtually connecting all participating agencies as a global graph without a fixed central coordinator. Inter-agency computing is protected by various technologies inherent in our framework, including homomorphic encryption and secure transmission. Moreover, each agency has a fair right to design or employ various graph learning models from its local or global perspective. Thus, CNL can collaboratively train GNN models based on decentralized graphs inferred from local and global graphs. Experiments on contagion dynamics prediction and traditional graph tasks (i.e., node classification and link prediction) demonstrate that our CNL architecture outperforms state-of-the-art GNNs developed at individual sites, revealing that CNL can provide a reliable, fair, secure, privacy-preserving, and global perspective to build effective and personalized models for network applications. We hope this framework will address privacy concerns in graph-related research and integrate decentralized graph data structures to benefit the network research community in cooperation and innovation.

Xiaoxiao Liang, Juyuan Zhang, Liming Pan et al.

Inferring latent interaction structures from observed dynamics is a fundamental inverse problem in many-body interacting systems. Most neural approaches rely on black-box surrogates over trainable graphs, achieving accuracy at the expense of mechanistic interpretability. Symbolic regression offers explicit dynamical equations and stronger inductive biases, but typically assumes known topology and a fixed function library. We propose \textbf{COSINE} (\textbf{C}o-\textbf{O}ptimization of \textbf{S}ymbolic \textbf{I}nteractions and \textbf{N}etwork \textbf{E}dges), a differentiable framework that jointly discovers interaction graphs and sparse symbolic dynamics. To overcome the limitations of fixed symbolic libraries, COSINE further incorporates an outer-loop large language model that adaptively prunes and expands the hypothesis space using feedback from the inner optimization loop. Experiments on synthetic systems and large-scale real-world epidemic data demonstrate robust structural recovery and compact, mechanism-aligned dynamical expressions. Code: https://anonymous.4open.science/r/COSINE-6D43.

Chenghua Gong, Yihang Jiang, Hao Li et al.

Advanced opinion dynamics modeling is vital for deciphering social behavior, emphasizing its role in mitigating polarization and securing cyberspace. To synergize mechanistic interpretability with data-driven flexibility, recent studies have explored the integration of Physics-Informed Neural Networks (PINNs) for opinion modeling. Despite this promise, existing methods are tailored to incomplete priors, lacking a comprehensive physical system to integrate dynamics from local, global, and endogenous levels. Moreover, penalty-based constraints adopted in existing methods struggle to deeply encode physical priors, leading to optimization pathologies and discrepancy between latent representations and physical transparency. To this end, we offer a physical view to interpret opinion dynamics via Diffusion-Convection-Reaction (DCR) system inspired by interacting particle theory. Building upon the Neural ODEs, we define the neural opinion dynamics to coordinate neural networks with physical priors, and further present the OPINN, a physics-informed neural framework for opinion dynamics modeling. Evaluated on real-world and synthetic datasets, OPINN achieves state-of-the-art performance in opinion evolution forecasting, offering a promising paradigm for the nexus of cyber, physical, and social systems.

Jiayu Weng, Xinyi Zhu, Jing Liu et al.

Chemical reaction networks are widely used to model stochastic dynamics in chemical kinetics, systems biology and epidemiology. Solving the chemical master equation that governs these systems poses a significant challenge due to the large state space exponentially growing with system sizes. The development of autoregressive neural networks offers a flexible framework for this problem; however, its efficiency is limited especially for high-dimensional systems and in scenarios with rare events. Here, we push the frontier of neural-network approach by exploiting faster optimizations such as natural gradient descent and time-dependent variational principle, achieving a 5- to 22-fold speedup, and by leveraging enhanced-sampling strategies to capture rare events. We demonstrate reduced computational cost and higher accuracy over the previous neural-network method in challenging reaction networks, including the mitogen-activated protein kinase (MAPK) cascade network, the hitherto largest biological network handled by the previous approaches of solving the chemical master equation. We further apply the approach to spatially extended reaction-diffusion systems, the Schlögl model with rare events, on two-dimensional lattices, beyond the recent tensor-network approach that handles one-dimensional lattices. The present approach thus enables efficient modeling of chemical reaction networks in general.

Liang Zhang, Qiang Wu, Jun Shen et al.

Many studies confirmed that a proper traffic state representation is more important than complex algorithms for the classical traffic signal control (TSC) problem. In this paper, we (1) present a novel, flexible and efficient method, namely advanced max pressure (Advanced-MP), taking both running and queuing vehicles into consideration to decide whether to change current signal phase; (2) inventively design the traffic movement representation with the efficient pressure and effective running vehicles from Advanced-MP, namely advanced traffic state (ATS); and (3) develop a reinforcement learning (RL) based algorithm template, called Advanced-XLight, by combining ATS with the latest RL approaches, and generate two RL algorithms, namely "Advanced-MPLight" and "Advanced-CoLight" from Advanced-XLight. Comprehensive experiments on multiple real-world datasets show that: (1) the Advanced-MP outperforms baseline methods, and it is also efficient and reliable for deployment; and (2) Advanced-MPLight and Advanced-CoLight can achieve the state-of-the-art.

Qiang Wu, Liang Zhang, Jun Shen et al.

Since conventional approaches could not adapt to dynamic traffic conditions, reinforcement learning (RL) has attracted more attention to help solve the traffic signal control (TSC) problem. However, existing RL-based methods are rarely deployed considering that they are neither cost-effective in terms of computing resources nor more robust than traditional approaches, which raises a critical research question: how to construct an adaptive controller for TSC with less training and reduced complexity based on RL-based approach? To address this question, in this paper, we (1) innovatively specify the traffic movement representation as a simple but efficient pressure of vehicle queues in a traffic network, namely efficient pressure (EP); (2) build a traffic signal settings protocol, including phase duration, signal phase number and EP for TSC; (3) design a TSC approach based on the traditional max pressure (MP) approach, namely efficient max pressure (Efficient-MP) using the EP to capture the traffic state; and (4) develop a general RL-based TSC algorithm template: efficient Xlight (Efficient-XLight) under EP. Through comprehensive experiments on multiple real-world datasets in our traffic signal settings' protocol for TSC, we demonstrate that efficient pressure is complementary to traditional and RL-based modeling to design better TSC methods. Our code is released on Github.

Hao Wang, Yue Deng, Linyuan Lü et al.

Graphs can be used to describe complex systems. Recently, whole graph embedding (graph representation learning) can compress a graph into a compact lower-dimension vector while preserving intrinsic properties, earning much attention. However, most graph embedding methods have problems such as tedious parameter tuning or poor explanation. This paper presents a simple and hyperparameter-free whole graph embedding method based on the DHC (Degree, H-index, and Coreness) theorem and Shannon Entropy (E), abbreviated as DHC-E. The DHC-E can provide a trade-off between simplicity and quality for supervised classification learning tasks involving molecular, social, and brain networks. Moreover, it performs well in lower-dimensional graph visualization. Overall, the DHC-E is simple, hyperparameter-free, and explainable for whole graph embedding with promising potential for exploring graph classification and lower-dimensional graph visualization.

Shuqi Xu, Manuel Sebastian Mariani, Linyuan Lü et al.

Despite the increasing use of citation-based metrics for research evaluation purposes, we do not know yet which metrics best deliver on their promise to gauge the significance of a scientific paper or a patent. We assess 17 network-based metrics by their ability to identify milestone papers and patents in three large citation datasets. We find that traditional information-retrieval evaluation metrics are strongly affected by the interplay between the age distribution of the milestone items and age biases of the evaluated metrics. Outcomes of these metrics are therefore not representative of the metrics' ranking ability. We argue in favor of a modified evaluation procedure that explicitly penalizes biased metrics and allows us to reveal metrics' performance patterns that are consistent across the datasets. PageRank and LeaderRank turn out to be the best-performing ranking metrics when their age bias is suppressed by a simple transformation of the scores that they produce, whereas other popular metrics, including citation count, HITS and Collective Influence, produce significantly worse ranking results.

Shilun Zhang, Matúš Medo, Linyuan Lü et al.

When we search online for content, we are constantly exposed to rankings. For example, web search results are presented as a ranking, and online bookstores often show us lists of best-selling books. While popularity-based ranking algorithms (like Google's PageRank) have been extensively studied in previous works, we still lack a clear understanding of their potential systemic consequences. In this work, we fill this gap by introducing a new model of network growth that allows us to compare the properties of the networks generated under the influence of different ranking algorithms. We show that by correcting for the omnipresent age bias of popularity-based ranking algorithms, the resulting networks exhibit a significantly larger agreement between the nodes' inherent quality and their long-term popularity, and a less concentrated popularity distribution. To further promote popularity diversity, we introduce and validate a perturbation of the original rankings where a small number of randomly-selected nodes are promoted to the top of the ranking. Our findings move the first steps toward a model-based understanding of the long-term impact of popularity-based ranking algorithms, and could be used as an informative tool for the design of improved information filtering tools.

Leilei Wu, Zhuoming Ren, Xiao-Long Ren et al.

The ongoing rapid development of the e-commercial and interest-base websites make it more pressing to evaluate objects' accurate quality before recommendation by employing an effective reputation system. The objects' quality are often calculated based on their historical information, such as selected records or rating scores, to help visitors to make decisions before watching, reading or buying. Usually high quality products obtain a higher average ratings than low quality products regardless of rating biases or errors. However many empirical cases demonstrate that consumers may be misled by rating scores added by unreliable users or deliberate tampering. In this case, users' reputation, i.e., the ability to rating trustily and precisely, make a big difference during the evaluating process. Thus, one of the main challenges in designing reputation systems is eliminating the effects of users' rating bias on the evaluation results. To give an objective evaluation of each user's reputation and uncover an object's intrinsic quality, we propose an iterative balance (IB) method to correct users' rating biases. Experiments on two online video-provided Web sites, namely MovieLens and Netflix datasets, show that the IB method is a highly self-consistent and robust algorithm and it can accurately quantify movies' actual quality and users' stability of rating. Compared with existing methods, the IB method has higher ability to find the "dark horses", i.e., not so popular yet good movies, in the Academy Awards.

Xiaofang Deng, Leilei Wu, Xiaolong Ren et al.

Recommender systems, inferring users' preferences from their historical activities and personal profiles, have been an enormous success in the last several years. Most of the existing works are based on the similarities of users, objects or both that derived from their purchases records in the online shopping platforms. Such approaches, however, are facing bottlenecks when the known information is limited. The extreme case is how to recommend products to new users, namely the so-called cold-start problem. The rise of the online social networks gives us a chance to break the glass ceiling. Birds of a feather flock together. Close friends may have similar hidden pattern of selecting products and the advices from friends are more trustworthy. In this paper, we integrate the individual's social relationships into recommender systems and propose a new method, called Social Mass Diffusion (SMD), based on a mass diffusion process in the combined network of users' social network and user-item bipartite network. The results show that the SMD algorithm can achieve higher recommendation accuracy than the Mass Diffusion (MD) purely on the bipartite network. Especially, the improvement is striking for small degree users. Moreover, SMD provides a good solution to the cold-start problem. The recommendation accuracy for new users significantly higher than that of the conventional popularity-based algorithm. These results may shed some light on the new designs of better personalized recommender systems and information services.

Qian-Ming Zhang, Linyuan Lü, Wen-Qiang Wang et al.

Uncovering factors underlying the network formation is a long-standing challenge for data mining and network analysis. In particular, the microscopic organizing principles of directed networks are less understood than those of undirected networks. This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred. Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks. Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. In summary, our main contribution is twofold: (i) We propose a new mechanism for the local organization of directed networks; (ii) We design the corresponding link prediction algorithm, which can not only testify our hypothesis, but also find out direct applications in missing link prediction and friendship recommendation.

Linyuan Lü, Matus Medo, Chi Ho Yeung et al.

The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article, we review recent developments in recommender systems and discuss the major challenges. We compare and evaluate available algorithms and examine their roles in the future developments. In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed. We emphasize that recommendation has a great scientific depth and combines diverse research fields which makes it of interests for physicists as well as interdisciplinary researchers.