Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient method to learn a balanced signed graph Laplacian directly from data. Specifically, extending a previous linear programming (LP) based sparse inverse covariance estimation method called CLIME, we formulate a new LP problem for each Laplacian column $i$, where the linear constraints restrict weight signs of edges stemming from node $i$, so that nodes of same / different polarities are connected by positive / negative edges. Towards optimal model selection, we derive a suitable CLIME parameter $\rho$ based on a combination of the Hannan-Quinn information criterion and a minimum feasibility criterion. We solve the LP problem efficiently by tailoring a sparse LP method based on ADMM. We theoretically prove local solution convergence of our proposed iterative algorithm. Extensive experimental results on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables reuse of spectral filters, wavelets, and graph convolutional nets (GCN) constructed for positive graphs.
Heterogeneous graph neural networks (HGNNs) excel at capturing structural and semantic information in heterogeneous graphs (HGs), while struggling to generalize across domains and tasks. Recently, some researchers have turned to integrating HGNNs with large language models (LLMs) for more generalizable heterogeneous graph learning. However, these approaches typically extract structural information via HGNNs as HG tokens, and disparities in embedding spaces between HGNNs and LLMs have been shown to bias the LLM's comprehension of HGs. Moreover, as these HG tokens are often derived from node-level tasks, the model's ability to generalize across tasks remains limited. To this end, we propose a simple yet effective Masked Language Modeling-based method, called MLM4HG. MLM4HG introduces metapath-based textual sequences instead of HG tokens to extract structural and semantic information inherent in HGs, and designs customized textual templates to unify different graph tasks into a coherent cloze-style "mask" token prediction paradigm. Specifically, MLM4HG first converts HGs from various domains to texts based on metapaths, and subsequently combines them with the unified task texts to form a HG-based corpus. Moreover, the corpus is fed into a pretrained LM for fine-tuning with a constrained target vocabulary, enabling the fine-tuned LM to generalize to unseen target HGs. Extensive cross-domain and multi-task experiments on four real-world datasets demonstrate the superior generalization performance of MLM4HG over state-of-the-art methods in both few-shot and zero-shot scenarios. Our code is available at https://github.com/BUPT-GAMMA/MLM4HG.
Graph neural networks (GNNs) have achieved significant success in graph representation learning and have been applied to various domains. However, many real-world graphs contain sensitive personal information, such as user profiles in social networks, raising serious privacy concerns when graph learning is performed using GNNs. To address this issue, locally private graph learning protocols have gained considerable attention. These protocols leverage the privacy advantages of local differential privacy (LDP) and the effectiveness of GNN's message-passing in calibrating noisy data, offering strict privacy guarantees for users' local data while maintaining high utility (e.g., node classification accuracy) for graph learning. Despite these advantages, such protocols may be vulnerable to data poisoning attacks, a threat that has not been considered in previous research. Identifying and addressing these threats is crucial for ensuring the robustness and security of privacy-preserving graph learning frameworks. This work introduces the first data poisoning attack targeting locally private graph learning protocols. The attacker injects fake users into the protocol, manipulates these fake users to establish links with genuine users, and sends carefully crafted data to the server, ultimately compromising the utility of private graph learning. The effectiveness of the attack is demonstrated both theoretically and empirically. In addition, several defense strategies have also been explored, but their limited effectiveness highlights the need for more robust defenses.
Multi-modal graphs, which integrate diverse multi-modal features and relations, are ubiquitous in real-world applications. However, existing multi-modal graph learning methods are typically trained from scratch for specific graph data and tasks, failing to generalize across various multi-modal graph data and tasks. To bridge this gap, we explore the potential of Multi-modal Graph Large Language Models (MG-LLM) to unify and generalize across diverse multi-modal graph data and tasks. We propose a unified framework of multi-modal graph data, task, and model, discovering the inherent multi-granularity and multi-scale characteristics in multi-modal graphs. Specifically, we present five key desired characteristics for MG-LLM: 1) unified space for multi-modal structures and attributes, 2) capability of handling diverse multi-modal graph tasks, 3) multi-modal graph in-context learning, 4) multi-modal graph interaction with natural language, and 5) multi-modal graph reasoning. We then elaborate on the key challenges, review related works, and highlight promising future research directions towards realizing these ambitious characteristics. Finally, we summarize existing multi-modal graph datasets pertinent for model training. We believe this paper can contribute to the ongoing advancement of the research towards MG-LLM for generalization across multi-modal graph data and tasks.
This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix of the data. The corresponding graph learning problem then scales to the squares of the number of variables (nodes), which is usually problematic at large dimension. To tackle this issue, we propose a graph learning framework that leverages a low-rank factorization of the conditional correlation matrix. In order to solve for the resulting optimization problems, we derive tools required to apply Riemannian optimization techniques for this particular structure. The proposal is then particularized to a low-rank constrained counterpart of the GLasso algorithm, i.e., the penalized maximum likelihood estimation of a Gaussian graphical model. Experiments on synthetic and real data evidence that a very efficient dimension-versus-performance trade-off can be achieved with this approach.
Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in representing and understanding diverse modalities. However, they typically focus on modality alignment in a pairwise manner while overlooking structural relationships across data points. Integrating multimodality with structured graph information (i.e., multimodal graphs, MMGs) is essential for real-world applications such as social networks, healthcare, and recommendation systems. Existing MMG learning methods fall into three paradigms based on how they leverage MLLMs: Encoder, Aligner, and Predictor. MLLM-as-Encoder focuses on enhancing graph neural networks (GNNs) via multimodal feature fusion; MLLM-as-Aligner aligns multimodal attributes in language or hidden space to enable LLM-based graph reasoning; MLLM-as-Predictor treats MLLMs as standalone reasoners with in-context learning or fine-tuning. Despite their advances, the MMG field lacks a unified benchmark to fairly evaluate across these approaches, making it unclear what progress has been made. To bridge this gap, we present Graph-MLLM, a comprehensive benchmark for multimodal graph learning by systematically evaluating these three paradigms across six datasets with different domains. Through extensive experiments, we observe that jointly considering the visual and textual attributes of the nodes benefits graph learning, even when using pre-trained text-to-image alignment models (e.g., CLIP) as encoders. We also find that converting visual attributes into textual descriptions further improves performance compared to directly using visual inputs. Moreover, we observe that fine-tuning MLLMs on specific MMGs can achieve state-of-the-art results in most scenarios, even without explicit graph structure information. We hope that our open-sourced library will facilitate rapid, equitable evaluation and inspire further innovative research in this field.
Graph learning has been crucial to many real-world tasks, but they are often studied with a closed-world assumption, with all possible labels of data known a priori. To enable effective graph learning in an open and noisy environment, it is critical to inform the model users when the model makes a wrong prediction to in-distribution data of a known class, i.e., misclassification detection or when the model encounters out-of-distribution from novel classes, i.e., out-of-distribution detection. This paper introduces Evidential Reasoning Network (EVINET), a framework that addresses these two challenges by integrating Beta embedding within a subjective logic framework. EVINET includes two key modules: Dissonance Reasoning for misclassification detection and Vacuity Reasoning for out-of-distribution detection. Extensive experiments demonstrate that EVINET outperforms state-of-the-art methods across multiple metrics in the tasks of in-distribution classification, misclassification detection, and out-of-distribution detection. EVINET demonstrates the necessity of uncertainty estimation and logical reasoning for misclassification detection and out-of-distribution detection and paves the way for open-world graph learning. Our code and data are available at https://github.com/SSSKJ/EviNET.
The growing interests and applications of graph learning in diverse domains have propelled the development of a unified model generalizing well across different graphs and tasks, known as the Graph Foundation Model (GFM). Existing research has leveraged text-attributed graphs (TAGs) to tackle the heterogeneity in node features among graphs. However, they primarily focus on homogeneous TAGs (HoTAGs), leaving heterogeneous TAGs (HeTAGs), where multiple types of nodes/edges reside, underexplored. To enhance the capabilities and applications of GFM, we introduce H$^2$GFM, a novel framework designed to generalize across both HoTAGs and HeTAGs. Our model projects diverse meta-relations among graphs under a unified textual space, and employs a context encoding to capture spatial and higher-order semantic relationships. To achieve robust node representations, we propose a novel context-adaptive graph transformer (CGT), effectively capturing information from both context neighbors and their relationships. Furthermore, we employ a mixture of CGT experts to capture the heterogeneity in structural patterns among graph types. Comprehensive experiments on a wide range of HoTAGs and HeTAGs as well as learning scenarios demonstrate the effectiveness of our model.
Existing graph benchmarks assume non-spatial, simple edges, collapsing physically distinct paths into a single link. We introduce HSG-12M, the first large-scale dataset of $\textbf{spatial multigraphs}-$graphs embedded in a metric space where multiple geometrically distinct trajectories between two nodes are retained as separate edges. HSG-12M contains 11.6 million static and 5.1 million dynamic $\textit{Hamiltonian spectral graphs}$ across 1401 characteristic-polynomial classes, derived from 177 TB of spectral potential data. Each graph encodes the full geometry of a 1-D crystal's energy spectrum on the complex plane, producing diverse, physics-grounded topologies that transcend conventional node-coordinate datasets. To enable future extensions, we release $\texttt{Poly2Graph}$: a high-performance, open-source pipeline that maps arbitrary 1-D crystal Hamiltonians to spectral graphs. Benchmarks with popular GNNs expose new challenges in learning from multi-edge geometry at scale. Beyond its practical utility, we show that spectral graphs serve as universal topological fingerprints of polynomials, vectors, and matrices, forging a new algebra-to-graph link. HSG-12M lays the groundwork for geometry-aware graph learning and new opportunities of data-driven scientific discovery in condensed matter physics and beyond.
Graph learning models have demonstrated great prowess in learning expressive representations from large-scale graph data in a wide variety of real-world scenarios. As a prevalent strategy for training powerful graph learning models, the "pre-training, adaptation" scheme first pre-trains graph learning models on unlabeled graph data in a self-supervised manner and then adapts them to specific downstream tasks. During the adaptation phase, graph prompting emerges as a promising approach that learns trainable prompts while keeping the pre-trained graph learning models unchanged. In this paper, we present a systematic review of recent advancements in graph prompting. First, we introduce representative graph pre-training methods that serve as the foundation step of graph prompting. Next, we review mainstream techniques in graph prompting and elaborate on how they design learnable prompts for graph prompting. Furthermore, we summarize the real-world applications of graph prompting from different domains. Finally, we discuss several open challenges in existing studies with promising future directions in this field.
Human-Object Interaction (HOI) recognition in videos requires understanding both visual patterns and geometric relationships as they evolve over time. Visual and geometric features offer complementary strengths. Visual features capture appearance context, while geometric features provide structural patterns. Effectively fusing these multimodal features without compromising their unique characteristics remains challenging. We observe that establishing robust, entity-specific representations before modeling interactions helps preserve the strengths of each modality. Therefore, we hypothesize that a bottom-up approach is crucial for effective multimodal fusion. Following this insight, we propose the Geometric Visual Fusion Graph Neural Network (GeoVis-GNN), which uses dual-attention feature fusion combined with interdependent entity graph learning. It progressively builds from entity-specific representations toward high-level interaction understanding. To advance HOI recognition to real-world scenarios, we introduce the Concurrent Partial Interaction Dataset (MPHOI-120). It captures dynamic multi-person interactions involving concurrent actions and partial engagement. This dataset helps address challenges like complex human-object dynamics and mutual occlusions. Extensive experiments demonstrate the effectiveness of our method across various HOI scenarios. These scenarios include two-person interactions, single-person activities, bimanual manipulations, and complex concurrent partial interactions. Our method achieves state-of-the-art performance.
Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social science, and industrial manufacturing, the causal units of interest are groups of variables rather than individual scalar measurements. Motivated by these applications, we extend nonlinear additive noise models to handle random vectors, establishing a two-step approach for causal graph learning: First, infer the causal order among random vectors. Second, perform model selection to identify the best graph consistent with this order. We introduce effective and novel solutions for both steps in the vector case, demonstrating strong performance in simulations. Finally, we apply our method to real-world assembly line data with partial knowledge of causal ordering among variable groups.
The identification of drug-target interactions (DTI) is crucial for drug discovery and repositioning, as it reveals potential uses of existing drugs, aiding in the acceleration of the drug development process and reducing associated costs. Despite the similarity information in DTI is important, most models are limited to mining direct similarity information within homogeneous graphs, overlooking the potential yet rich similarity information in heterogeneous graphs. Inspired by real-world social interaction behaviors, we propose SOC-DGL, which comprises two specialized modules: the Affinity-Driven Graph Learning (ADGL) module and the Equilibrium-Driven Graph Learning (EDGL) module. The ADGL module adopts a comprehensive social interaction strategy, leveraging an affinity-enhanced global drug-target graph to learn both global DTI and the individual similarity information of drugs and targets. In contrast, the EDGL module employs a higher-order social interaction strategy, amplifying the influence of even-hop neighbors through an even-polynomial graph filter grounded in balance theory, enabling the indirect mining of higher-order homogeneous information. This dual approach enables SOC-DGL to effectively and comprehensively capture similarity information across diverse interaction scales within the affinity matrices and drug-target association matrices, significantly enhancing the model's generalization capability and predictive accuracy in DTI tasks. To address the issue of imbalance in drug-target interaction datasets, this paper proposes an adjustable imbalance loss function that mitigates the impact of sample imbalance by adjusting the weight of negative samples and a parameter. Extensive experiments on four benchmark datasets demonstrate significant accuracy improvements achieved by SOC-DGL, particularly in scenarios involving data imbalance and unseen drugs or targets.
Self-supervised topological deep learning (TDL) represents a nascent but underexplored area with significant potential for modeling higher-order interactions in simplicial complexes and cellular complexes to derive representations of unlabeled graphs. Compared to simplicial complexes, cellular complexes exhibit greater expressive power. However, the advancement in self-supervised learning for cellular TDL is largely hindered by two core challenges: \textit{extrinsic structural constraints} inherent to cellular complexes, and intrinsic semantic redundancy in cellular representations. The first challenge highlights that traditional graph augmentation techniques may compromise the integrity of higher-order cellular interactions, while the second underscores that topological redundancy in cellular complexes potentially diminish task-relevant information. To address these issues, we introduce Cellular Complex Contrastive Learning with Adaptive Trimming (CellCLAT), a twofold framework designed to adhere to the combinatorial constraints of cellular complexes while mitigating informational redundancy. Specifically, we propose a parameter perturbation-based augmentation method that injects controlled noise into cellular interactions without altering the underlying cellular structures, thereby preserving cellular topology during contrastive learning. Additionally, a cellular trimming scheduler is employed to mask gradient contributions from task-irrelevant cells through a bi-level meta-learning approach, effectively removing redundant topological elements while maintaining critical higher-order semantics. We provide theoretical justification and empirical validation to demonstrate that CellCLAT achieves substantial improvements over existing self-supervised graph learning methods, marking a significant attempt in this domain.
We propose a denoising method of multimodal graph signals by iteratively solving signal restoration and graph learning problems. Many complex-structured data, i.e., those on sensor networks, can capture multiple modalities at each measurement point, referred to as modalities. They are also assumed to have an underlying structure or correlations in modality as well as space. Such multimodal data are regarded as graph signals on a twofold graph and they are often corrupted by noise. Furthermore, their spatial/modality relationships are not always given a priori: We need to estimate twofold graphs during a denoising algorithm. In this paper, we consider a signal denoising method on twofold graphs, where graphs are learned simultaneously. We formulate an optimization problem for that and parameters in an iterative algorithm are learned from training data by unrolling the iteration with deep algorithm unrolling. Experimental results on synthetic and real-world data demonstrate that the proposed method outperforms existing model- and deep learning-based graph signal denoising methods.
Large Language Model-based Multi-Agent Systems (MASs) have emerged as a powerful paradigm for tackling complex tasks through collaborative intelligence. Nevertheless, the question of how agents should be structurally organized for optimal cooperation remains largely unexplored. In this position paper, we aim to gently redirect the focus of the MAS research community toward this critical dimension: develop topology-aware MASs for specific tasks. Specifically, the system consists of three core components - agents, communication links, and communication patterns - that collectively shape its coordination performance and efficiency. To this end, we introduce a systematic, three-stage framework: agent selection, structure profiling, and topology synthesis. Each stage would trigger new research opportunities in areas such as language models, reinforcement learning, graph learning, and generative modeling; together, they could unleash the full potential of MASs in complicated real-world applications. Then, we discuss the potential challenges and opportunities in the evaluation of multiple systems. We hope our perspective and framework can offer critical new insights in the era of agentic AI.
Agent-Based Models (ABMs) are powerful tools for studying emergent properties in complex systems. In ABMs, agent behaviors are governed by local interactions and stochastic rules. However, these rules are, in general, non-differentiable, limiting the use of gradient-based methods for optimization, and thus integration with real-world data. We propose a novel framework to learn a differentiable surrogate of any ABM by observing its generated data. Our method combines diffusion models to capture behavioral stochasticity and graph neural networks to model agent interactions. Distinct from prior surrogate approaches, our method introduces a fundamental shift: rather than approximating system-level outputs, it models individual agent behavior directly, preserving the decentralized, bottom-up dynamics that define ABMs. We validate our approach on two ABMs (Schelling's segregation model and a Predator-Prey ecosystem) showing that it replicates individual-level patterns and accurately forecasts emergent dynamics beyond training. Our results demonstrate the potential of combining diffusion models and graph learning for data-driven ABM simulation.
In recent years, large language models (LLMs) have demonstrated remarkable generalization capabilities across various natural language processing (NLP) tasks. Similarly, graph foundation models (GFMs) have emerged as a promising direction in graph learning, aiming to generalize across diverse datasets through large-scale pre-training. However, unlike language models that rely on explicit token representations, graphs lack a well-defined unit for generalization, making it challenging to design effective pre-training strategies. In this work, we propose REEF, a novel framework that leverages relation tokens as the basic units for GFMs. Inspired by the token vocabulary in LLMs, we construct a relation vocabulary of relation tokens to store relational information within graphs. To accommodate diverse relations, we introduce two hypernetworks that adaptively generate the parameters of aggregators and classifiers in graph neural networks based on relation tokens. In addition, we design another hypernetwork to construct dataset-specific projectors and incorporate a dataset-level feature bias into the initial node representations, enhancing flexibility across different datasets with the same relation. Further, we adopt graph data augmentation and a mixed-dataset pre-training strategy, allowing REEF to capture relational diversity more effectively and exhibit strong generalization capabilities. Extensive experiments show that REEF significantly outperforms existing methods on both pre-training and transfer learning tasks, underscoring its potential as a powerful foundation model for graph-based applications.
Traditional graph neural networks (GNNs), which rely on homophily-driven message passing, struggle with heterophilic graphs where connected nodes exhibit dissimilar features and different labels. While existing methods address heterophily through graph structure refinement or adaptation of neighbor aggregation functions, they often overlook the semantic potential of node text, rely on suboptimal message representation for propagation and compromise performance on homophilic graphs. To address these limitations, we propose a novel language model (LM)-enhanced message passing approach for heterophilic graph leaning (LEMP4HG). Specifically, in the context of text-attributed graph, we provide paired node texts for LM to generate their connection analysis, which are encoded and then fused with paired node textual embeddings through a gating mechanism. The synthesized messages are semantically enriched and adaptively balanced with both nodes' information, which mitigates contradictory signals when neighbor aggregation in heterophilic regions. Furthermore, we introduce an active learning strategy guided by our heuristic MVRD (Modulated Variation of Reliable Distance), selectively enhancing node pairs suffer most from message passing, reducing the cost of analysis generation and side effects on homophilic regions. Extensive experiments validate that our approach excels on heterophilic graphs and performs robustly on homophilic ones, with a graph convolutional network (GCN) backbone and a practical budget.
Neural Architecture Search (NAS) is a powerful technique for discovering high-performing CNN architectures, but most existing methods rely on costly training or extensive sampling. Zero-shot NAS offers a training-free alternative by using proxies to predict architecture performance. However, existing proxies are often suboptimal -- frequently outperformed by simple metrics like parameter count or FLOPs -- and they generalize poorly across different search spaces. Moreover, current model-based proxies struggle to adapt to new operators without access to ground-truth accuracy, limiting their transferability. We propose TG-NAS, a universal, model-based zero-cost (ZC) proxy that combines a Transformer-based operator embedding generator with a Graph Convolutional Network (GCN) to predict architecture performance. Unlike prior model-based predictors, TG-NAS requires no retraining and generalizes across arbitrary search spaces. It serves as a standalone ZC proxy with strong data efficiency, robustness, and cross-space consistency. Extensive evaluations across diverse NAS benchmarks demonstrate TG-NAS's superior rank correlation and generalizability compared to existing proxies. Additionally, it improves search efficiency by up to 300x and discovers architectures achieving 93.75% CIFAR-10 accuracy on NAS-Bench-201 and 74.9% ImageNet top-1 accuracy on the DARTS space, establishing TG-NAS as a promising foundation for efficient, generalizable NAS.