Real-world medical data often includes measurements from multiple signals that are collected at irregular and asynchronous time intervals. For example, different types of blood tests can be measured at different times and frequencies, resulting in fragmented and unevenly scattered temporal data. Similar issues of irregular sampling of different attributes occur in other domains, such as monitoring of large systems using event log files or the spread of fake news on social networks. Effectively learning from such data requires models that can handle sets of temporally sparse and heterogeneous signals. In this paper, we propose Graph Mixing Additive Networks (GMAN), a novel and interpretable-by-design model for learning over irregular sets of temporal signals. Our method achieves state-of-the-art performance in real-world medical tasks, including a 4-point increase in the AUROC score of in-hospital mortality prediction, compared to existing methods. We further showcase GMAN's flexibility by applying it to a fake news detection task. We demonstrate how its interpretability capabilities, including node-level, graph-level, and subset-level importance, allow for transition phases detection and gaining medical insights with real-world high-stakes implications. Finally, we provide theoretical insights on GMAN expressive power.
The recent success of State-Space Models (SSMs) in sequence modeling has motivated their adaptation to graph learning, giving rise to Graph State-Space Models (GSSMs). However, existing GSSMs operate by applying SSM modules to sequences extracted from graphs, often compromising core properties such as permutation equivariance, message-passing compatibility, and computational efficiency. In this paper, we introduce a new perspective by embedding the key principles of modern SSM computation directly into the Message-Passing Neural Network framework, resulting in a unified methodology for both static and temporal graphs. Our approach, MP-SSM, enables efficient, permutation-equivariant, and long-range information propagation while preserving the architectural simplicity of message passing. Crucially, MP-SSM enables an exact sensitivity analysis, which we use to theoretically characterize information flow and evaluate issues like vanishing gradients and over-squashing in the deep regime. Furthermore, our design choices allow for a highly optimized parallel implementation akin to modern SSMs. We validate MP-SSM across a wide range of tasks, including node classification, graph property prediction, long-range benchmarks, and spatiotemporal forecasting, demonstrating both its versatility and strong empirical performance.
Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. Conventional graph learning approaches typically rely on fixed structural assumptions or fully observed data, limiting their effectiveness in more complex, noisy, or evolving settings. Consequently, real-world graph data often violates the assumptions of traditional graph learning methods, in particular, it leads to four fundamental challenges: (1) Incompleteness, real-world graphs have missing nodes, edges, or attributes; (2) Imbalance, the distribution of the labels of nodes or edges and their structures for real-world graphs are highly skewed; (3) Cross-domain Heterogeneity, graphs from different domains exhibit incompatible feature spaces or structural patterns; and (4) Dynamic Instability, graphs evolve over time in unpredictable ways. Recent advances in Large Language Models (LLMs) offer the potential to tackle these challenges by leveraging rich semantic reasoning and external knowledge. This survey provides a comprehensive review of how LLMs can be integrated with graph learning to address the aforementioned challenges. For each challenge, we review both traditional solutions and modern LLM-driven approaches, highlighting how LLMs contribute unique advantages. Finally, we discuss open research questions and promising future directions in this emerging interdisciplinary field. To support further exploration, we have curated a repository of recent advances on graph learning challenges: https://github.com/limengran98/Awesome-Literature-Graph-Learning-Challenges.
Due to the highly sensitive nature of certain data in cross-border sharing, collaborative cross-border recommendations and data sharing are often subject to stringent privacy protection regulations, resulting in insufficient data for model training. Consequently, achieving efficient cross-border business recommendations while ensuring privacy security poses a significant challenge. Although federated learning has demonstrated broad potential in collaborative training without exposing raw data, most existing federated learning-based GNN training methods still rely on federated averaging strategies, which perform suboptimally on highly heterogeneous graph data. To address this issue, we propose FedGRec, a privacy-preserving federated graph learning method for cross-border recommendations. FedGRec captures user preferences from distributed multi-domain data to enhance recommendation performance across all domains without privacy leakage. Specifically, FedGRec leverages collaborative signals from local subgraphs associated with users or items to enrich their representation learning. Additionally, it employs dynamic spatiotemporal modeling to integrate global and local user preferences in real time based on business recommendation states, thereby deriving the final representations of target users and candidate items. By automatically filtering relevant behaviors, FedGRec effectively mitigates noise interference from unreliable neighbors. Furthermore, through a personalized federated aggregation strategy, FedGRec adapts global preferences to heterogeneous domain data, enabling collaborative learning of user preferences across multiple domains. Extensive experiments on three datasets demonstrate that FedGRec consistently outperforms competitive single-domain and cross-domain baselines while effectively preserving data privacy in cross-border recommendations.
Graph Transformers, leveraging the global attention to capture long-range dependencies in graph structures, have significantly advanced graph machine learning, but face prohibitive computational complexity. Tokenized Graph Learning Models (TGLMs) address this issue by converting graphs into ordered token lists for scalable processing. Besides, TGLMs also empower Large Language Models (LLMs) to handle text-attributed graphs more effectively and thus are also employed in Graph LLMs. However, existing TGLMs rely on hand-designed token lists and their adaptability to diverse graph learning scenarios remains unexplored. In this paper, we first conduct extensive empirical and theoretical preliminary studies for hand-designed token lists. Surprisingly, we identify an unexplored hop-overpriority problem: the common pre-defined token lists overemphasize nearby nodes and overwhelm the ability of TGLMs to balance local and global signals. This phenomenon is especially harmful for heterophilic graphs. To address this problem, we propose the Learnable Graph Token List (LGTL), a plug-and-play module to replace hand-designed token lists in TGLMs. Specifically, LGTL adaptively adjusts the weights across hops and prioritizes informative nodes within hops through a graph attention gate module and a selection module, respectively. In this way, contextually informative nodes can be adaptively emphasized for both homophilic and heterophilic graphs. Besides, we theoretically show that LGTL can address the hop-overpriority problem. Extensive experiments on benchmarks validate the efficacy of LGTL across both Graph Transformers and Graph LLM backbones.
Graph neural networks (GNNs) has been predominantly driven by message-passing, where node representations are iteratively updated via local neighborhood aggregation. Despite their success, message-passing suffers from fundamental limitations -- including constrained expressiveness, over-smoothing, over-squashing, and limited capacity to model long-range dependencies. These issues hinder scalability: increasing data size or model size often fails to yield improved performance, limiting the viability of GNNs as backbones for graph foundation models. In this work, we explore pathways beyond message-passing and introduce Generative Graph Pattern Machine (G$^2$PM), a generative Transformer pre-training framework for graphs. G$^2$PM represents graph instances (nodes, edges, or entire graphs) as sequences of substructures, and employs generative pre-training over the sequences to learn generalizable, transferable representations. Empirically, G$^2$PM demonstrates strong scalability: on the ogbn-arxiv benchmark, it continues to improve with model sizes up to 60M parameters, outperforming prior generative approaches that plateau at significantly smaller scales (e.g., 3M). In addition, we systematically analyze the model design space, highlighting key architectural choices that contribute to its scalability and generalization. Across diverse tasks -- including node classification, graph classification, and transfer learning -- G$^2$PM consistently outperforms strong baselines, establishing a compelling foundation for scalable graph learning. The code and dataset are available at https://github.com/Zehong-Wang/G2PM.
Recent advances in graph machine learning (ML) with the introduction of Graph Neural Networks (GNNs) have led to a widespread interest in applying these approaches to business applications at scale. GNNs enable differentiable end-to-end (E2E) learning of model parameters given graph structure which enables optimization towards popular node, edge (link) and graph-level tasks. While the research innovation in new GNN layers and training strategies has been rapid, industrial adoption and utility of GNNs has lagged considerably due to the unique scale challenges that large-scale graph ML problems create. In this work, we share our approach to training, inference, and utilization of GNNs at Snapchat. To this end, we present GiGL (Gigantic Graph Learning), an open-source library to enable large-scale distributed graph ML to the benefit of researchers, ML engineers, and practitioners. We use GiGL internally at Snapchat to manage the heavy lifting of GNN workflows, including graph data preprocessing from relational DBs, subgraph sampling, distributed training, inference, and orchestration. GiGL is designed to interface cleanly with open-source GNN modeling libraries prominent in academia like PyTorch Geometric (PyG), while handling scaling and productionization challenges that make it easier for internal practitioners to focus on modeling. GiGL is used in multiple production settings, and has powered over 35 launches across multiple business domains in the last 2 years in the contexts of friend recommendation, content recommendation and advertising. This work details high-level design and tools the library provides, scaling properties, case studies in diverse business settings with industry-scale graphs, and several key lessons learned in employing graph ML at scale on large social data. GiGL is open-sourced at https://github.com/snap-research/GiGL.
In the past few years, time series foundation models have achieved superior predicting accuracy. However, real-world time series often exhibit significant diversity in their temporal patterns across different time spans and domains, making it challenging for a single model architecture to fit all complex scenarios. In addition, time series data may have multiple variables exhibiting complex correlations between each other. Recent mainstream works have focused on modeling times series in a channel-independent manner in both pretraining and finetuning stages, overlooking the valuable inter-series dependencies. To this end, we propose \textbf{Time Tracker} for better predictions on multivariate time series data. Firstly, we leverage sparse mixture of experts (MoE) within Transformers to handle the modeling of diverse time series patterns, thereby alleviating the learning difficulties of a single model while improving its generalization. Besides, we propose Any-variate Attention, enabling a unified model structure to seamlessly handle both univariate and multivariate time series, thereby supporting channel-independent modeling during pretraining and channel-mixed modeling for finetuning. Furthermore, we design a graph learning module that constructs relations among sequences from frequency-domain features, providing more precise guidance to capture inter-series dependencies in channel-mixed modeling. Based on these advancements, Time Tracker achieves state-of-the-art performance in predicting accuracy, model generalization and adaptability.
Graph Neural Networks (GNNs) have been widely used for graph analysis. Federated Graph Learning (FGL) is an emerging learning framework to collaboratively train graph data from various clients. However, since clients are required to upload model parameters to the server in each round, this provides the server with an opportunity to infer each client's data privacy. In this paper, we focus on label distribution attacks(LDAs) that aim to infer the label distributions of the clients' local data. We take the first step to attack client's label distributions in FGL. Firstly, we observe that the effectiveness of LDA is closely related to the variance of node embeddings in GNNs. Next, we analyze the relation between them and we propose a new attack named EC-LDA, which significantly improves the attack effectiveness by compressing node embeddings. Thirdly, extensive experiments on node classification and link prediction tasks across six widely used graph datasets show that EC-LDA outperforms the SOTA LDAs. For example, EC-LDA attains optimal values under both Cos-sim and JS-div evaluation metrics in the CoraFull and LastFM datasets. Finally, we explore the robustness of EC-LDA under differential privacy protection.
Graph-structured data pervades domains such as social networks, biological systems, knowledge graphs, and recommender systems. While foundation models have transformed natural language processing, vision, and multimodal learning through large-scale pretraining and generalization, extending these capabilities to graphs -- characterized by non-Euclidean structures and complex relational semantics -- poses unique challenges and opens new opportunities. To this end, Graph Foundation Models (GFMs) aim to bring scalable, general-purpose intelligence to structured data, enabling broad transfer across graph-centric tasks and domains. This survey provides a comprehensive overview of GFMs, unifying diverse efforts under a modular framework comprising three key components: backbone architectures, pretraining strategies, and adaptation mechanisms. We categorize GFMs by their generalization scope -- universal, task-specific, and domain-specific -- and review representative methods, key innovations, and theoretical insights within each category. Beyond methodology, we examine theoretical foundations including transferability and emergent capabilities, and highlight key challenges such as structural alignment, heterogeneity, scalability, and evaluation. Positioned at the intersection of graph learning and general-purpose AI, GFMs are poised to become foundational infrastructure for open-ended reasoning over structured data. This survey consolidates current progress and outlines future directions to guide research in this rapidly evolving field. Resources are available at https://github.com/Zehong-Wang/Awesome-Foundation-Models-on-Graphs.
Temporal Graph Neural Networks (TGNNs) have gained growing attention for modeling and predicting structures in temporal graphs. However, existing TGNNs primarily focus on pairwise interactions while overlooking higher-order structures that are integral to link formation and evolution in real-world temporal graphs. Meanwhile, these models often suffer from efficiency bottlenecks, further limiting their expressive power. To tackle these challenges, we propose a Higher-order structure Temporal Graph Neural Network, which incorporates hypergraph representations into temporal graph learning. In particular, we develop an algorithm to identify the underlying higher-order structures, enhancing the model's ability to capture the group interactions. Furthermore, by aggregating multiple edge features into hyperedge representations, HTGN effectively reduces memory cost during training. We theoretically demonstrate the enhanced expressiveness of our approach and validate its effectiveness and efficiency through extensive experiments on various real-world temporal graphs. Experimental results show that HTGN achieves superior performance on dynamic link prediction while reducing memory costs by up to 50\% compared to existing methods.
Recently, large language models (LLMs) have significantly advanced text-attributed graph (TAG) learning. However, existing methods inadequately handle data uncertainty in open-world scenarios, especially concerning limited labeling and unknown-class nodes. Prior solutions typically rely on isolated semantic or structural approaches for unknown-class rejection, lacking effective annotation pipelines. To address these limitations, we propose Open-world Graph Assistant (OGA), an LLM-based framework that combines adaptive label traceability, which integrates semantics and topology for unknown-class rejection, and a graph label annotator to enable model updates using newly annotated nodes. Comprehensive experiments demonstrate OGA's effectiveness and practicality.
Session search involves a series of interactive queries and actions to fulfill user's complex information need. Current strategies typically prioritize sequential modeling for deep semantic understanding, overlooking the graph structure in interactions. While some approaches focus on capturing structural information, they use a generalized representation for documents, neglecting the word-level semantic modeling. In this paper, we propose Symbolic Graph Ranker (SGR), which aims to take advantage of both text-based and graph-based approaches by leveraging the power of recent Large Language Models (LLMs). Concretely, we first introduce a set of symbolic grammar rules to convert session graph into text. This allows integrating session history, interaction process, and task instruction seamlessly as inputs for the LLM. Moreover, given the natural discrepancy between LLMs pre-trained on textual corpora, and the symbolic language we produce using our graph-to-text grammar, our objective is to enhance LLMs' ability to capture graph structures within a textual format. To achieve this, we introduce a set of self-supervised symbolic learning tasks including link prediction, node content generation, and generative contrastive learning, to enable LLMs to capture the topological information from coarse-grained to fine-grained. Experiment results and comprehensive analysis on two benchmark datasets, AOL and Tiangong-ST, confirm the superiority of our approach. Our paradigm also offers a novel and effective methodology that bridges the gap between traditional search strategies and modern LLMs.
We propose a robust aggregation method for model parameters in federated learning (FL) under noisy communications. FL is a distributed machine learning paradigm in which a central server aggregates local model parameters from multiple clients. These parameters are often noisy and/or have missing values during data collection, training, and communication between the clients and server. This may cause a considerable drop in model accuracy. To address this issue, we learn a graph that represents pairwise relationships between model parameters of the clients during aggregation. We realize it with a joint problem of graph learning and signal (i.e., model parameters) restoration. The problem is formulated as a difference-of-convex (DC) optimization, which is efficiently solved via a proximal DC algorithm. Experimental results on MNIST and CIFAR-10 datasets show that the proposed method outperforms existing approaches by up to $2$--$5\%$ in classification accuracy under biased data distributions and noisy conditions.
Over-the-air computation (AirComp) has emerged as a promising technology that enables simultaneous transmission and computation through wireless channels. In this paper, we investigate the networked AirComp in multiple clusters allowing diversified data computation, which is yet challenged by the transceiver coordination and interference management therein. Particularly, we aim to maximize the multi-cluster weighted-sum AirComp rate, where the transmission scalar as well as receive beamforming are jointly investigated while addressing the interference issue. From an optimization perspective, we decompose the formulated problem and adopt the alternating optimization technique with an iterative process to approximate the solution. Then, we reinterpret the iterations through the principle of algorithm unfolding, where the channel condition and mutual interference in the AirComp network constitute an underlying graph. Accordingly, the proposed unfolding architecture learns the weights parameterized by graph neural networks, which is trained through stochastic gradient descent approach. Simulation results show that our proposals outperform the conventional schemes, and the proposed unfolded graph learning substantially alleviates the interference and achieves superior computation performance, with strong and efficient adaptation to the dynamic and scalable networks.
We consider the problem of inferring the conditional independence graph (CIG) of high-dimensional Gaussian vectors from multi-attribute data. Most existing methods for graph estimation are based on single-attribute models where one associates a scalar random variable with each node. In multi-attribute graphical models, each node represents a random vector. In this paper we provide a unified theoretical analysis of multi-attribute graph learning using a penalized log-likelihood objective function. We consider both convex (sparse-group lasso) and sparse-group non-convex (log-sum and smoothly clipped absolute deviation (SCAD) penalties) penalty/regularization functions. An alternating direction method of multipliers (ADMM) approach coupled with local linear approximation to non-convex penalties is presented for optimization of the objective function. For non-convex penalties, theoretical analysis establishing local consistency in support recovery, local convexity and precision matrix estimation in high-dimensional settings is provided under two sets of sufficient conditions: with and without some irrepresentability conditions. We illustrate our approaches using both synthetic and real-data numerical examples. In the synthetic data examples the sparse-group log-sum penalized objective function significantly outperformed the lasso penalized as well as SCAD penalized objective functions with $F_1$-score and Hamming distance as performance metrics.
Temporal Graph Networks (TGNs), while being accurate, face significant training inefficiencies due to irregular supervision signals in dynamic graphs, which induce sparse gradient updates. We first theoretically establish that aggregating historical node interactions into pseudo-labels reduces gradient variance, accelerating convergence. Building on this analysis, we propose History-Averaged Labels (HAL), a method that dynamically enriches training batches with pseudo-targets derived from historical label distributions. HAL ensures continuous parameter updates without architectural modifications by converting idle computation into productive learning steps. Experiments on the Temporal Graph Benchmark (TGB) validate our findings and an assumption about slow change of user preferences: HAL accelerates TGNv2 training by up to 15x while maintaining competitive performance. Thus, this work offers an efficient, lightweight, architecture-agnostic, and theoretically motivated solution to label sparsity in temporal graph learning.
Fine-grained economic mapping through urban representation learning has emerged as a crucial tool for evidence-based economic decisions. While existing methods primarily rely on supervised or unsupervised approaches, they often overlook semi-supervised learning in data-scarce scenarios and lack unified multi-task frameworks for comprehensive sectoral economic analysis. To address these gaps, we propose SemiGTX, an explainable semi-supervised graph learning framework for sectoral economic mapping. The framework is designed with dedicated fusion encoding modules for various geospatial data modalities, seamlessly integrating them into a cohesive graph structure. It introduces a semi-information loss function that combines spatial self-supervision with locally masked supervised regression, enabling more informative and effective region representations. Through multi-task learning, SemiGTX concurrently maps GDP across primary, secondary, and tertiary sectors within a unified model. Extensive experiments conducted in the Pearl River Delta region of China demonstrate the model's superior performance compared to existing methods, achieving R2 scores of 0.93, 0.96, and 0.94 for the primary, secondary and tertiary sectors, respectively. Cross-regional experiments in Beijing and Chengdu further illustrate its generality. Systematic analysis reveals how different data modalities influence model predictions, enhancing explainability while providing valuable insights for regional development planning. This representation learning framework advances regional economic monitoring through diverse urban data integration, providing a robust foundation for precise economic forecasting.
Recent advances in graph machine learning have shifted to data-centric paradigms, driven by two emerging fields: (1) Federated graph learning (FGL) enables multi-client collaboration but faces challenges from data and task heterogeneity, limiting its practicality; (2) Graph foundation models (GFM) offer strong domain generalization but are usually trained on single machines, missing out on cross-silo data and resources. These paradigms are complementary, and their integration brings notable benefits. Motivated by this, we propose FedGFM, a novel decentralized GFM training paradigm. However, a key challenge is knowledge entanglement, where multi-domain knowledge merges into indistinguishable representations, hindering downstream adaptation. To address this, we present FedGFM+, an enhanced framework with two core modules to reduce knowledge entanglement: (1) AncDAI: A global anchor-based domain-aware initialization strategy. Before pre-training, each client encodes its local graph into domain-specific prototypes that serve as semantic anchors. Synthetic embeddings around these anchors initialize the global model. We theoretically prove these prototypes are distinguishable across domains, providing a strong inductive bias to disentangle domain-specific knowledge. (2) AdaDPP: A local adaptive domain-sensitive prompt pool. Each client learns a lightweight graph prompt capturing domain semantics during pre-training. During fine-tuning, prompts from all clients form a pool from which the GFM selects relevant prompts to augment target graph attributes, improving downstream adaptation. FedGFM+ is evaluated on 8 diverse benchmarks across multiple domains and tasks, outperforming 20 baselines from supervised learning, FGL, and federated GFM variants.
To forecast traffic with both spatial and temporal dimensions, we unroll a mixed-graph-based optimization algorithm into a lightweight and interpretable transformer-like neural net. Specifically, we construct two graphs: an undirected graph $\mathcal{G}^u$ capturing spatial correlations across geography, and a directed graph $\mathcal{G}^d$ capturing sequential relationships over time. We formulate a prediction problem for the future samples of signal $\mathbf{x}$, assuming it is "smooth" with respect to both $\mathcal{G}^u$ and $\mathcal{G}^d$, where we design new $\ell_2$ and $\ell_1$-norm variational terms to quantify and promote signal smoothness (low-frequency reconstruction) on a directed graph. We construct an iterative algorithm based on alternating direction method of multipliers (ADMM), and unroll it into a feed-forward network for data-driven parameter learning. We insert graph learning modules for $\mathcal{G}^u$ and $\mathcal{G}^d$, which are akin to the self-attention mechanism in classical transformers. Experiments show that our unrolled networks achieve competitive traffic forecast performance as state-of-the-art prediction schemes, while reducing parameter counts drastically. Our code is available in https://github.com/SingularityUndefined/Unrolling-GSP-STForecast.