ICML 2025 Papers

Graph Neural Networks (GNNs) extend convolutional neural networks to operate on graphs. Despite their impressive performances in various graph learning tasks, the theoretical understanding of their generalization capability is still lacking. Previous GNN generalization bounds ignore the underlying graph structures, often leading to bounds that increase with the number of nodes – a behavior contrary to the one experienced in practice. In this paper, we take a manifold perspective to establish the statistical generalization theory of GNNs on graphs sampled from a manifold in the spectral domain. As demonstrated empirically, we prove that the generalization bounds of GNNs decrease linearly with the size of the graphs in the logarithmic scale, and increase linearly with the spectral continuity constants of the filter functions. Notably, our theory explains both node-level and graph-level tasks. Our result has two implications: i) guaranteeing the generalization of GNNs to unseen data over manifolds; ii) providing insights into the practical design of GNNs, i.e., restrictions on the discriminability of GNNs are necessary to obtain a better generalization performance. We demonstrate our generalization bounds of GNNs using synthetic and multiple real-world datasets.

Existing offline hierarchical reinforcement learning methods rely on high-level policy learning to generate subgoal sequences. However, their efficiency degrades as task horizons increase, and they lack effective strategies for stitching useful state transitions across different trajectories. We propose Graph-Assisted Stitching (GAS), a novel framework that formulates subgoal selection as a graph search problem rather than learning an explicit high-level policy. By embedding states into a Temporal Distance Representation (TDR) space, GAS clusters semantically similar states from different trajectories into unified graph nodes, enabling efficient transition stitching. A shortest-path algorithm is then applied to select subgoal sequences within the graph, while a low-level policy learns to reach the subgoals. To improve graph quality, we introduce the Temporal Efficiency (TE) metric, which filters out noisy or inefficient transition states, significantly enhancing task performance. GAS outperforms prior offline HRL methods across locomotion, navigation, and manipulation tasks. Notably, in the most stitching-critical task, it achieves a score of 88.3, dramatically surpassing the previous state-of-the-art score of 1.0. Our source code is available at: https://github.com/qortmdgh4141/GAS.

In recent years, the pursuit of higher expressive power in graph neural networks (GNNs) has often led to more complex aggregation mechanisms and deeper architectures. To address these issues, we have identified redundant structures in GNNs, and by pruning them, we propose Pruned MP-GNNs, K-Path GNNs, and K-Hop GNNs based on their original architectures. We show that 1) Although some structures are pruned in Pruned MP-GNNs and Pruned K-Path GNNs, their expressive power has not been compromised. 2) K-Hop MP-GNNs and their pruned architecture exhibit equivalent expressiveness on regular and strongly regular graphs. 3) The complexity of pruned K-Path GNNs and pruned K-Hop GNNs is lower than that of MP-GNNs, yet their expressive power is higher. Experimental results validate our refinements, demonstrating competitive performance across benchmark datasets with improved efficiency.

The growing demand for personalized learning underscores the importance of accurately predicting students' future performance to support tailored education and optimize instructional strategies. Traditional approaches predominantly focus on temporal modeling using historical response records and learning trajectories. While effective, these methods often fall short in capturing the intricate interactions between students and learning content, as well as the subtle semantics of these interactions. To address these gaps, we present EduLLM, the first framework to leverage large language models in combination with hypergraph learning for student performance prediction. The framework incorporates FraS-HNN ($\underline{\mbox{Fra}}$melet-based $\underline{\mbox{S}}$igned $\underline{\mbox{H}}$ypergraph $\underline{\mbox{N}}$eural $\underline{\mbox{N}}$etworks), a novel spectral-based model for signed hypergraph learning, designed to model interactions between students and multiple-choice questions. In this setup, students and questions are represented as nodes, while response records are encoded as positive and negative signed hyperedges, effectively capturing both structural and semantic intricacies of personalized learning behaviors. FraS-HNN employs framelet-based low-pass and high-pass filters to extract multi-frequency features. EduLLM integrates fine-grained semantic features derived from LLMs, synergizing with signed hypergraph representations to enhance prediction accuracy. Extensive experiments conducted on multiple educational datasets demonstrate that EduLLM significantly outperforms state-of-the-art baselines, validating the novel integration of LLMs with FraS-HNN for signed hypergraph learning.

Despite the growing popularity of graph attention mechanisms, their theoretical understanding remains limited. This paper aims to explore the conditions under which these mechanisms are effective in node classification tasks through the lens of Contextual Stochastic Block Models (CSBMs). Our theoretical analysis reveals that incorporating graph attention mechanisms is *not universally beneficial*. Specifically, by appropriately defining *structure noise* and *feature noise* in graphs, we show that graph attention mechanisms can enhance classification performance when structure noise exceeds feature noise. Conversely, when feature noise predominates, simpler graph convolution operations are more effective. Furthermore, we examine the over-smoothing phenomenon and show that, in the high signal-to-noise ratio (SNR) regime, graph convolutional networks suffer from over-smoothing, whereas graph attention mechanisms can effectively resolve this issue. Building on these insights, we propose a novel multi-layer Graph Attention Network (GAT) architecture that significantly outperforms single-layer GATs in achieving *perfect node classification* in CSBMs, relaxing the SNR requirement from $\omega(\sqrt{\log n})$ to $\omega(\sqrt{\log n} / \sqrt[3]{n})$. To our knowledge, this is the first study to delineate the conditions for perfect node classification using multi-layer GATs. Our theoretical contributions are corroborated by extensive experiments on both synthetic and real-world datasets, highlighting the practical implications of our findings.

We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi, Gupta, Lee, and Panigrahi (NeurIPS 2024). We consider an edge-based version of this model, where each edge provides two bits of information, corresponding to predictions about whether each of its endpoints belong to an optimal solution. Even with weak predictions where each bit is only $\varepsilon$-correlated with the true solution, this information allows us to break approximation barriers in the standard setting. We develop algorithms with improved approximation ratios for MaxCut, Vertex Cover, Set Cover, and Maximum Independent Set problems (among others). Across these problems, our algorithms share a unifying theme, where we separately satisfy constraints related to high degree vertices (using predictions) and low-degree vertices (without using predictions) and carefully combine the answers.

Message-passing graph neural networks (MPNNs) and structural features (SFs) are cornerstones for the link prediction task. However, as a common and intuitive mode of understanding, the potential of visual perception has been overlooked in the MPNN community. For the first time, we equip MPNNs with vision structural awareness by proposing an effective framework called Graph Vision Network (GVN), along with a more efficient variant (E-GVN). Extensive empirical results demonstrate that with the proposed frameworks, GVN consistently benefits from the vision enhancement across seven link prediction datasets, including challenging large-scale graphs. Such improvements are compatible with existing state-of-the-art (SOTA) methods and GVNs achieve new SOTA results, thereby underscoring a promising novel direction for link prediction.

We introduce *GraphGPT*, a novel self-supervised *generative pre-trained* model for graph learning based on the *Graph Eulerian Transformer* (**GET**). First, we propose **GET**, which combines a standard transformer encoder or decoder architecture with an innovative graph-to-sequence transformation method. This method converts graphs or sampled subgraphs into sequences of tokens representing nodes, edges, and attributes in a reversible manner using Eulerian paths. We pre-train **GET** using either of the two self-supervised tasks: next-token prediction (NTP) and scheduled masked-token prediction (SMTP). The pre-trained model is then fine-tuned for downstream tasks such as graph-, edge-, and node-level prediction. Despite its simplicity, GraphGPT achieves performance comparable to or surpassing state-of-the-art methods on multiple large-scale Open Graph Benchmark (OGB) datasets. It demonstrates exceptional results on the molecular property prediction dataset PCQM4Mv2 and the protein-protein interaction dataset ogbl-ppa. Notably, generative pre-training enables scaling GraphGPT to 2 billion parameters while maintaining performance gains — a breakthrough that overcomes the scalability limitations of traditional Graph Neural Networks (GNNs) and prior graph transformers (GTs). To advance research in graph foundation models and facilitate scientific discovery in chemistry, materials science, and related fields, we have released the source code (https://github.com/alibaba/graph-gpt) and model checkpoints (https://www.modelscope.cn/organization/Alibaba-DT).

Graph Neural Networks (GNNs) are widely used for node classification tasks but often fail to generalize when training and test nodes come from different distributions, limiting their practicality. To address this challenge, recent approaches have adopted invariant learning and sample reweighting techniques from the out-of-distribution (OOD) generalization field. However, invariant learning-based methods face difficulties when applied to graph data, as they rely on the impractical assumption of obtaining real environment labels and strict invariance, which may not hold in real-world graph structures. Moreover, current sample reweighting methods tend to overlook topological information, potentially leading to suboptimal results. In this work, we introduce the Topology-Aware Dynamic Reweighting (TAR) framework to address distribution shifts by leveraging the inherent graph structure. TAR dynamically adjusts sample weights through gradient flow on the graph edges during training. Instead of relying on strict invariance assumptions, we theoretically prove that our method is able to provide distributional robustness, thereby enhancing the out-of-distribution generalization performance on graph data. Our framework's superiority is demonstrated through standard testing on extensive node classification OOD datasets, exhibiting marked improvements over existing methods.

Graph Neural Networks (GNNs) face a critical limitation known as oversmoothing, where increasing network depth leads to homogenized node representations, severely compromising their expressiveness. We present a novel dynamical systems perspective on this challenge, revealing oversmoothing as an emergent property of GNNs' convergence to low-dimensional attractor states. Based on this insight, we introduce **DYNAMO-GAT**, which combines noise-driven covariance analysis with Anti-Hebbian learning to dynamically prune attention weights, effectively preserving distinct attractor states. We provide theoretical guarantees for DYNAMO-GAT's effectiveness and demonstrate its superior performance on benchmark datasets, consistently outperforming existing methods while requiring fewer computational resources. This work establishes a fundamental connection between dynamical systems theory and GNN behavior, providing both theoretical insights and practical solutions for deep graph learning.

Recent advances in CV and NLP have inspired researchers to develop general-purpose graph foundation models through pre-training across diverse domains. However, a fundamental challenge arises from the substantial differences in graph topologies across domains. Additionally, real-world graphs are often sparse and prone to noisy connections and adversarial attacks. To address these issues, we propose the Multi-Domain Graph Foundation Model (MDGFM), a unified framework that aligns and leverages cross-domain topological information to facilitate robust knowledge transfer. MDGFM bridges different domains by adaptively balancing features and topology while refining original graphs to eliminate noise and align topological structures. To further enhance knowledge transfer, we introduce an efficient prompt-tuning approach. By aligning topologies, MDGFM not only improves multi-domain pre-training but also enables robust knowledge transfer to unseen domains. Theoretical analyses provide guarantees of MDGFM's effectiveness and domain generalization capabilities. Extensive experiments on both homophilic and heterophilic graph datasets validate the robustness and efficacy of our method.

This paper proposes SHARP-Distill (\textbf{S}peedy \textbf{H}ypergraph \textbf{A}nd \textbf{R}eview-based \textbf{P}ersonalised \textbf{Distill}ation), a novel knowledge distillation approach based on the teacher-student framework that combines Hypergraph Neural Networks (HGNNs) with language models to enhance recommendation quality while significantly improving inference time. The teacher model leverages HGNNs to generate user and item embeddings from interaction data, capturing high-order and group relationships, and employing a pre-trained language model to extract rich semantic features from textual reviews. We utilize a contrastive learning mechanism to ensure structural consistency between various representations. The student includes a shallow and lightweight GCN called CompactGCN designed to inherit high-order relationships while reducing computational complexity. Extensive experiments on real-world datasets demonstrate that SHARP-Distill achieves up to 68× faster inference time compared to HGNN and 40× faster than LightGCN while maintaining competitive recommendation accuracy.

Hyper-relational knowledge graphs (HKGs) enrich knowledge graphs by extending a triplet to a hyper-relational fact, where a set of qualifiers adds auxiliary information to a triplet. While many HKG representation learning methods have been proposed, they often fail to effectively utilize the HKG's structure. This paper demonstrates that thoroughly leveraging the structure of an HKG is crucial for reasoning on HKGs, and a purely structure-based representation learning method can achieve state-of-the-art performance on various link prediction tasks. We propose MAYPL, which learns to initialize representation vectors based on the structure of an HKG and employs an attentive neural message passing consisting of fact-level message computation and entity-centric and relation-centric aggregations, thereby computing the representations based solely on the structure. Due to its structure-driven learning, MAYPL can conduct inductive inferences on new entities and relations. MAYPL outperforms 40 knowledge graph completion methods in 10 datasets, compared with different baseline methods on different datasets to be tested from diverse perspectives.

Long-range graph tasks --- those dependent on interactions between `distant' nodes --- are an open problem in graph neural network research. Real-world benchmark tasks, especially the Long Range Graph Benchmark, have become popular for validating the long-range capability of proposed architectures. However, this is an empirical approach that lacks both robustness and theoretical underpinning; a more principled characterization of the long-range problem is required. To bridge this gap, we formalize long-range interactions in graph tasks, introduce a **range measure** for operators on graphs, and validate it with synthetic experiments. We then leverage our measure to examine commonly used tasks and architectures, and discuss to what extent they are, in fact, long-range. We believe our work advances efforts to define and address the long-range problem on graphs, and that our range measure will aid evaluation of new datasets and architectures.

Graph Neural Networks (GNNs) have shown remarkable success in learning from graph-structured data. However, their application to directed graphs (digraphs) presents unique challenges, primarily due to the inherent asymmetry in node relationships. Traditional GNNs are adept at capturing unidirectional relations but fall short in encoding the mutual path dependencies between nodes, such as asymmetrical shortest paths typically found in digraphs. Recognizing this gap, we introduce Commute Graph Neural Networks (CGNN), an approach that seamlessly integrates node-wise commute time into the message passing scheme. The cornerstone of CGNN is an efficient method for computing commute time using a newly formulated digraph Laplacian. Commute time is then integrated into the neighborhood aggregation process, with neighbor contributions weighted according to their respective commute time to the central node in each layer. It enables CGNN to directly capture the mutual, asymmetric relationships in digraphs. Extensive experiments on 8 benchmarking datasets confirm the superiority of CGNN against 13 state-of-the-art methods.

The local inductive bias of message-passing graph neural networks (GNNs) hampers their ability to exploit key structural information (e.g., connectivity and cycles). Positional encoding (PE) and Persistent Homology (PH) have emerged as two promising approaches to mitigate this issue. PE schemes endow GNNs with location-aware features, while PH methods enhance GNNs with multiresolution topological features. However, a rigorous theoretical characterization of the relative merits and shortcomings of PE and PH has remained elusive. We bridge this gap by establishing that neither paradigm is more expressive than the other, providing novel constructions where one approach fails but the other succeeds. Our insights inform the design of a novel learnable method, PiPE (Persistence-informed Positional Encoding), which is provably more expressive than both PH and PE. PiPE demonstrates strong performance across a variety of tasks (e.g., molecule property prediction, graph classification, and out-of-distribution generalization), thereby advancing the frontiers of graph representation learning. Code is available at https://github.com/Aalto-QuML/PIPE

Attention mechanisms are critical to the success of large language models (LLMs), driving significant advancements in multiple fields. However, for graph-structured data, which requires emphasis on topological connections, they fall short compared to message-passing mechanisms on fixed links, such as those employed by Graph Neural Networks (GNNs). This raises a question: ``Does attention fail for graphs in natural language settings?'' Motivated by these observations, we embarked on an empirical study from the perspective of attention mechanisms to explore how LLMs process graph-structured data. The goal is to gain deeper insights into the attention behavior of LLMs over graph structures. Through a series of experiments, we uncovered unique phenomena regarding how LLMs apply attention to graph-structured data and analyzed these findings to improve the modeling of such data by LLMs. The primary findings of our research are: 1) While LLMs can recognize graph data and capture text-node interactions, they struggle to model inter-node relationships within graph structures due to inherent architectural constraints. 2) The attention distribution of LLMs across graph nodes does not align with ideal structural patterns, indicating a failure to adapt to graph topology nuances. 3) Neither fully connected attention (as in LLMs) nor fixed connectivity (as in GNNs) is optimal; each has specific limitations in its application scenarios. Instead, intermediate-state attention windows improve LLM training performance and seamlessly transition to fully connected windows during inference. Source code: \href{https://anonymous.4open.science/r/LLM_exploration-B21F}{anonymous.4open.science/LLM\_exploration-B21F}

The out-of-distribution (OOD) generalization challenge is a longstanding problem in graph learning. Through studying the fundamental cause of data distribution shift, i.e., the changes of environments, significant progress has been achieved in addressing this issue. However, we observe that existing works still fail to effectively address complex environment shifts. Existing practices place excessive attention on extracting causal subgraphs, inevitably treating spurious subgraphs as environment variables. While spurious subgraphs are controlled by environments, the space of environment changes encompass more than the scale of spurious subgraphs. Therefore, existing efforts have a limited inference space for environments, leading to failure under severe environment changes. To tackle this issue, we propose a negative inference graph OOD framework (NeGo) to broaden the inference space for environment factors. Inspired by the successful practice of prompt learning in capturing underlying semantics and causal associations in large language models, we design a negative prompt environment inference to extract underlying environment information. We further introduce the environment-enhanced invariant subgraph learning to effectively exploit inferred environment embedding, ensuring the robust extraction of causal subgraph in the environment shifts. Lastly, we conduct a comprehensive evaluation of NeGo on real-world datasets and synthetic datasets across domains. NeGo outperforms baselines on nearly all datasets, which verify the effectiveness of our framework.

Static systems exhibit diverse structural properties, such as hierarchical, scale-free, and isotropic patterns, where different geometric spaces offer unique advantages. Methods combining multiple geometries have proven effective in capturing these characteristics. However, real-world systems often evolve dynamically, introducing significant challenges in modeling their temporal changes. To overcome this limitation, we propose a unified cross-geometric learning framework for dynamic systems, which synergistically integrates Euclidean and hyperbolic spaces, aligning embedding spaces with structural properties through fine-grained substructure modeling. Our framework further incorporates a temporal state aggregation mechanism and an evolution-driven optimization objective, enabling comprehensive and adaptive modeling of both nodal and relational dynamics over time. Extensive experiments on diverse real-world dynamic graph datasets highlight the superiority of our approach in capturing complex structural evolution, surpassing existing methods across multiple metrics.