ICML 2025 Papers

Data sets used in recent work on graph similarity scoring and matching tasks suffer from significant limitations. Using Graph Edit Distance (GED) as a showcase, we highlight pervasive issues such as train-test leakage and poor generalization, which have misguided the community's understanding and assessment of the capabilities of a method or model. These limitations arise, in part, because preparing labeled data is computationally expensive for combinatorial graph problems. We establish some key properties of GED that enable scalable data augmentation for training, and adversarial test set generation. Together, our analysis, experiments and insights establish new, sound guidelines for designing and evaluating future neural networks, and suggest open challenges for future research.

Modern sequence models (e.g., Transformers and linear RNNs) emerged as dominant backbones of recent deep learning frameworks, mainly due to their efficiency, representational power, and/or ability to capture long-range dependencies. Recently, adopting these sequence models for graph-structured data has gained popularity as the alternative to Message Passing Neural Networks (MPNNs). There is, however, a lack of a common foundation about what constitutes a good graph sequence model, and a mathematical description of the benefits and deficiencies in adopting different sequence models for learning on graphs. To this end, we introduce the Graph Sequence Model (GSM), a unifying framework for applying sequence models to graph data. The GSM framework allows us to understand, evaluate, and compare the power of different sequence model backbones in graph tasks. Building on this insight, we propose GSM++, a fast hybrid model that hierarchically tokenizes the graph using Hierarchical Affinity Clustering (HAC) and then encodes these sequences via a hybrid architecture. The theoretical and experimental findings confirm that GSM++ outperforms baseline models on most benchmarks.

While uncertainty estimation for graphs recently gained traction, most methods rely on homophily and deteriorate in heterophilic settings. We address this by analyzing message passing neural networks from an information-theoretic perspective and developing a suitable analog to data processing inequality to quantify information throughout the model's layers. In contrast to non-graph domains, information about the node-level prediction target can *increase* with model depth if a node's features are semantically different from its neighbors. Therefore, on heterophilic graphs, the latent embeddings of an MPNN each provide different information about the data distribution - different from homophilic settings. This reveals that considering all node representations simultaneously is a key design principle for epistemic uncertainty estimation on graphs beyond homophily. We empirically confirm this with a simple post-hoc density estimator on the joint node embedding space that provides state-of-the-art uncertainty on heterophilic graphs. At the same time, it matches prior work on homophilic graphs without explicitly exploiting homophily through post-processing.

The Euler Characteristic Transform (ECT) is an efficiently computable geometrical-topological invariant that characterizes the global shape of data. In this paper, we introduce the local Euler Characteristic Transform ($\ell$-ECT), a novel extension of the ECT designed to enhance expressivity and interpretability in graph representation learning. Unlike traditional Graph Neural Networks (GNNs), which may lose critical local details through aggregation, the $\ell$-ECT provides a lossless representation of local neighborhoods. This approach addresses key limitations in GNNs by preserving nuanced local structures while maintaining global interpretability. Moreover, we construct a rotation-invariant metric based on $\ell$-ECTs for spatial alignment of data spaces. Our method demonstrates superior performance compared to standard GNNs on various benchmarking node classification tasks, while also offering theoretical guarantees of its effectiveness.

Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize adjacency matrix representations, this work revisits an alternative approach that represents graphs as sequences of node set and edge set. We advocate for this approach due to its efficient encoding of graphs and propose a novel representation. Based on this representation, we introduce the Graph Generative Pre-trained Transformer (G2PT), an auto-regressive model that learns graph structures via next-token prediction. To further exploit G2PT's capabilities as a general-purpose foundation model, we explore fine-tuning strategies for two downstream applications: goal-oriented generation and graph property prediction. We conduct extensive experiments across multiple datasets. Results indicate that G2PT achieves superior generative performance on both generic graph and molecule datasets. Furthermore, G2PT exhibits strong adaptability and versatility in downstream tasks from molecular design to property prediction.

Graph diffusion generative models (GDGMs) have emerged as powerful tools for generating high-quality graphs. However, their broader adoption faces challenges in \emph{scalability and size generalization}. GDGMs struggle to scale to large graphs due to their high memory requirements, as they typically operate in the full graph space, requiring the entire graph to be stored in memory during training and inference. This constraint limits their feasibility for large-scale real-world graphs. GDGMs also exhibit poor size generalization, with limited ability to generate graphs of sizes different from those in the training data, restricting their adaptability across diverse applications. To address these challenges, we propose the stochastic block graph diffusion (SBGD) model, which refines graph representations into a block graph space. This space incorporates structural priors based on real-world graph patterns, significantly reducing memory complexity and enabling scalability to large graphs. The block representation also improves size generalization by capturing fundamental graph structures. Empirical results show that SBGD achieves significant memory improvements (up to 6$\times$) while maintaining comparable or even superior graph generation performance relative to state-of-the-art methods. Furthermore, experiments demonstrate that SBGD better generalizes to unseen graph sizes. The significance of SBGD extends beyond being a scalable and effective GDGM; \emph{it also exemplifies the principle of modularization in generative modelling, offering a new avenue for exploring generative models by decomposing complex tasks into more manageable components.}

Real-world multimodal data usually exhibit complex structural relationships beyond traditional one-to-one mappings like image-caption pairs. Entities across modalities interact in intricate ways, with images and text forming diverse interconnections through contextual dependencies and co-references. Graphs provide powerful structural information for modeling intra-modal and inter-modal relationships. However, previous works fail to distinguish multi-hop neighbors and treat the graph as a standalone modality, which fragments the overall understanding. This limitation presents two key challenges in multimodal learning: (1) integrating structural information from multi-hop neighbors into foundational models, and (2) fusing modality-specific information in a principled manner. To address these challenges, we revisit the role of graphs in multimodal learning within the era of foundation models and propose Graph4MM, a graph-based multimodal learning framework. To be specific, we introduce Hop-Diffused Attention, which integrates multi-hop structural information into self-attention through causal masking and hop diffusion. Furthermore, we design MM-QFormer, a multi-mapping querying transformer for cross-modal fusion. Through theoretical and empirical analysis, we show that leveraging structures to integrate both intra- and inter-modal interactions improves multimodal understanding beyond treating them as a standalone modality. Experiments on both generative and discriminative tasks show that Graph4MM outperforms larger VLMs, LLMs, and multimodal graph baselines, achieving a 6.93% average improvement.

$E(3)$-equivariant neural networks have demonstrated success across a wide range of 3D modelling tasks. A fundamental operation in these networks is the tensor product, which interacts two geometric features in an equivariant manner to create new features. Due to the high computational complexity of the tensor product, significant effort has been invested to optimize the runtime of this operation. For example, Luo et al. (2024) recently proposed the Gaunt tensor product (GTP) which promises a significant speedup. In this work, we provide a careful, systematic analysis of a number of tensor product operations. In particular, we emphasize that different tensor products are not performing the same operation. The reported speedups typically come at the cost of expressivity. We introduce measures of expressivity and interactability to characterize these differences. In addition, we realized the original implementation of GTP can be greatly simplified by directly using a spherical grid at no cost in asymptotic runtime. This spherical grid approach is faster on our benchmarks and in actual training of the MACE interatomic potential by 30\%. Finally, we provide the first systematic microbenchmarks of the various tensor product operations. We find that the theoretical runtime guarantees can differ wildly from empirical performance, demonstrating the need for careful application-specific benchmarking. Code is available at https://github.com/atomicarchitects/PriceofFreedom

Accurate predictions rely on the expressiveness power of graph deep learning frameworks like graph neural networks and graph transformers, where a positional encoding mechanism has become much more indispensable in recent state-of-the-art (SOTA) works to record the canonical position information. However, the current positional encoding limits in three aspects, at least: (1) most positional encodings are pre-defined, and fixed functions, which are inadequate to adapt to the complex attributed graphs; (2) a few pioneering works propose the learnable positional encoding but still limited to the structural information, leaving the real-world time-evolving topological and feature information untouched; (3) most positional encodings should be equipped with transformer's attention mechanism to fully release the power, where the dense or relational attention is often unaffordable on large-scale structured data. Hence, we study the possibility of Learnable Spatial-Temporal Positional Encoding in an effective and efficient manner and then propose a simple temporal link prediction model named L-STEP. Briefly, for L-STEP, we (1) prove the proposed positional learning scheme can preserve the graph property from the spatial-temporal spectral viewpoint, (2) verify that MLPs can fully exploit the expressiveness and reach Transformers' performance on that encoding, (3) change different initial positional encoding inputs to show robustness, (4) analyze the theoretical complexity and obtain less empirical running time than SOTA, and (5) demonstrate its temporal link prediction out-performance on 13 classic datasets and with 10 algorithms in both transductive and inductive settings using 3 different sampling strategies. Also, L-STEP obtains the leading performance in the newest large-scale TGB benchmark.

Large Language Models (LLMs) have demonstrated remarkable potential in scientific domains, yet a fundamental question remains unanswered: Can we simulate human research communities with LLMs? Addressing this question can deepen our understanding of the processes behind idea brainstorming and inspire the automatic discovery of novel scientific insights. In this work, we propose ResearchTown, a multi-agent framework for research community simulation. Within this framework, the human research community is simplified as an agent-data graph, where researchers and papers are represented as agent-type and data-type nodes, respectively, and connected based on their collaboration relationships. We also introduce TextGNN, a text-based inference framework that models various research activities (e.g., paper reading, paper writing, and review writing) as special forms of a unified message-passing process on the agent-data graph. To evaluate the quality of the research community simulation, we present ResearchBench, a benchmark that uses a node-masking prediction task for scalable and objective assessment based on similarity. Our experiments reveal three key findings: (1) ResearchTown can provide a realistic simulation of collaborative research activities, including paper writing and review writing; (2) ResearchTown can maintain robust simulation with multiple researchers and diverse papers; (3) ResearchTown can generate interdisciplinary research ideas that potentially inspire pioneering research directions.

Federated Graph Learning (FGL) has gained significant attention as a privacy-preserving approach to collaborative learning, but the computational demands increase substantially as datasets grow and Graph Neural Network (GNN) layers deepen. To address these challenges, we propose $\textbf{EAGLES}$, a unified sparsification framework. EAGLES applies client-consensus parameter sparsification to generate multiple unbiased subnetworks at varying sparsity levels, reducing the need for iterative adjustments and mitigating performance degradation. In the graph structure domain, we introduced a dual-expert approach: a $\textit{graph sparsification expert}$ uses multi-criteria node-level sparsification, and a $\textit{graph synergy expert}$ integrates contextual node information to produce optimal sparse subgraphs. Furthermore, the framework introduces a novel distance metric that leverages node contextual information to measure structural similarity among clients, fostering effective knowledge sharing. We also introduce the $\textbf{Harmony Sparsification Principle}$, EAGLES balances model performance with lightweight graph and model structures. Extensive experiments demonstrate its superiority, achieving competitive performance on various datasets, such as reducing training FLOPS by 82\% $\downarrow$ and communication costs by 80\% $\downarrow$ on the ogbn-proteins dataset, while maintaining high performance.

Shallow node embeddings like node2vec (N2V) can be used for nodes without features or to supplement existing features with structure-based information. Embedding methods like N2V are limited in their application on new nodes, which restricts them to the transductive setting where the entire graph, including the test nodes, is available during training. We propose inductive node2vec (iN2V), which combines a post-hoc procedure to compute embeddings for nodes unseen during training and modifications to the original N2V training procedure to prepare the embeddings for this post-hoc procedure. We conduct experiments on several benchmark datasets and demonstrate that iN2V is an effective approach to bringing transductive embeddings to an inductive setting. Using iN2V embeddings improves node classification by 1 point on average, with up to 6 points of improvement depending on the dataset and the number of unseen nodes. Our iN2V is a plug-in approach to create new or enrich existing embeddings. It can also be combined with other embedding methods, making it a versatile approach for inductive node representation learning. Code to reproduce the results is available at https://github.com/Foisunt/iN2V.

Multi-view clustering has gained significant attention for integrating multi-view information in multimedia applications. With the growing complexity of graph data, multi-view graph clustering (MVGC) has become increasingly important. Existing methods primarily use Graph Neural Networks (GNNs) to encode structural and feature information, but applying GNNs within contrastive learning poses specific challenges, such as integrating graph data with node features and handling both homophilic and heterophilic graphs. To address these challenges, this paper introduces Node-Guided Contrastive Encoding (NGCE), a novel MVGC approach that leverages node features to guide embedding generation. NGCE enhances compatibility with GNN filtering, effectively integrates homophilic and heterophilic information, and strengthens contrastive learning across views. Extensive experiments demonstrate its robust performance on six homophilic and heterophilic multi-view benchmark datasets.

Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design for GNNs remains impoverished. In this paper, we consider the benefits of architectures that maintain and update edge embeddings. On the theoretical front, under a suitable computational abstraction for a layer in the model, as well as memory constraints on the embeddings, we show that there are natural tasks on graphical models for which architectures leveraging edge embeddings can be much shallower. Our techniques are inspired by results on time-space tradeoffs in theoretical computer science. Empirically, we show architectures that maintain edge embeddings almost always improve on their node-based counterparts---frequently significantly so in topologies that have "hub" nodes.

Dynamic graphs evolve continuously, presenting challenges for traditional graph learning due to their changing structures and temporal dependencies. Recent advancements have shown potential in addressing these challenges by developing suitable meta-learning-based dynamic graph neural network models. However, most meta-learning approaches for dynamic graphs rely on fixed weight update parameters, neglecting the essential intrinsic complex high-order topological information of dynamically evolving graphs. We have designed Dowker Zigzag Persistence (DZP), an efficient and stable dynamic graph persistent homology representation method based on Dowker complex and zigzag persistence, to capture the high-order features of dynamic graphs. Armed with the DZP ideas, we propose TMetaNet, a new meta-learning parameter update model based on dynamic topological features. By utilizing the distances between high-order topological features, TMetaNet enables more effective adaptation across snapshots. Experiments on real-world datasets demonstrate TMetaNet's state-of-the-art performance and resilience to graph noise, illustrating its high potential for meta-learning and dynamic graph analysis. Our code is available at https://github.com/Lihaogx/TMetaNet.

The distribution shifts and the scarcity of labels prevent graph learning methods, especially graph neural networks (GNNs), from generalizing across domains. Compared to Unsupervised Domain Adaptation (UDA) with embedding alignment, Unsupervised Graph Domain Adaptation (UGDA) becomes more challenging in light of the attribute and topology entanglement in the representation. Beyond embedding alignment, UGDA turns to topology alignment but is limited by the ability of the employed topology model and the estimation of pseudo labels. To alleviate this issue, this paper proposed a Disentangled Graph Spectral Domain adaptation (DGSDA) by disentangling attribute and topology alignments and directly aligning flexible graph spectral filters beyond topology. Specifically, Bernstein polynomial approximation, which mimics the behavior of the function to be approximated to a remarkable degree, is employed to capture complicated topology characteristics and avoid the expensive eigenvalue decomposition. Theoretical analysis reveals the tight GDA bound of DGSDA and the rationality of polynomial coefficient regularization. Quantitative and qualitative experiments justify the superiority of the proposed DGSDA.

In this work, we address the test-time adaptation challenge in graph neural networks (GNNs), focusing on overcoming the limitations in flexibility and generalization inherent in existing data-centric approaches. To this end, we propose a novel research problem, test-time graph neural dataset search, which seeks to learn a parameterized test-time graph distribution to enhance the inference performance of unseen test graphs on well-trained GNNs. Specifically, we propose a generative Projection based test-time Graph Neural Dataset Search method, named PGNDS, which maps the unseen test graph distribution back to the known training distribution through a generation process guided by well-trained GNNs. The proposed PGNDS framework consists of three key modules: (1) dual conditional diffusion for GNN-guided generative projection through test-back-to-training distribution mapping; (2) dynamic search from the generative sampling space to select the most expressive test graphs; (3) ensemble inference to aggregate information from original and adapted test graphs. Extensive experiments on real-world graphs demonstrate the superior ability of our proposed PGNDS for improved test-time GNN inference.

Graph Neural Ordinary Differential Equations (GODE) integrate the Variational Autoencoder (VAE) framework with differential equations, effectively modeling latent space uncertainty and continuous dynamics, excelling in graph data evolution and incompleteness. However, existing GODE face challenges in capturing time-varying relationships and nonlinear node state evolution, which limits their ability to model complex dynamic graphs. To address these issues, we propose the ControlSynth Graph ODE (CSG-ODE). In the VAE encoding phase, CSG-ODE introduces an information transmission-based inter-node importance weighting mechanism, integrating it with latent correlations to guide adaptive graph convolutional recurrent networks for temporal node embedding. During decoding, CSG-ODE employs ODE to model node dynamics, capturing nonlinear evolution through sub-networks with nonlinear activations. For scenarios or prediction tasks that require stability, we extend CSG-ODE to stable CSG-ODE (SCSG-ODE) by constraining weight matrices to learnable anti-symmetric forms, theoretically ensuring enhanced stability. Experiments on traffic, motion capture, and simulated physical systems datasets demonstrate that CSG-ODE outperforms state-of-the-art GODE, while SCSG-ODE achieves both superior performance and optimal stability.

Subgraph representation learning has attracted growing interest due to its wide applications in various domains. However, existing methods primarily focus on local neighborhood structures while overlooking the significant impact of global structural information, in particular the influence of multi-hop neighbors beyond immediate neighborhoods. This presents two key challenges: how to effectively capture the structural relationships between distant nodes, and how to prevent excessive aggregation of global structural information from weakening the discriminative ability of subgraph representations. To address these challenges, we propose GPEN (Global Position Encoding Network). GPEN leverages a hierarchical tree structure to encode each node's global position based on its path distance to the root node, enabling a systematic way to capture relationships between distant nodes. Furthermore, we introduce a boundary-aware convolution module that selectively integrates global structural information while maintaining the unique structural patterns of each subgraph. Extensive experiments on eight public datasets identify that GPEN significantly outperforms state-of-the-art methods in subgraph representation learning.