ICLR 2025 Papers

Despite the progress in quantum computing, one major bottleneck against the practical utility is its susceptibility to noise, which frequently occurs in current quantum systems. Existing quantum error mitigation (QEM) methods either lack generality to noise and circuit types or fail to capture the global dependencies of entire systems in addition to circuit structure. In this work, we first propose a unique circuit-to-graph encoding scheme with qubit-wise noisy measurement aggregated. Then, we introduce GTranQEM, a non-message passing graph transformer designed to mitigate errors in expected circuit measurement outcomes effectively. GTranQEM is equipped with a quantum-specific positional encoding, a structure matrix as attention bias guiding nonlocal aggregation, and a virtual quantum-representative node to further grasp graph representations, which guarantees to model the long-range entanglement. Experimental evaluations demonstrate that GTranQEM outperforms state-of-the-art QEM methods on both random and structured quantum circuits across noise types and scales among diverse settings.

Self-supervised learning (SSL) has shown great potential in learning generalizable representations for graph-structured data. However, existing SSL-based graph pre-training methods largely focus on improving graph representations by learning the structure information based on disturbing or reconstructing graphs, which ignores an important issue: the importance of different nodes in the graph structure may vary. To fill this gap, we propose a Centrality-guided Graph Pre-training (CenPre) framework to integrate the distinct importance of nodes in graph structure into the corresponding representations of nodes based on the centrality in graph theory. In this way, the different roles played by different nodes can be effectively leveraged when learning graph structure. The proposed CenPre contains three modules for node representation pre-training and alignment. The node-level importance learning module fuses the fine-grained node importance into node representation based on degree centrality, allowing the aggregation of node representations with equal/similar importance. The graph-level importance learning module characterizes the importance between all nodes in the graph based on eigenvector centrality, enabling the exploitation of graph-level structure similarities/differences when learning node representation. Finally, a representation alignment module aligns the pre-trained node representation using the original one, essentially allowing graph representations to learn structural information without losing their original semantic information, thereby leading to better graph representations. Extensive experiments on a series of real-world datasets demonstrate that the proposed CenPre outperforms the state-of-the-art baselines in the tasks of node classification, link prediction, and graph classification.

Predicting the ground-state 3D molecular conformations from 2D molecular graphs is critical in computational chemistry due to its profound impact on molecular properties. Deep learning (DL) approaches have recently emerged as promising alternatives to computationally-heavy classical methods such as density functional theory (DFT). However, we discover that existing DL methods inadequately model inter-atomic forces, particularly for non-bonded atomic pairs, due to their naive usage of bonds and pairwise distances. Consequently, significant prediction errors occur for atoms with low degree (ie., low coordination numbers) whose conformations are primarily influenced by non-bonded interactions. To address this, we propose ReBIND, a novel framework that rewires molecular graphs by adding edges based on the Lennard-Jones potential to capture non-bonded interactions for low-degree atoms. Experimental results demonstrate that ReBIND significantly outperforms state-of-the-art methods across various molecular sizes, achieving up to a 20% reduction in prediction error. The code is available in: https://github.com/holymollyhao/ReBIND

Recently, graph invariant learning has become the _de facto_ approach to tackle the Out-of-Distribution (OOD) generalization failure in graph representation learning. They generically follow the framework of invariant risk minimization to capture the invariance of graph data from different environments. Despite some success, it remains unclear to what extent existing approaches have captured invariant features for OOD generalization on graphs. In this work, we find that representative OOD methods such as IRM and VRex, and their variants on graph invariant learning may have captured a limited set of invariant features. To tackle this challenge, we propose $\texttt{LIRS}$, a novel learning framework designed to **L**earn graph **I**nvariance by **R**emoving **S**purious features. Different from most existing approaches that _directly_ learn the invariant features, $\texttt{LIRS}$ takes an _indirect_ approach by first learning the spurious features and then removing them from the ERM-learned features, which contains both spurious and invariant features. We demonstrate that learning the invariant graph features in an _indirect_ way can learn a more comprehensive set of invariant features. Moreover, our proposed method outperforms the second-best method by as much as 25.50% across all competitive baseline methods, highlighting its effectiveness in learning graph invariant features.

Preconditioning is at the heart of iterative solutions of large, sparse linear systems of equations in scientific disciplines. Several algebraic approaches, which access no information beyond the matrix itself, are widely studied and used, but ill-conditioned matrices remain very challenging. We take a machine learning approach and propose using graph neural networks as a general-purpose preconditioner. They show attractive performance for many problems and can be used when the mainstream preconditioners perform poorly. Empirical evaluation on over 800 matrices suggests that the construction time of these graph neural preconditioners (GNPs) is more predictable and can be much shorter than that of other widely used ones, such as ILU and AMG, while the execution time is faster than using a Krylov method as the preconditioner, such as in inner-outer GMRES. GNPs have a strong potential for solving large-scale, challenging algebraic problems arising from not only partial differential equations, but also economics, statistics, graph, and optimization, to name a few.

Topological deep learning (TDL) has emerged as a powerful tool for modeling higher-order interactions in relational data. However, phenomena such as oversquashing in topological message-passing remain understudied and lack theoretical analysis. We propose a unifying axiomatic framework that bridges graph and topological message-passing by viewing simplicial and cellular complexes and their message-passing schemes through the lens of relational structures. This approach extends graph-theoretic results and algorithms to higher-order structures, facilitating the analysis and mitigation of oversquashing in topological message-passing networks. Through theoretical analysis and empirical studies on simplicial networks, we demonstrate the potential of this framework to advance TDL.

Graph Convolutional Networks (GCNs) have emerged as powerful tools for learning on graph-structured data, yet the behavior of dropout in these models remains poorly understood. This paper presents a comprehensive theoretical analysis of dropout in GCNs, revealing that its primary role differs fundamentally from standard neural networks - preventing oversmoothing rather than co-adaptation. We demonstrate that dropout in GCNs creates dimension-specific stochastic sub-graphs, leading to a form of structural regularization not present in standard neural networks. Our analysis shows that dropout effects are inherently degree-dependent, resulting in adaptive regularization that considers the topological importance of nodes. We provide new insights into dropout's role in mitigating oversmoothing and derive novel generalization bounds that account for graph-specific dropout effects. Furthermore, we analyze the synergistic interaction between dropout and batch normalization in GCNs, uncovering a mechanism that enhances overall regularization. Our theoretical findings are validated through extensive experiments on both node-level and graph-level tasks across 14 datasets. Notably, GCN with dropout and batch normalization outperforms state-of-the-art methods on several benchmarks, demonstrating the practical impact of our theoretical insights.

This paper addresses the challenge of incremental learning in growing graphs with increasingly complex tasks. The goal is to continuously train a graph model to handle new tasks while retaining proficiency in previous tasks via memory replay. Existing methods usually overlook the importance of memory diversity, limiting in selecting high-quality memory from previous tasks and remembering broad previous knowledge within the scarce memory on graphs. To address that, we introduce a novel holistic Diversified Memory Selection and Generation (DMSG) framework for incremental learning in graphs, which first introduces a buffer selection strategy that considers both intra-class and inter-class diversities, employing an efficient greedy algorithm for sampling representative training nodes from graphs into memory buffers after learning each new task. Then, to adequately rememorize the knowledge preserved in the memory buffer when learning new tasks, a diversified memory generation replay method is introduced. This method utilizes a variational layer to generate the distribution of buffer node embeddings and sample synthesized ones for replaying. Furthermore, an adversarial variational embedding learning method and a reconstruction-based decoder are proposed to maintain the integrity and consolidate the generalization of the synthesized node embeddings, respectively. Extensive experimental results on publicly accessible datasets demonstrate the superiority of DMSG over state-of-the-art methods.

Despite extensive research efforts focused on Out-of-Distribution (OOD) detection on images, OOD detection on nodes in graph learning remains underexplored. The dependence among graph nodes hinders the trivial adaptation of existing approaches on images that assume inputs to be i.i.d. sampled, since many unique features and challenges specific to graphs are not considered, such as the heterophily issue. Recently, GNNSafe, which considers node dependence, adapted energy-based detection to the graph domain with state-of-the-art performance, however, it has two serious issues: 1) it derives node energy from classification logits without specifically tailored training for modeling data distribution, making it less effective at recognizing OOD data; 2) it highly relies on energy propagation, which is based on homophily assumption and will cause significant performance degradation on heterophilic graphs, where the node tends to have dissimilar distribution with its neighbors. To address the above issues, we suggest training Energy-based Models (EBMs) by Maximum Likelihood Estimation (MLE) to enhance data distribution modeling and removing energy propagation to overcome the heterophily issues. However, training EBMs via MLE requires performing Markov Chain Monte Carlo (MCMC) sampling on both node feature and node neighbors, which is challenging due to the node interdependence and discrete graph topology. To tackle the sampling challenge, we introduce Decoupled Graph Energy-based Model (DeGEM), which decomposes the learning process into two parts—a graph encoder that leverages topology information for node representations and an energy head that operates in latent space. Additionally, we propose a Multi-Hop Graph encoder (MH) and Energy Readout (ERo) to enhance node representation learning, Conditional Energy (CE) for improved EBM training, and Recurrent Update for the graph encoder and energy head to promote each other. This approach avoids sampling adjacency matrices and removes the need for energy propagation to extract graph topology information. Extensive experiments validate that DeGEM, without OOD exposure during training, surpasses previous state-of-the-art methods, achieving an average AUROC improvement of 6.71% on *homophilic* graphs and 20.29% on *heterophilic* graphs, and even outperform methods trained with OOD exposure. Our code is available at: [https://github.com/draym28/DeGEM](https://github.com/draym28/DeGEM).

Graph neural networks (GNNs) have recently emerged as powerful tools for solving complex optimization problems, often being employed to approximate solution mappings. Empirical evidence shows that even shallow GNNs (with fewer than ten layers) can achieve strong performance in predicting optimal solutions to linear programming (LP) problems. This finding is somewhat counter-intuitive, as LPs are global optimization problems, while shallow GNNs predict based on local information. Although previous theoretical results suggest that GNNs have the expressive power to solve LPs, they require deep architectures whose depth grows at least polynomially with the problem size, and thus leave the underlying principle of this empirical phenomenon still unclear. In this paper, we examine this phenomenon through the lens of distributed computing and average-case analysis. We establish that the expressive power of GNNs for LPs is closely related to well-studied distributed algorithms for LPs. Specifically, we show that any $d$-round distributed LP algorithm can be simulated by a $d$-depth GNN, and vice versa. In particular, by designing a new distributed LP algorithm and then unrolling it, we prove that constant-depth, constant-width GNNs suffice to solve sparse binary LPs effectively. Here, in contrast with previous analyses focusing on worst-case scenarios, in which we show that GNN depth must increase with problem size by leveraging an impossibility result about distributed LP algorithms, our analysis shifts the focus to the average-case performance, and shows that constant GNN depth then becomes sufficient no matter how large the problem size is. Our theory is validated by numerical results.

Subgraph representation learning has been effective in solving various real-world problems. However, current graph neural networks (GNNs) produce suboptimal results for subgraph-level tasks due to their inability to capture complex interactions within and between subgraphs. To provide a more expressive and efficient alternative, we propose WLKS, a Weisfeiler-Lehman (WL) kernel generalized for subgraphs by applying the WL algorithm on induced $k$-hop neighborhoods. We combine kernels across different $k$-hop levels to capture richer structural information that is not fully encoded in existing models. Our approach can balance expressiveness and efficiency by eliminating the need for neighborhood sampling. In experiments on eight real-world and synthetic benchmarks, WLKS significantly outperforms leading approaches on five datasets while reducing training time, ranging from 0.01x to 0.25x compared to the state-of-the-art.

When reading a document, glancing at the spatial layout of a document is an initial step to understand it roughly. Traditional document layout analysis (DLA) methods, however, offer only a superficial parsing of documents, focusing on basic instance detection and often failing to capture the nuanced spatial and logical relationships between instances. These limitations hinder DLA-based models from achieving a gradually deeper comprehension akin to human reading. In this work, we propose a novel graph-based Document Structure Analysis (gDSA) task. This task requires that model not only detects document elements but also generates spatial and logical relations in form of a graph structure, allowing to understand documents in a holistic and intuitive manner. For this new task, we construct a relation graph-based document structure analysis dataset(GraphDoc) with 80K document images and 4.13M relation annotations, enabling training models to complete multiple tasks like reading order, hierarchical structures analysis, and complex inter-element relationship inference. Furthermore, a document relation graph generator (DRGG) is proposed to address the gDSA task, which achieves performance with 57.6% at $mAP_g$@$0.5$ for a strong benchmark baseline on this novel task and dataset. We hope this graphical representation of document structure can mark an innovative advancement in document structure analysis and understanding. The new dataset and code will be made publicly available.

Benchmarking the capabilities and limitations of large language models (LLMs) in graph-related tasks is becoming an increasingly popular and crucial area of research. Recent studies have shown that LLMs exhibit a preliminary ability to understand graph structures and node features. However, the potential of LLMs in graph pattern mining remains largely unexplored. This is a key component in fields such as computational chemistry, biology, and social network analysis. To bridge this gap, this work introduces a comprehensive benchmark to assess LLMs' capabilities in graph pattern tasks. We have developed a benchmark that evaluates whether LLMs can understand graph patterns based on either terminological or topological descriptions. Additionally, our benchmark tests the LLMs' capacity to autonomously discover graph patterns from data. The benchmark encompasses both synthetic and real datasets, and a variety of models, with a total of 11 tasks and 7 models. Our experimental framework is designed for easy expansion to accommodate new models and datasets. Our findings reveal that: (1) LLMs have preliminary abilities to understand graph patterns, with O1-mini outperforming in the majority of tasks; (2) Formatting input graph data to align with the knowledge acquired during pretraining can enhance performance; (3) LLMs employ diverse potential algorithms to solve one task, with performance varying based on their execution capabilities.

Most existing graph diffusion models have significant bias problems. We observe that the forward diffusion’s maximum perturbation distribution in most models deviates from the standard Gaussian distribution, while reverse sampling consistently starts from a standard Gaussian distribution, which results in a reverse-starting bias. Together with the inherent exposure bias of diffusion models, this results in degraded generation quality. This paper proposes a comprehensive approach to mitigate both biases. To mitigate reverse-starting bias, we employ a newly designed Langevin sampling algorithm to align with the forward maximum perturbation distribution, establishing a new reverse-starting point. To address the exposure bias, we introduce a score correction mechanism based on a newly defined score difference. Our approach, which requires no network modifications, is validated across multiple models, datasets, and tasks, achieving state-of-the-art results.

Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into a vector, known as polyhedra representation learning, is crucial for manipulating these shapes with mathematical and statistical tools for tasks like classification, clustering, and generation. Recent years have witnessed significant strides in this domain, yet most efforts focus on the vertex sequence of a polyhedron, neglecting the complex surface modeling crucial in real-world polyhedral objects. This study proposes \textbf{PolyhedronNet}, a general framework tailored for learning representations of 3D polyhedral objects. We propose the concept of the surface-attributed graph to seamlessly model the vertices, edges, faces, and their geometric interrelationships within a polyhedron. To effectively learn the representation of the entire surface-attributed graph, we first propose to break it down into local rigid representations to effectively learn each local region's relative positions against the remaining regions without geometric information loss. Subsequently, we propose PolyhedronGNN to hierarchically aggregate the local rigid representation via intra-face and inter-face geometric message passing modules, to obtain a global representation that minimizes information loss while maintaining rotation and translation invariance. Our experimental evaluations on four distinct datasets, encompassing both classification and retrieval tasks, substantiate PolyhedronNet's efficacy in capturing comprehensive and informative representations of 3D polyhedral objects.

The "pre-train, prompt-tuning'' paradigm has demonstrated impressive performance for tuning pre-trained heterogeneous graph neural networks (HGNNs) by mitigating the gap between pre-trained models and downstream tasks. However, most prompt-tuning-based works may face at least two limitations: (i) the model may be insufficient to fit the graph structures well as they are generally ignored in the prompt-tuning stage, increasing the training error to decrease the generalization ability; and (ii) the model may suffer from the limited labeled data during the prompt-tuning stage, leading to a large generalization gap between the training error and the test error to further affect the model generalization. To alleviate the above limitations, we first derive the generalization error bound for existing prompt-tuning-based methods, and then propose a unified framework that combines two new adapters with potential labeled data extension to improve the generalization of pre-trained HGNN models. Specifically, we design dual structure-aware adapters to adaptively fit task-related homogeneous and heterogeneous structural information. We further design a label-propagated contrastive loss and two self-supervised losses to optimize dual adapters and incorporate unlabeled nodes as potential labeled data. Theoretical analysis indicates that the proposed method achieves a lower generalization error bound than existing methods, thus obtaining superior generalization ability. Comprehensive experiments demonstrate the effectiveness and generalization of the proposed method on different downstream tasks.

Pre-training powerful Graph Neural Networks (GNNs) with unlabeled graph data in a self-supervised manner has emerged as a prominent technique in recent years. However, inevitable objective gaps often exist between pre-training and downstream tasks. To bridge this gap, graph prompt tuning techniques design and learn graph prompts by manipulating input graphs or reframing downstream tasks as pre-training tasks without fine-tuning the pre-trained GNN models. While recent graph prompt tuning methods have proven effective in adapting pre-trained GNN models for downstream tasks, they overlook the crucial role of edges in graph prompt design, which can significantly affect the quality of graph representations for downstream tasks. In this study, we propose EdgePrompt, a simple yet effective graph prompt tuning method from the perspective of edges. Unlike previous studies that design prompt vectors on node features, EdgePrompt manipulates input graphs by learning additional prompt vectors for edges and incorporates the edge prompts through message passing in the pre-trained GNN models to better embed graph structural information for downstream tasks. Our method is compatible with prevalent GNN architectures pre-trained under various pre-training strategies and is universal for different downstream tasks. We provide comprehensive theoretical analyses of our method regarding its capability of handling node classification and graph classification as downstream tasks. Extensive experiments on ten graph datasets under four pre-training strategies demonstrate the superiority of our proposed method against six baselines. Our code is available at https://github.com/xbfu/EdgePrompt.

Deep generative models have recently achieved significant success in modeling graph data, including dynamic graphs, where topology and features evolve over time. However, unlike in vision and natural language domains, evaluating generative models for dynamic graphs is challenging due to the difficulty of visualizing their output, making quantitative metrics essential. In this work, we develop a new quality metric for evaluating generative models of dynamic graphs. Current metrics for dynamic graphs typically involve discretizing the continuous-evolution of graphs into static snapshots and then applying conventional graph similarity measures. This approach has several limitations: (a) it models temporally related events as i.i.d. samples, failing to capture the non-uniform evolution of dynamic graphs; (b) it lacks a unified measure that is sensitive to both features and topology; (c) it fails to provide a scalar metric, requiring multiple metrics without clear superiority; and (d) it requires explicitly instantiating each static snapshot, leading to impractical runtime demands that hinder evaluation at scale. We propose a novel metric based on the Johnson-Lindenstrauss lemma, applying random projections directly to dynamic graph data. This results in an expressive, scalar, and application-agnostic measure of dynamic graph similarity that overcomes the limitations of traditional methods. We also provide a comprehensive empirical evaluation of metrics for continuous-time dynamic graphs, demonstrating the effectiveness of our approach compared to existing methods. Our implementation is available at https://github.com/ryienh/jl-metric.

Graph Neural Networks (GNNs) have demonstrated remarkable performance in various graph-based machine learning tasks, yet evaluating the importance of neighbors of testing nodes remains largely unexplored due to the challenge of assessing data importance without test labels. To address this gap, we propose Shapley-Guided Utility Learning (SGUL), a novel framework for graph inference data valuation. SGUL innovatively combines transferable data-specific and modelspecific features to approximate test accuracy without relying on ground truth labels. By incorporating Shapley values as a preprocessing step and using feature Shapley values as input, our method enables direct optimization of Shapley value prediction while reducing computational demands. SGUL overcomes key limitations of existing methods, including poor generalization to unseen test-time structures and indirect optimization. Experiments on diverse graph datasets demonstrate that SGUL consistently outperforms existing baselines in both inductive and transductive settings. SGUL offers an effective, efficient, and interpretable approach for quantifying the value of test-time neighbors.