ICML 2026 论文列表

Graph generation is a fundamental task with broad applications, such as drug discovery. Recently, discrete flow matching-based graph generation, a.k.a., graph flow model (GFM), has emerged due to its superior performance and flexible sampling. However, effectively aligning GFMs with complex human preferences or task-specific objectives remains a significant challenge. In this paper, we propose Graph-GRPO, an online reinforcement learning (RL) framework for training GFMs under verifiable rewards. Our method makes two key contributions: (1) We derive an analytical expression for the transition probability of GFMs, replacing the Monte Carlo sampling and enabling fully differentiable rollouts for RL training; (2) We propose a refinement strategy that randomly perturbs specific nodes and edges in a graph, and regenerates them, allowing for localized exploration and self-improvement of generation quality. Extensive experiments on both synthetic and real datasets demonstrate the effectiveness of Graph-GRPO. With only 50 denoising steps, our method achieves 95.0\% and 97.5\% Valid-Unique-Novelty scores on the planar and tree datasets, respectively. Moreover, Graph-GRPO achieves state-of-the-art performance on the molecular optimization tasks, outperforming graph-based and fragment-based RL methods as well as classic genetic algorithms. Code is available in https://github.com/Zhubaoheng/Graph-GRPO.

Graph Foundation Models (GFMs), built upon the *Pre-training and Adaptation* paradigm, have emerged as a research hotspot in graph learning. For GNN-based GFMs, graph prompt tuning has become the prevailing adaptation method for downstream tasks. Although recent methods explain why graph prompt tuning works, how to rigorously measure its adaptation capacity remains an open problem. Addressing this problem is critical for understanding the capability limits of graph prompt tuning and for developing more powerful adaptation methods. In this paper, we propose Prismatic Space Theory (PS-Theory), a novel mathematical framework to quantify the capacity of adaptation methods, while focusing on establishing the upper bound for the adaptation capacity of graph prompt tuning. Building upon the proposed PS-Theory, we further introduce **M**essage **T**uning for **G**FMs (MTG), a lightweight approach that injects a small set of learnable message prototypes into each layer of the GNN backbone to adaptively guide message fusion without updating pre-trained weights. Through our PS-Theory, we prove that the adaptation capacity of MTG can exceed the theoretical upper bound of graph prompt tuning. Extensive experiments demonstrate that MTG consistently outperforms graph prompt baselines across diverse benchmark datasets, providing strong empirical support for our theoretical findings.

Generalizing pretrained models to unseen datasets without retraining is a central challenge toward foundation models. Achieving fully inductive inference on numerical data is particularly difficult due to large variations in feature dimensionality and semantics across datasets. We observe that, in the presence of graph structure, numerical data admits a distinct structure-induced representational axis beyond the feature space, which we formalize as the *view space*. This view space enables a unified representation of graphs with heterogeneous features and motivates *Graph View Transformation* (GVT), a class of parametric mappings that can be shared across arbitrary graphs. We instantiate this framework with Recurrent GVT, an architecture for fully inductive node representation learning in node classification. Pretrained on OGBN-Arxiv and evaluated on 27 benchmarks, Recurrent GVT outperforms GraphAny, the prior fully inductive graph model, by +8.93%, and surpasses 12 individually tuned GNNs by at least +3.30%. These results establish the view space as a principled and practical foundation for learning across graphs with heterogeneous feature spaces. Code and checkpoints are available in https://github.com/dooho00/graph-view-space.

Extending traditional graph anomaly detection (GAD) from one-for-one to one-for-all paradigms, generalist GAD aims to learn a universal detector for identifying anomalies on unseen graphs without graph-specific retraining. Nevertheless, existing approaches primarily focus on aligning heterogeneous features across different data domains via PCA-based projection, which harmonizes feature dimensions but neglects semantic alignment. As a result, GAD models fail to acquire semantically transferable knowledge from source-domain pre-training, and even exhibit negative transfer on unseen graphs. To address this issue, we propose a Relational Fingerprint-based generalist GAD approach (REFI-GAD for short), aligning heterogeneous raw features with a universal and semantics-aware relational fingerprint (REFI) that encodes anomaly-indicative cues from both contextual and structural perspectives. Building on REFI, we design a fingerprint-grounded generalist GAD model, which combines a transformer-based encoder to capture domain-invariant knowledge with an SNR-guided refinement module for domain-specific adaptation. Extensive experiments on 14 datasets demonstrate that REFI-GAD significantly outperforms state-of-the-art methods.

Spectral clustering is hindered by its $O(n^{3})$ time complexity, and although anchor-based approximations reduce this to $O(nm^{2})$ ($m \ll n$), they often yield degenerate or unbalanced partitions in the absence of explicit cluster-size control. To address this limitation, we propose \textbf{SC-FAGC (Size-Constrained Fast Anchor Graph Clustering)}, a unified formulation that integrates entropy regularization and bilateral cardinality constraints within an anchor-based spectral clustering framework, enforcing user-specified lower and upper bounds on anchor-level cluster sizes to avoid trivial or highly unbalanced solutions. To solve the resulting non-convex problem efficiently, we develop an \textbf{Iteratively Re-weighted (IRW)} optimization scheme that linearizes the objective and solves each subproblem via a \textbf{Double-Bounded Optimal Transport (DB-OT)} solver based on the \textbf{Sinkhorn--Knopp} algorithm, guaranteeing convergence while maintaining scalability. Extensive experiments on benchmark datasets demonstrate that SC-FAGC consistently achieves state-of-the-art performance across six standard clustering metrics while strictly enforcing the prescribed anchor-level constraints. Moreover, it induces effective data-level size control after label transmission, offering a principled and scalable solution for large-scale graph clustering with controllable partition structure.

Message-passing neural networks (MPNNs) often suffer from an information bottleneck when capturing long-range dependencies, leading to the oversquashing (OSQ) phenomenon. Alongside spatial connectivity enrichment (e.g., rewiring), recent studies have shown that spectral filtering can yield strong long-range learning outcomes, as spectral operators enable global information mixing that alleviates OSQ. These approaches achieve this either by stabilizing the Jacobian energies in deep propagation or by guaranteeing OSQ mitigation under strong theoretical assumptions. We examine the practical attainability of these guarantees and show that the associated Jacobian sensitivity lower bound is generally difficult to achieve in practice. We then propose S$^3$GNN, which mitigates OSQ without such restrictive assumptions by lightweightly reintroducing omitted components with substantially lower computational complexity, while standard stability constraints on feature transformations remain effective under our new dynamics. Extensive experiments across diverse domains (e.g., long-range benchmarks, KGQA, and mesh-based fluid dynamics) demonstrate that S$^3$GNN achieves up to an order-of-magnitude error reduction with up to 50\% fewer parameters. Our code can be found in https://github.com/EEthanShi/S3-GNN.git.

Supervised Graph Outlier Detection has long been constrained by severe class imbalance, and although recent diffusion-based augmentation methods have improved sample quality, their practical utility is hindered by the high computational costs of multi-step iterative sampling and the stochasticity of the generation process. To overcome these bottlenecks, we propose Graph Outlier Synthesis via Origin Consistency Model (GOCM), a single-step graph outlier synthesis framework based on a consistency model. Theoretically, we pioneer the Origin Consistency (OC) mechanism by employing an ``Interval-based Origin Inference'' strategy, which mathematically derives a direct mapping from the noise trajectory to the data origin, achieving robust and efficient single-step sample generation. Architecturally, to address the complexity of heterogeneous graphs containing multiple relations, we design the Multi-input Variational Graph Auto-Encoder (MiVGAE), which decouples intricate structures via relation-level message passing and cross-relation fusion, mapping them into a unified latent space, from which GOCM synthesizes high-quality outlier nodes. Extensive experiments on multiple real-world datasets demonstrate that GOCM achieves superior detection performance with significantly improved generation efficiency. The source code is publicly available at: https://anonymous.4open.science/r/RFS-2026-EB63/.

Multi-modal brain network analysis aims to predict neuropsychiatric status from functional connectomes with heterogeneous phenotypes. However, most existing methods treat phenotypes as auxiliary features and perform late fusion, implicitly assuming that the connectome representation should be learned in the same way regardless of phenotype. However, in clinical neuroscience the same functional connectivity pattern may support different conclusions under different phenotype contexts. To bridge this gap, we propose PhenoBrain, a novel framework for multi-modal brain network analysis that injects phenotype information at the mechanism level rather than only at the classifier level. Specifically, we propose a phenotype-conditioned long-range routing mechanism, which learns a subject-specific multi-hop communication kernel to model long-range connectome interactions. Furthermore, we propose a phenotypic-guided attention mechanism regulation method, which uses phenotypic information as a conditional prior to regulate the learning process of attention in brain networks. To verify the effectiveness of our method, we constructed two multi-modal brain network analysis datasets based on open-source image data. Extensive experiments demonstrate that PhenoBrain achieves state-of-the-art performance.

Recent studies show that Hypergraph Neural Networks (HGNNs) are vulnerable to adversarial attacks, while adversarial learning in the context of hypergraphs remains substantially under-investigated. In particular, all existing attacks on HGNNs are white-box and customized for either structural or feature perturbation. But in reality, the attacker might not have access to the target model parameters. Motivated by this knowledge gap, we propose a generic meta-objective-based learning framework, MeLA, that leverages the hypergraph Laplacian to conduct gray-box, structural, and feature perturbations under explicit perturbation budgets. In contrast to the attack literature, there is no adversarial training mechanism for HGNNs to defend against such attacks. Hence, we propose a novel adversarial training mechanism for HGNNs to obtain a robust classifier. We further prove the convergence of our robust training. Extensive experiments across various HGNN models and datasets show that (a) our proposed attack is effective in poisoning and evasion settings, and (b) our adversarial training enhances defense against adversarial attacks.

Designing high-performance neural networks for new tasks requires balancing optimization quality with search efficiency. Current methods fail to achieve this balance: neural architectural search is computationally expensive, while model retrieval often yields suboptimal static checkpoints. To resolve this dilemma, we model the performance gains induced by fine-grained architectural modifications as edit-effect evidence and build evidence graphs from prior tasks. By constructing a retrieval-augmented model refinement framework, our proposed M-DESIGN dynamically weaves historical evidence to discover near-optimal modification paths. M-DESIGN features an adaptive retrieval mechanism that quickly calibrates the evolving transferability of edit-effect evidence from different sources. To handle out-of-distribution shifts, we introduce predictive task planners that extrapolate gains from multi-hop evidence, thereby reducing reliance on an exhaustive repository. Based on our model knowledge base of 67,760 graph neural networks across 22 datasets, extensive experiments demonstrate that M-DESIGN consistently outperforms baselines, achieving the search-space best performance in 26 out of 33 cases under a strict budget.

Hypergraph contrastive learning is an effective paradigm for representation learning on higher-order relational data, yet existing methods largely ignore that hyperedges link nodes with multi-level semantics. Standard contrastive objectives emphasize instance discrimination via hyperspherical uniformity and tend to push embeddings apart in an indiscriminate manner. We show that this leads to a *Hierarchy–Uniformity Conflict*, whose geometric manifestation is *Semantic Flattening*, where the semantic depth of hyperedges collapses into a nearly flat cloud of instances. To address this issue, we introduce **HyperDepth**, a hypergraph contrastive learning framework that moves representations towards a hierarchy–uniformity equilibrium by jointly coordinating spectral and geometric signals. HyperDepth employs a decoupled spectral encoding scheme with adaptive gating so that high-frequency components focus on local instance discrimination while low-frequency components capture global hierarchical structure. On top of this, an energy-based hierarchical alignment module attaches a learnable prototype tree to the representation space and minimizes an interpretable energy functional to recover the semantic depth of hyperedges. Theoretically, under a mild frequency-separation assumption, we show that the local contrastive and global hierarchical objectives operate on orthogonal spectral components and admit equilibrium embeddings that preserve semantic depth while still retaining instance-level discrimination. Experiments on 15 hypergraph datasets and 17 supervised and self-supervised baselines, spanning homophilic and heterophilic regimes, show that HyperDepth attains strong performance with the best average rank.

Multi-domain graph pre-training is a crucial step in constructing foundational graph models with cross-domain generalization capabilities. However, existing methods predominantly rely on jointly training all source domain graphs, resulting in high computational costs. Furthermore, it remains unclear whether all source domain graph data contribute equally to effective transfer. This paper empirically reveals significant data redundancy in multi-domain graph pre-training. Based on this finding, we propose the Multi-domain Graph Pre-training Framework, MDGMIX, which combines boundary-aware subgraph mixing with hierarchical discrimination. By selecting boundary nodes to construct challenging mixed-domain subgraphs, MDGMIX employs coarse-grained domain discrimination and fine-grained domain decomposition losses to decouple shared patterns from domain-specific patterns. During adaptation, MDGMIX employs a lightweight prompt weighting mechanism to transfer source domain knowledge. Extensive experiments demonstrate that MDGMIX consistently outperforms strong baselines in few-shot classification tasks while exhibiting superior time and memory efficiency. The code is available at: https://github.com/zhengziyu77/MDGMIX

Foundation models have sparked a revolution via a pretraining-adaptation paradigm, with recent efforts extending this success to graphs. Unlike other modalities, graphs contain rich structural patterns, yet their structural transferability remains poorly understood. Prior studies consider common substructures in the discrete realm, and we are motivated by a fundamental question: Are common substructures transferable? The underlying theory is largely underexplored. In this work, we shift toward learning transferable structures through the lens of functional behavior. Theoretically, we connect transferable substructures to intrinsic geometry of the representation space. However, characterizing such intrinsic geometry has rarely been touched. Grounded in Riemannian geometry, we develop a graph intrinsic geometry learning framework—\textbf{Neural Vector Bundle}, which enables parsing intrinsic geometry with local coordinates. Building on this, we design \textbf{\textsc{Gauge}}, a pretrainable neural architecture that constructs the vector bundle, flattening geometrically compatible local coordinates, and a new Dirichlet loss, which also measures the transfer effort. We empirically validate its superior expressiveness in challenging tasks including zero-shot link prediction and graph isomorphism.

Graphs provide a natural representation of relational structure that arises across diverse domains. Despite this ubiquity, graph structure is typically learned in a modality- and task-isolated manner, where graph representations are constructed within individual task contexts and discarded thereafter. As a result, structural regularities across modalities and tasks are repeatedly reconstructed rather than accumulated at the level of intermediate graph representations. This motivates a representation-learning question: *how should graph structure be organized so that it can persist and accumulate across heterogeneous modalities and tasks?* We adopt a representation-centric perspective in which graph structure is treated as a structural substrate that persists across learning contexts. To instantiate this perspective, we propose **G-Substrate**, a **g**raph **substrate** framework that organizes learning around shared graph structures. G-Substrate comprises two complementary mechanisms: a unified structural schema that ensures compatibility among graph representations across heterogeneous modalities and tasks, and an interleaved role-based training strategy that exposes the same graph structure to multiple functional roles during learning. Experiments across multiple domains, modalities, and tasks show that G-Substrate outperforms task-isolated and naive multi-task learning methods. The codebase, model, and datasets are available at <https://github.com/zmli6/G-Substrate>.

Point forecasting for graph-structured multivariate time series is a fundamental problem, but rigorous uncertainty quantification for such predictions is still underexplored. Conformal prediction (CP) offers uncertainty estimation with a solid coverage guarantee under the exchangeability assumption, which requires the joint data distribution to be unchanged under permutation. However, in graph-structured time series, inherent cross-node coupling can violate the exchangeability condition, making direct application of CP unreliable. Inspired by the spectral graph theory, such coupling resides in global trends and can be characterized by the low-frequency components, while high-frequency components are nearly exchangeable. Therefore, we propose a novel concept named **S**pectral **G**raph **C**onditional **E**xchangeability (SGCE), which conditions exchangeable high-frequency components on low-frequency ones to preserve global trends and enable effective CP in the spectral domain. Based on SGCE, we further propose **S**pectral **C**onformal prediction via w**A**ve**LE**t transform (SCALE). SCALE uses graph wavelets to decompose low/high-frequency components and conformalizes high-frequency residuals via adaptive gating over a low-frequency embedding. Experimental results on real-world benchmark datasets across multiple application domains show that SCALE not only achieves valid coverage but also consistently improves the coverage-efficiency trade-off over the state-of-the-art CP methods.

Text-attributed Graphs (TAGs) incorporate textual node attributes with graph structures to describe rich relational semantics. Recent efforts to integrate Graph Neural Networks (GNNs) and Large Language Models (LLMs) have shown promise for learning on TAGs, yet achieving well-aligned representations remains challenging. Prior studies largely rely on heuristics that perform coarse-grained matching. They lack sufficient constraints and ignore distributional alignment, leading to representation drift and limited generalization. Building on Energy-based Models (EBMs), we propose an **E**nergy-based **R**epresentation **Align**ment (ERAlign) framework that projects GNN-encoded graph structure and LLM-derived text embeddings in a shared latent space to achieve distribution consistency. Concretely, layer-wise alignment is quantified by a distance metric and optimized via an EBM objective. By decreasing energy values, our framework yields well-aligned representations for downstream tasks. During training, we introduce Energy Discrepancy (ED) to avoid high sampling costs associated with intractable normalization. ED also carries theoretical guarantees of higher training efficiency and reduced energy landscape distortion. Empirical evaluations on eight TAG datasets demonstrate that ERAlign obtains state-of-the-art performance across varying levels of supervision and cross-task transfer scenarios.

Link prediction (LP) is a fundamental problem in graph learning and can be broadly categorized into node-based and subgraph-based approaches. While subgraph-based LP methods often achieve superior predictive performance by exploiting localized structural information, they suffer from efficiency bottlenecks due to the high computational cost of per-query subgraph message-passing during both training and inference. To address this challenge, we propose MIMO-LP, a Multi-Input Multi-Output (MIMO) framework that accelerates subgraph-based LP. Given a batch of query node pairs and their corresponding subgraphs extracted from a shared full graph, MIMO-LP superposes their message-passing processes into a shared latent space while ensuring minimal interference among them. This design enables MIMO-LP to multiplex multiple queries within a single forward pass during both training and inference, substantially reducing redundant message-passing computations in overlapping subgraph regions. Extensive experiments demonstrate that MIMO-LP achieves a 14x-44x speedup over existing one-to-one subgraph-based methods, while maintaining comparable predictive performance.

Shapley additive explanations (SHAP) are widely recognised as computationally intractable for neural networks, since they induce an exponential search space over the input features. In this work, we take a first step towards scaling exact SHAP computation to larger search spaces by introducing an algorithm that leverages recent advances in neural network verification to compute arbitrarily tight exact lower and upper bounds on SHAP values for neural networks, ultimately recovering the exact SHAP values. We demonstrate that our approach scales to orders of magnitude larger search spaces than state-of-the-art exact methods. This provides an important first step towards exact SHAP computation and establishes a principled cornerstone for evaluating statistical approximation methods on larger search spaces.

Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems. While equivariant networks offer a solution, they typically rely on local operations in the spatial domain, making the global receptive field—essential for PDE dynamics—computationally expensive. Conversely, Fourier Neural Operators (FNOs) efficiently capture global interactions, yet establishing 3D equivariance within them remains impractical due to the prohibitive cost of spectral group convolutions. To bridge this gap, we introduce EqGINO, a geometrically robust framework that enforces isotropy in the spectral domain. By design, EqGINO guarantees exact equivariance to the discrete symmetries inherent to the discretized computational domain. Beyond this discrete guarantee, our structural prior enables effective generalization to arbitrary continuous orientations even with a limited number of SE(3)-transformed training samples. Consequently, our method robustly models coordinate-invariant physical laws on complex irregular 3D geometries. Our code is available at https://github.com/sung-won-kim/EqGINO