ICML 2026 Papers

Over the past decade, Graph Neural Networks (GNNs) have become a standard tool for solving machine learning problems on graphs. While many aspects of GNNs have been studied in depth, including their efficiency and expressive power, the invertibility of these models has remained largely unexplored. Standard aggregation functions, such as the mean, max and sum operators, are not invertible, which limits their applicability in tasks requiring invertible transformations. In this work, we introduce an invertible GNN layer. By stacking multiple such layers, we construct fully invertible GNN models, which we refer to as InvGNNs. These models inherit the benefits of invertible neural networks, including low memory usage for deep architectures, exact likelihood computation, and generative modeling capabilities. We demonstrate that InvGNNs can match the expressive power of the 1-dimensional Weisfeiler-Leman algorithm, showing that invertibility does not compromise model expressiveness. On standard graph classification benchmarks, our model performs comparably to other well-established GNNs. Beyond classification, we demonstrate the potential of invertible layers through density estimation tasks, including outlier detection and node feature generation.

Graph anomaly detection (GAD) is a fundamental task in graph learning. However, most existing methods rely on the homophily assumption, which posits that connected nodes tend to share the same labels. This assumption often fails in the presence of edge heterophily, leading to degraded performance. We first observe that down-weighting heterophilic edges, relative to the original or randomly weighted graphs, results in a more concentrated spectral energy distribution, thereby facilitating the learning of discriminative spectral representations. Moreover, existing methods typically embed graphs in Euclidean spaces, neglecting the importance of heterophily in manifold spaces. Motivated by these observations, we propose HSMAD, a novel framework for GAD. It consists of two key components: the Heterophily-Weighted Spectral Filtering module, which reconstructs the Laplacian using heterophily-based edge weighting for spectral filtering, and the Heterophily-Routed Manifold Update module, which routes neighborhood messages to the appropriate manifold for node feature updates, enabling curvature-adaptive representation learning. These spectral and geometric representations are jointly leveraged for anomaly detection. Extensive experiments on six real-world datasets show that HSMAD achieves state-of-the-art performance across the average F1-Macro, AUROC, AUPRC, and G-Mean. Specifically, the average F1-Macro score improves by 2.66% over the best-performing method.

Deep attribute graph clustering aims to learn discriminative node representations by leveraging both node attributes and graph topology to partition nodes into distinct clusters. Although substantial progress has been made in attribute-graph clustering in recent years, two key challenges remain: noisy edges in the original adjacency matrix degrade the quality of information propagation, and redundant feature information across different feature views hampers the learning of discriminative representations. To address these issues, we propose a self-supervised attribute graph clustering method based on topological reconstruction and correlation decorrelation. First, we reconstruct the graph topology by computing intersections between k-nearest neighbors and the original adjacency relationships, while simultaneously leveraging global semantic information from K-means clustering to filter out noisy nodes. This reconstructed topology effectively mitigates information redundancy during feature aggregation in Graph Neural Networks. Second, unlike existing augmentation-based contrastive methods, we treat the feature representations from an auto-encoder (AE) and a graph auto-encoder (GAE) as two complementary natural views. We then apply mutual information minimization and a decorrelation constraint to suppress redundant information between views, yielding more discriminative node representations. Extensive experiments on four widely-used graph datasets—ACM, DBLP, CITE, and AMAP—demonstrate that our method consistently outperforms six state-of-the-art baselines.

Estimating the quality of register transfer level (RTL) designs is crucial in the electronic design automation (EDA) workflow, as it enables instant feedback on key performance metrics like area and delay without the need for time-consuming logic synthesis. While recent approaches have leveraged large language models (LLMs) to derive embeddings from RTL code and achieved promising results, they overlook the structural semantics essential for accurate quality estimation. In contrast, the control data flow graph (CDFG) view exposes the design's structural characteristics more explicitly, offering richer cues for representation learning. In this work, we introduce StructRTL, a novel structure-aware graph self-supervised learning framework for improved RTL design quality estimation. By learning structure-informed representations from CDFGs, StructRTL significantly outperforms prior art on various quality estimation tasks. To further boost performance, we incorporate a knowledge distillation strategy that transfers low-level insights from post-mapping netlists into the CDFG-based predictor. Experimental results demonstrate that StructRTL establishes new state-of-the-art results, highlighting the effectiveness of combining structural learning with cross-stage supervision.

Brain network classification is pivotal for diagnosing neurological disorders, yet identifying interpretable functional biomarkers fundamentally relies on precise parcellation. Unfortunately, conventional deep graph encoders applied to brain networks suffer from a critical theoretical limitation termed Spectral Unreachability. Through graph spectral analysis, this paper demonstrates that standard coupled encoder-pooling architectures inevitably oversmooth node representations, corrupting the high-frequency topological signals strictly required to delineate sharp module boundaries. To provide a structural remedy, the Hierarchical Spectral Parcellation Network (HiSP-Net) is proposed, which structurally decouples partition learning from feature smoothing via a project-then-align paradigm. Specifically, HiSP-Net maps representations directly into a partition space using a topology-agnostic projection block to preserve all-frequency details, while a Topology-Aware Alignment regularizer subsequently enforces spatial coherence. Extensive evaluations demonstrate that HiSP-Net consistently outperforms state-of-the-art baselines in classification, while successfully extracting stable and structurally coherent functional biomarkers. Source code is available at https://github.com/Kevin-916/HiSP-Net-demo/.

Open-vocabulary navigation requires embodied agents to manage significant perception uncertainty stemming from semantic ambiguity and model errors. However, most existing works settle for local optimal deterministic approaches, depriving complex navigation decision-making over multiple composite possibilities that are critical for globally better solutions. In this paper, we propose Probabilistic Scene Graph Navigation (PSG-Nav), which constructs a 3D Probabilistic Scene Graph that uses full semantic categorical distributions to account for perception uncertainty. To efficiently use the local distributions to compose and reason about the optimal navigation landmarks, we propose Multiverse Decision to sample multiple most likely world settings from the joint distribution, and evaluate navigation landmarks based on the compatibility between landmarks and multiverses. To mitigate false positives due to epistemic uncertainty in open-vocabulary navigation, we introduce the Evidential Experience Calibrator, which enables online lifelong adaptation by cross-validating detections against memories of past successes and failures. Extensive experiments on widely-used benchmarks MP3D, HM3D, and HSSD demonstrate that PSG-Nav establishes new state-of-the-art results, achieving Success Rates of 66.1%, 44.8%, and 67.9%, respectively. Code is available at: https://psg-nav.github.io

Hyper-relational knowledge graphs (HKGs) effectively represent complex facts. While inferring new knowledge in HKGs is a critical problem, current methods cast it as a simple link prediction, assuming that nearly all entities and relations within a fact are known, leaving only a single blank to be filled. However, this restricted assumption may not hold in real-world scenarios in which multiple, or even all, constituent components of a fact may be missing simultaneously. To bridge this gap, we introduce a task called fact generation: generating a valid hyper-relational fact from an arbitrarily masked query, i.e., completing a partially observed fact or generating a fact from scratch. We propose KREPE, the first generative representation learning method for HKGs that learns to model the probability distributions of missing components conditioned on the local fact components and global structure of HKGs via a masked discrete diffusion. KREPE models both the intra-fact dependencies by contextual message passing and inter-fact correlations by aggregating stochastically sampled contexts. KREPE seamlessly unifies link prediction and fact generation within a single training framework, achieving state-of-the-art performance on standard HKG link prediction benchmarks and outperforming LLM-based baselines in generating novel and correct facts.

Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in the resulting representations. As a result, most GNNs rely on local approximations such as polynomial Laplacian filters or message passing, which limit their ability to model long-range dependencies. In this paper, we introduce an exact factorization of the GFT into operators acting on subgraphs, which are then combined via a sequence of Cauchy matrices. Building on this factorization, we propose a new class of spectral GNNs, termed L2G-Net (Local to Global Net). Unlike existing spectral methods, which are either fully global (when using the GFT) or local (when using polynomial filters), L2G-Net operates by processing the spectral representations of subgraphs and then combining them via structured matrices. Our algorithm avoids full eigendecompositions, exploiting graph topology to construct the factorization with quadratic complexity in the number of nodes, scaled by the maximum cut size between subgraphs. Experiments stressing long-range dependencies on large graphs show that L2G-Net scales to regimes out of reach for the standard GFT, and is competitive with state-of-the-art methods with orders of magnitude fewer learnable parameters.

Graph Foundation Models (GFMs) aim to learn universal patterns through large-scale pretraining on diverse graphs and generalize to open-world scenarios. While GFMs have garnered significant attention, existing works primarily focus on sigle-modal graphs. However, many real-world graphs are multimodal, consisting of structures alongside diverse features derived from modalities such as text and images. To date, exploration into Multimodal Graph Foundation Models (MGFMs) remains limited. Incorporating multimodal data provides a more comprehensive view, allowing models to learn richer semantics, thereby advancing GFMs. We are therefore motivated to explore MGFMs, where the core challenge lies in synergistically encoding structures and multimodal features to achieve effective cross-modal alignment and fusion. To this end, we propose a graph foundation model with Cross-modal Alignment and Modality-aware Expert fusion, CAME. Specifically, CAME first generates graph embeddings for each individual modality. We then introduce a multimodal multi-expert encoding mechanism, which includes a dimension-wise routing strategy to fuse multimodal information. Finally, we employ a cross-modal contrastive loss to train CAME, enabling the adaptive alignment and fusion across different modalities. Extensive experiments demonstrate the effectiveness of CAME across multiple tasks and diverse multimodal graph datasets.

It is well established that spectral graph neural networks (GNNs) can universally approximate node signals; however, their expressive power remains bounded by the 1-dimensional Weisfeiler-Lehman test, which is mirrored in their lack of universality for higher-order signals. To go beyond this bound, we propose the Full-Spectrum GNNs (FSpecGNNs), a second-order generalization of classical spectral GNNs. FSpecGNN advances spectral filtering from two perspectives: (1) it lifts signals from the node domain to the node-pair domain; and (2) it extends the univariate spectral filter over eigenvalues to a bivariate filter over eigenvalue pairs. We show that classical spectral GNNs arise as a diagonal special case of FSpecGNNs, and prove that FSpecGNNs can be at most as expressive as Local 2-GNN while universally approximating node-pair signals, the latter being particularly beneficial for heterophilic graph learning. Moreover, FSpecGNNs admit scalable implementations that avoid explicit node-pair-level computations; combined with a low-rank approximation that reduces full-spectrum convolution to a combination of polynomial spectral filters, it enables learning on large graphs. Empirically, FSpecGNNs validate the predicted expressivity on substructure-counting benchmarks and delivers strong performance on heterophilic benchmarks. Our code is available at https://github.com/xwangxshi/FSpecGNN.

The scalable solution of large sparse linear systems is a bottleneck in scientific computing and graph analysis. While algebraic multigrid (AMG) offers optimal linear scaling, its performance is severely constrained by the trade-off between the sparsity and convergence quality of coarse-grid operators. Classical AMG heuristics struggle to balance these objectives, often sacrificing stability or performance for sparsity. We propose RAPNet, a graph neural network (GNN) framework that resolves this trade-off by learning to generate sparse, robust coarse operators directly from the sparse algebraic system. Key to our approach is a level-wise training strategy that enables learning from small subgraphs and generalization to million-node domains, bypassing the bottlenecks of prior neural AMG attempts. RAPNet executes exclusively during the solver setup phase, ensuring that the solve phase retains its favorable computational properties. We show that our method outperforms classical non-Galerkin baselines on diverse PDE discretizations and graph Laplacians, making it particularly effective for multi-query tasks such as eigenproblems, time-dependent simulations, and inverse or design problems.

Semi-supervised graph anomaly detection (GAD), which assumes a subset of labeled normal nodes for training, is widely studied. However, existing methods learn normality only from these labeled nodes, often overfitting their patterns and causing high detection errors, such as many false positives. To overcome this limitation, we propose $GraphNC$, a graph normality calibration framework that leverages both labeled and unlabeled data to calibrate the normality from a teacher (a pre-trained semi-supervised GAD model) jointly in anomaly score and representation spaces. GraphNC includes two main components, anomaly score distribution alignment ($ScoreDA$) and perturbation-based normality regularization ($NormReg$). ScoreDA optimizes our model’s anomaly scores by aligning them with the teacher’s score distribution. Because the teacher provides accurate scores for most normal nodes and some anomalies, this alignment pulls the scores of the two classes toward opposite ends, making them more separable. To reduce the impact of inaccurate teacher scores, NormReg regularizes normality in the representation space, making normal node representations more compact via a perturbation-guided consistency loss applied only to the labeled nodes. Comprehensive experiments on six benchmarks demonstrate that GraphNC (1) consistently and substantially enhances the performance of teacher models from different GAD methods (2) achieves new state-of-the-art performance. Our code is available at https://github.com/mala-lab/GraphNC.

This paper studies the problem of graph out-of-distribution (OOD) detection, which aims to identify anomaly graphs out of a graph dataset. Prior efforts usually focus on the utilization of topological structures with unsupervised graph learning to foster typical pattern recognition, which overlooks the semantic structure preserved in contextually affine neighborhoods. Towards this end, we propose a novel approach named Contextual Affinity Exploration with Twin Concordance (CLINIC) for graph OOD detection. The core of CLINIC is to explore and exploit the contextual affinity of the graph data samples for discriminative graph representations. In particular, our CLINIC first builds a contextual affinity graph to depict the semantic structure in the hidden space. More importantly, we introduce high-order affinity to enhance geometric understanding of the structure by utilizing a meta-graph neural network. To enhance representation discriminability with high robustness, we introduce twin concordance learning, which not only minimizes the difference of affinity distributions across different views, but also encourages the consistency between contextually affinitive neighbors. Finally, we introduce a compression strategy to expand the decision boundary for enhanced separation between in-distribution and out-of-distribution graphs. Extensive experimental results demonstrate the superiority of our CLINIC across ten real datasets in comparison to various baselines.

Graph foundation models (GFMs) seek transferable representations across graph domains but are limited by structural heterogeneity and incompatible node feature spaces. We propose Structure-Centric Graph Foundation Models (SCGFM), which treat graph topology as the primary source of transferable knowledge. Modeling graphs as metric measure spaces, SCGFM introduces learnable geometric bases that define a shared structural coordinate system. Graphs are aligned to these bases via Gromov–Wasserstein distances, yielding structure-aligned latent representations that accommodate heterogeneous graph topologies. To address feature incompatibility, SCGFM employs a structure-aware feature re-encoding mechanism that unifies node representations without assuming a fixed feature dimensionality or requiring dataset-specific preprocessing. Experiments on graph- and node-level tasks demonstrate strong in-domain and cross-domain generalization, outperforming existing GFM approaches.

Graph Mixture-of-Experts (Graph-MoE) offers a way to scale GNNs via adaptive capacity allocation, with the goal of allowing different experts to capture diverse graph patterns. Its effectiveness heavily depends on the coordination between routing decisions and expert specialization. However, through extensive empirical study, we identify two critical phenomena. First, discrimination loss occurs on both the expert and routing sides, where GNN experts become highly homogenized and the router collapses to a small subset of experts, failing to reflect diverse graph semantics. Second, routing uncertainty is prevalent, as existing routers produce uncertain expert assignments for most nodes, and such uncertainty exhibits a strong negative correlation with model performance. To address these issues, we propose C$^2$GMoE, a novel Graph-MoE framework featuring Contrastive routing and Confidence-aware fusion. We introduce a group-wise contrastive routing strategy that provides explicit guidance for routing optimization by aligning node-level routing decisions with semantic clusters while satisfying load-balancing constraints. Moreover, through a theoretical analysis of generalization error, we develop a confidence-aware fusion mechanism that adaptively reweights expert predictions according to their confidence. Extensive experiments across multiple benchmarks demonstrate the effectiveness of our proposed C$^2$GMoE.

Existing parameter isolation-based continual learning methods employ diverse designs to accommodate more tasks within limited model capacity, but often incur increasing computational overhead as model capacity expands for growing task streams. To address this efficiency bottleneck, we propose CAGNN, a graph continual learning framework with a biological neuron-inspired architecture that features capacity-agnostic efficiency. CAGNN leverages graph contextual information to construct task-specific subnetworks and decouples them during training and inference, reducing full-network propagation overhead while enabling knowledge transfer across tasks. Extensive experiments demonstrate CAGNN's superior effectiveness and computational efficiency over state-of-the-art methods.

The increasing prevalence of large-scale hypergraphs poses significant computational challenges for hypergraph neural network (HNN) training. To address this, hypergraph condensation (HGC) distills large real hypergraphs into compact yet informative synthetic ones, beyond graph condensation (GC) methods limited to pairwise relations. However, existing HGC methods rely on decoupled training architectures, where structure generators are pre-trained on the original hypergraph but not jointly optimized with condensed features during refinement, resulting in misaligned structures that degrade downstream utility. Moreover, trajectory-based optimization incurs substantial computational overhead in refinement, limiting condensation efficiency. To tackle these issues, we propose \textbf{A}nchor-guided \textbf{H}yper\textbf{G}raph \textbf{C}ondensation with \textbf{D}ual-level \textbf{D}iscrimination (\textbf{AHGCDD}), which consists of three key components: (1) a node initialization module based on Heat Kernel PageRank (HKPR) to encode structural knowledge into feature semantics; (2) an anchor-guided hyperedge synthesis strategy for joint optimization of condensed features and structure; (3) a theoretically grounded dual-level discrimination objective for utility-preserving condensation without redundant HNN training. Extensive experiments demonstrate the superior effectiveness and efficiency of AHGCDD.

Graph neural networks often degrade on heterophilous graphs because repeated neighbor aggregation can reinforce self-aligned low-frequency components while suppressing phase-inconsistent signals. We propose GESC, a complex-valued graph network that augments attention-based message passing with gauge-consistent U(1) transport and projection-based self-interference cancellation. For each transported neighbor message, GESC removes the component parallel to the target representation before computing attention and applies a sign-aware gate based on gauge-invariant complex alignment. We prove gauge equivariance of the hidden update and derive coefficient-frozen stability bounds showing that SIC contracts self-parallel message components. On nine benchmarks, GESC ranks first on seven datasets and remains within the top three on the other two. These results suggest that explicit self-parallel cancellation is an effective mechanism for improving message passing under heterophily. Our code is available at https://github.com/ChoiYoonHyuk/GESC.

In the graph label selection problem, one is given an $n$-vertex graph and a budget $k$, and seeks to select $k$ vertices whose labels enable accurate prediction of the labels on the remaining vertices. This problem formalizes distilling a small representative set from the whole graph. We present the first $\tilde{O}(\log^{1.5} n)$-approximation algorithm for graph label selection under the standard budget constraint. Prior work either relies on resource augmentation, allowing substantially more than $k$ labeled vertices, or consists primarily of heuristics without provable guarantees. Finally, we demonstrate that practical heuristic variants of our algorithm scale to significantly larger graphs than previous methods, while essentially retaining their quality.