ICML 2026 Papers

Stereotactic electroencephalography (sEEG) provides temporally precise intracranial recordings but is inherently constrained by sparse and irregular spatial sampling due to clinical limitations on electrode implantation. Signal reconstruction under this setting aims to infer neural activity at unmonitored locations, potentially expanding the coverage of neural recordings without increasing the number of implanted electrodes. However, most existing sEEG reconstruction methods underutilize the spatial information of electrode contacts in both encoding and modeling, and rely on deterministic objectives that favor average patterns, leading to over-smoothed reconstructions. We propose EpiTwin, a conditional spatial graph transformer for sEEG signal reconstruction, comprising three key components. Hybrid Spatial Positional Encoding (HSPE) constructs explicit spatial identities from electrode coordinates, graph topology, and anatomical priors. Geometry–Functional Biased Attention (GFBA) incorporates geometric distance and data-driven functional similarity biases into attention computation. The adversarial refinement training employs a multi-scale discriminator to counter reconstruction over-smoothing. Experiments on real-world clinical sEEG data demonstrate that EpiTwin consistently achieves lower reconstruction error under electrode series-level masking, outperforming recent foundation models such as LaBraM with a 16.8\% relative reduction in RMSE. Furthermore, EpiTwin effectively mitigates spectral over-smoothing and improves reconstruction fidelity.

We introduce vector diffusion wavelets (VDWs), a novel family of wavelets inspired by the vector diffusion maps algorithm that was introduced to analyze data lying in the tangent bundle of a Riemannian manifold. We show that these wavelets may be effectively incorporated into a family of geometric graph neural networks, which we refer to as VDW-GNNs. We demonstrate that such networks are effective on synthetic point cloud data, as well as on real-world data derived from wind field and neural activity measurements. Theoretically, we prove that these new wavelets have desirable frame theoretic properties, similar to traditional diffusion wavelets. Additionally, we prove that these wavelets have useful symmetries with respect to rotations and translations.

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds with varying numbers of points. The universality properties of such any-dimensional models remain poorly understood, as universality is traditionally studied for models accepting inputs of a fixed size, defined on a compact subset of their domain. In sharp contrast, any-dimensional models can be viewed as sequences of functions defined on growing-sized inputs, and it is not clear in which sense they can be universal. We develop a systematic approach to establish any-dimensional universality by identifying any-dimensional functions with a unique function that takes inputs in a suitable infinite-dimensional limit space containing inputs of all finite sizes, as well as their limits. Using the symmetries of these inputs and relations between inputs of different sizes, we show that this limit space admits a natural topology with rich families of compact sets on which any-dimensional universality can be established. We illustrate our approach by showing that several existing architectures fail to be universal, and we propose simple modifications that restore universality.

Positional encodings (PEs) enhance the power of graph neural networks (GNNs), both theoretically and empirically. Two of the most popular families of PEs---spectral (e.g., Laplacian eigenspaces, effective resistance) and random walk (polynomials of the adjacency matrix)---are theoretically equivalent in expressive power, and both are known to lie between the 1-WL and 3-WL tests in terms of expressivity. However, this equivalence assumes the GNN uses the "complete'' version of these PEs, which requires $O(n^3)$ time and space complexity. Practitioners therefore commonly use truncated variants of these encodings (e.g., the first $k$ eigenspaces or powers of adjacency matrix). However, the theoretical properties of these truncated PEs are unknown. In this work, we initiate the study of these truncated PEs. Theoretically, we show that, under truncation, several families of PEs are fundamentally different in expressive power. As a corollary, we show that truncated spectral PEs are no longer stronger than the 1-WL test. We also study a family of spectral PEs, the $k$-harmonic distances, to highlight the differences in expressive power of even closely related truncated PEs. Finally, we experimentally show that a mix of truncated PEs is preferable to any single family on real-world datasets.

Parameter sharing is a key model compression technique, yet existing methods overlook the geometric properties of the loss landscape, often causing severe accuracy degradation under high compression ratios. Inspired by second-order optimization, we propose Curvature-aware Graph Coloring (CGC), a cross-layer parameter sharing framework that treats each network layer as a graph node, with each node assigned to a shared low-rank basis. CGC leverages Hessian eigenspace information to group layers with similar curvature profiles, aligning the perturbations introduced by parameter sharing with the low-curvature (flat) directions of the loss ellipsoid. This effectively mitigates performance loss while enabling flexible, global cross-layer sharing. Experiments on LLaMA-7B and Swin Transformer show that CGC achieves 28\%–50\% parameter compression with Top-1 accuracy loss no more than 0.01\% on Swin—or even accuracy gains on LLaMA—while delivering over 60\% higher inference throughput, significantly outperforming SVD-based and heuristic-based methods. This work demonstrates that curvature-guided, geometry-aware sharing is essential for efficient, stable, and high-ratio model compression.

Graph neural networks (GNNs) are widely used, but how parameter sparsity affects the expressivity of relational (RGNNs) and temporal (TGNNs) variants is poorly understood. The Strong Expressive Lottery Ticket Hypothesis (SELTH) posits the existence of sparse GNNs that preserve Weisfeiler-Leman (WL) expressivity on static graphs. We generalize this existence result to a probabilistic statement for multi-relational and temporal domains via the relational WL (RWL). We prove that sufficiently parameterized RGNNs contain sparse subnetworks that maintain 1-RWL expressivity and derive a lower bound on the probability that a random pruning yields such a subnetwork. We show that common TGNNs and cross-graph message passing schemes admit RGNN reformulations such that they inherit these guarantees and, moreover, that the expressivity of a sparse RGNN is connected to its optimization behavior under common update regimes. Experiments instantiate the bound, compare it to empirical probabilities on synthetic data, and study how pre-training expressivity relates to optimization and prediction quality metrics on temporal and molecular benchmarks.

We show that contrary to conventional wisdom in the community, graph neural networks (GNNs) are not continuous with respect to all natural modes of graph convergence. As a result, GNNs may generate substantially different latent representations for graphs that are very similar. In particular they assign vastly different latent embeddings to graphs that represent the same underlying object at different resolution scales. We trace this failure of continuity back to a structural obstruction arising from commonly used information-propagation schemes. Building on this insight we then derive a principled modification to standard GNN architectures which equips models with continuity across scales. The proposed modification enables consistent integration of distinct resolutions and reliable generalization between them. We systematically validate our theoretical findings in a wide range of numerical experiments.

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.

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/.

While LLM-driven Neural Architecture Search (NAS) leverages exceptional code generation and reasoning, it suffers from a critical "Semantic-Physical Misalignment": LLMs prioritize high-level semantic plausibility but are agnostic to intrinsic physical dynamics such as gradient flow, whereas Zero-Cost Proxies (ZCPs) capture these local sensitivities but lack global semantic planning. To bridge this gap, we propose SAGE-NAS, a closed-loop evolutionary framework that synergizes an LLM-Based Semantic Agent with a Graph-Based Evaluator. Specifically, SAGE-NAS coordinates an LLM-driven Semantic Agent to construct candidate architectures by dynamically scheduling complementary sub-policies that balance exploitation with exploration. Furthermore, the framework integrates a Dual-Modality Graph Evaluator that serves as a rapid performance predictor by fusing ZCP statistics with topological features, and a State-Aware Behavioral Atlas that guides sparsity-driven exploration to escape local optima. Experiments demonstrate that SAGE-NAS achieves state-of-the-art performance across multiple mainstream search spaces and downstream tasks, exhibiting a superior balance between search efficiency, model accuracy, and cross-task generalization capability.

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.

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.

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.

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.