🕸️ Graph Learning¶

🧪 ICML2026 · 9 paper notes

📌 Same area in other venues: 💬 ACL2026 (10) · 📷 CVPR2026 (8) · 🔬 ICLR2026 (21) · 🤖 AAAI2026 (38) · 🧠 NeurIPS2025 (52) · 📹 ICCV2025 (1)

🔥 Top topics: GNNs ×2 · Diffusion Models ×2

Anchor-guided Hypergraph Condensation with Dual-level Discrimination: AHGCDD rewrites hypergraph condensation (HGC) from the decoupled paradigm of "train structure generator first, then match training trajectories" into an end-to-end framework: Heat-Kernel-PageRank injects structural information into initial features, an anchor-guided approach synthesizes sparse, learnable hyperedges based on feature distances, and a dual-level discrimination loss (class prototype MMD + instance-level contrastive) replaces expensive HNN retraining. On five hypergraph benchmarks, it achieves ≥SOTA accuracy with up to 144× speedup.
Full-Spectrum Graph Neural Network: Expressive and Scalable: This work generalizes the classical spectral GNN’s univariate eigenvalue filter \(g(\lambda_i)\) to a bivariate filter \(g(\lambda_i,\lambda_j)\), lifting the signal from the node domain to the node-pair domain. Theoretically, it can approximate Local 2-GNN (surpassing 1-WL), and avoids explicit \(n^2\times n^2\) computation via low-rank tensor decomposition, achieving strong results on node classification for heterophilic graphs and substructure counting.
Information-Geometric Adaptive Sampling for Graph Diffusion: This work treats the sampling trajectory of the reverse SDE in graph diffusion as a parameterized curve on a Riemannian statistical manifold, deriving a training-free Drift Variation Score (DVS) from the Fisher-Rao metric to measure the local "information curvature" of the trajectory. Step sizes are adaptively scaled so that each step advances an equal length on the information manifold, achieving higher FCD / MMD fidelity with fewer steps in molecular (QM9/ZINC250k) and graph (Planar/SBM/Ego) generation.
Learning Graph Foundation Models on Riemannian Graph-of-Graphs: R-GFM treats "subgraphs with different hop counts" as nodes in a higher-level Graph-of-Graphs, and uses a dynamic MoE routing mechanism to assign each GoG to the Riemannian manifold (hyperbolic / Euclidean / spherical) with the best-matched curvature. This simultaneously addresses two inherent limitations of existing graph foundation models: fixed receptive fields and single Euclidean embedding. It achieves up to 49% relative improvement on downstream tasks.
On the Expressive Power of GNNs to Solve Linear SDPs: This work, from the perspective of the Weisfeiler–Leman hierarchy, for the first time characterizes the minimal GNN expressiveness required to learn solutions to linear SDPs. It proves that standard variable-constraint bipartite message passing (VC-WL) and higher-order VC-2-WL are insufficient, while the VC-2-FWL architecture, equivalent to 2-FWL, is sufficient to simulate the update steps of the PDHG solver. On synthetic and SDPLIB datasets, using high-quality predictions as warm-starts yields up to 80% acceleration.
Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves: PolyNSD replaces the "one-step spatial diffusion" in Sheaf Neural Networks with a learnable \(K\)-order polynomial spectral filter on the normalized sheaf Laplacian, computed stably via Chebyshev three-term recurrence. A single layer thus achieves \(K\)-hop receptive field and controllable low/band/high-pass response. An unexpected finding is that using only diagonal restriction maps outperforms all existing NSDs requiring dense high-dimensional stalks, with significant reductions in parameters, memory, and runtime.
Quantile-Free Uncertainty Quantification in Graph Neural Networks: QpiGNN proposes a "quantile-free, post-hoc-free" GNN node-level prediction interval framework, using a dual-head GNN (one head predicts the mean, the other predicts the half-width) combined with a label-level joint loss that directly optimizes "coverage + interval width." Across 19 synthetic/real datasets, it achieves an average 22% improvement in coverage and a 50% reduction in interval width.
Structure-Centric Graph Foundation Model via Geometric Bases: SCGFM reframes cross-domain graph foundation modeling as a "triangulation" problem in metric measure spaces: it learns a set of \(K\) trainable geometric bases \(\{B_k\}\), represents each graph by the softmax of its Gromov–Wasserstein distances \(\delta_k\) to these bases to obtain a set of structural coordinates \(\mathbf{w}\), and uses the OT plan on the bases to aggregate node features into a unified dimension. This approach eliminates the traditional GFM constraint of "must align node feature spaces," and outperforms baselines in both in-domain and OOD few-shot graph/node classification.
Unsat Core Prediction through Polarity-Aware Representation Learning over Clause-Literal Hypergraphs: This work models CNF formulas as a "clause–literal hypergraph + clause association graph," decomposes variable representations into polarity-invariant and polarity-equivariant components at the variable level, and trains with polarity-flip consistency regularization, significantly boosting unsat-core variable prediction accuracy.