To combat oversmoothing in Graph Convolutional Networks, Sheaf Neural Networks (SNNs) were proposed as a generalization by equipping the graph with a sheaf structure and replacing the graph Laplacian with a sheaf Laplacian $\mathcal{L}$. Existing analyses connect sheaf diffusion to oversmoothing via the harmonic space ($\ker\mathcal{L}$), taking its absolute dimension as an indicator of anti-oversmoothing capacity.
arXiv:2608. 16180v1 Announce Type: new Abstract: To combat oversmoothing in Graph Convolutional Networks, Sheaf Neural Networks (SNNs) were proposed as a generalization by equipping the graph with a sheaf structure and replacing the graph Laplacian with a sheaf Laplacian $\mathcal{L}$.
By Junwen Dong, Yuhan Peng, Hao Li, Huitao Feng, Kelin Xia
Scaffold is a new unsupervised graph sparsification framework for graph neural networks that uses support graph theory preconditioners to jointly control dilation and congestion, thereby preserving short communication paths while avoiding bottlenecks. It achieves superior aggregate ranking across 19 homophilic and heterophilic benchmarks, recovering or closely approaching full‑graph GNN performance with only 10%–50% of the original edges. The method reduces memory usage to less than half and cuts end‑to‑end training time, including sparsification overhead.
By Siddhartha Shankar Das, Sai Karthik Navuluru, S M Ferdous, Ryan A. Rossi, Baris Coskunuzer, Lakshman Tamil, Edoardo Serra, Alex Pothen, Robert Rallo, Mahantesh M Halappanavar
The paper introduces SheafDEQ, a subhomogeneous deep-equilibrium architecture that uses adaptive neural-sheaf propagation to allow richer, edge-dependent transformations in implicit graph neural networks while guaranteeing a unique equilibrium. The authors prove that SheafDEQ’s equilibrium is globally reachable from any positive initialization and remains contractive even with bounded communication staleness. Experiments demonstrate that SheafDEQ outperforms fixed-propagation implicit baselines on tasks such as Sums, MNIST Terrain, Coordinates, and community detection, especially as graph connectivity becomes increasingly heterophilic.
By R\'emi Bourgerie, \v{S}ar\={u}nas Girdzijauskas, Viktoria Fodor
arXiv:2609.39673v1 Announce Type: new
Abstract: Can a pretrained graph model replace training and tuning a separate predictor for each dataset? Answering this requires evaluating prediction quality a...
By Jinmo Lee, Dooho Lee, Minho Jeong, Jaemin Yoo
arXiv:2608. 02128v1 Announce Type: new Abstract: Training Graph Neural Networks on large graphs is challenged by the memory cost of storing all node representations across layers.
By Antonin Joly, Nicolas Keriven, Aline Roumy