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 $\mathcal{L}$.
arXiv:2608. 02558v1 Announce Type: new Abstract: Sheaf Neural Networks (SNNs) generalize message passing by replacing scalar edge weights of standard Graph Neural Networks (GNNs) with learnable, edge-dependent restriction maps between node stalks.
arXiv:2610.01322v1 Announce Type: cross Abstract: We introduce the Clifford Sheaf Neural Network (CSNN), an equivariant sheaf neural network for geometric graphs that places a Clifford algebra on eac...
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.
arXiv:2604. 20308v2 Announce Type: replace Abstract: Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule.
arXiv:2606. 16112v1 Announce Type: cross Abstract: Residual architectures are ubiquitous in deep learning, but they suffer from a subtle structural limitation: the norm of the residual stream can grow rapidly with depth.
arXiv:2606. 05863v1 Announce Type: new Abstract: Grokking suggests that fitting the training data and learning a simple underlying rule may occur on different time scales.
arXiv:2607. 21885v1 Announce Type: new Abstract: Coarsening-based training for graph neural networks (GNNs), i.
Modern sensing, communication, and learning systems generate heterogeneous network signals, with local data differing in dimension, modality, and geometric structure. Processing such data requires a mathematical framework capable of simultaneously modeling heterogeneous local signal spaces and the transformations relating them.
arXiv:2608. 10016v1 Announce Type: cross Abstract: Heterogeneous federated systems require agents to learn and exchange informative representations despite differences in data distributions, sensing modalities, model architectures, latent dimensionalities, and local learning objectives.
arXiv:2607. 22381v1 Announce Type: new Abstract: Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances.
arXiv:2608. 01318v1 Announce Type: cross Abstract: Modern sensing, communication, and learning systems generate heterogeneous network signals, with local data differing in dimension, modality, and geometric structure.