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. 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.
By Stefano Fiorini, Edoardo Coppola, Pietro Li\`o
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.
By Yuhan Peng, Junwen Dong, Yuzhi Zeng, Hao Li, Ce Ju, Huitao Feng, Diaaeldin Taha, Anna Wienhard, Kelin Xia
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.
By Tom\'as Figliolia, Beren Millidge
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.
By Gabriele D'Acunto, Enrico Grimaldi, Valeria Avino, Mario Edoardo Pandolfo, Leonardo Di Nino, Sergio Barbarossa, Paolo Di Lorenzo
arXiv:2607. 21885v1 Announce Type: new Abstract: Coarsening-based training for graph neural networks (GNNs), i.
By Guoming Li, Jian Yang, Xukun Wang, Zixiao Wang, Shangsong Liang, Yifan Chen