arXiv:2607. 19514v1 Announce Type: new Abstract: Geometric architectures are often justified by internal mechanisms such as rotations, yet task performance alone cannot show whether those mechanisms drive predictions.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
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: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:2607. 21607v1 Announce Type: cross Abstract: Graph Neural Networks propagate information through local message passing, but the graph topologies themselves can silently prevent any amount of training from solving long-range tasks.
arXiv:2607. 06634v1 Announce Type: new Abstract: Compact networks built from Clifford algebra Cl(3,0) primitives are exactly SO(3)-equivariant and learn synthetic 3D vector laws from few samples.
arXiv:2601. 21207v4 Announce Type: replace-cross Abstract: Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures.
arXiv:2607. 09967v1 Announce Type: cross Abstract: Many neural networks operations have a multiplicative nature rather than additive: halving or doubling a norm are analogous relatively but require unequal optimization distances when taking linear steps.