arXiv Machine Learning July 23, 2026 By Ankit Grover, R\'emi Bourgerie

Do Sheaf Neural Networks Use Holonomy? A Measure--Intervene--Control Study

Read the original on arXiv Machine Learning →

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.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv Machine Learning

Aug 4

Benchmarking Sheaf Neural Networks for Inductive Tasks

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

diffusion benchmarks

arXiv Machine Learning

Jun 2

Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning

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

benchmarks

arXiv Machine Learning

Jul 27

Spectral Flow Certificates for Depth-Aware Long-Range Propagation in Graph Neural Networks

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.

By Ranjan Veerabhadraswamy, Ajith Jubilson Emerson

benchmarks

arXiv Machine Learning

Jul 9

When Do Geometric Algebra Layers Beat Scalarization? A Controlled Study on SO(3)-Equivariant Vector Laws

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.

By Fabien Polly

arXiv AI

Sep 1

Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphs

arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...

By Alessio Borgi, Mario Severino, Fabrizio Silvestri, Pietro Li\`o

arXiv AI

Jul 23

A Sheaf-Theoretic and Topological Perspective on Complex Network Modeling and Attention Mechanisms in Graph Neural Models

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.

By Chuan-Shen Hu

diffusion

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