A Bochner Weitzenböck Decomposition for Cellular Sheaf Laplacians, Curvature and Neural Sheaf Diffusion
We extend the Bochner-Weitzenböck decomposition to cellular sheaf Laplacians, splitting it into a positive semidefinite term, the Bochner sheaf Laplacian, and a block diagonal term, the Forman curvature.
ProofPaper ↗
Key points
- We give a holonomy characterization of their kernel, prove the related Cheeger inequalities, and attach to them a random walk that generalizes the Gremban expansion.
- We then apply this machinery to Sheaf Neural Networks, whose learnt Laplacian is otherwise unobserved.
- The Bochner interpretation yields a node-level conviction score that acts as an operational importance measure under frozen-model interventions, while the Forman profile provides a local descriptor of the learnt operator.
Sources (1)
- [1]A Bochner Weitzenböck Decomposition for Cellular Sheaf Laplacians, Curvature and Neural Sheaf DiffusionarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 04:13 PM
We extend the Bochner-Weitzenböck decomposition to cellular sheaf Laplacians, splitting it into a positive semidefinite term, the Bochner sheaf Laplacian, and a block diagonal term, the Forman curvature.
We give a holonomy characterization of their kernel, prove the related Cheeger inequalities, and attach to them a random walk that generalizes the Gremban expansion.
Extractive summary: sentences quoted from the sources.
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