Clifford Sheaf Neural Networks
Clifford Sheaf Neural Networks use K-term sandwich maps for grade-mixing equivariant regression on geometric graphs.
The paper introduces Clifford Sheaf Neural Networks, equivariant models that place a Clifford algebra on each stalk of a cellular sheaf and transport multivector features along graph edges. After finding versor conjugation too weak, the authors use K-term sandwich restriction maps that are not required to be algebra homomorphisms. The resulting sheaf Laplacian is positive semidefinite by construction and can mix grades. They characterize which grades the maps couple, how much of the endomorphism space they span, and their conditioning.
- CSNN assigns Clifford algebras to stalks of cellular sheaves on geometric graphs.
- K-term sandwich maps replace expressively weak versor conjugation.
- The resulting sheaf Laplacian is positive semidefinite and mixes grades.
- In Cl(3,0,0), the maps commute with the central pseudoscalar.
- AI models
- Clifford Sheaf Neural Network
From the original article
1 min read at arxiv.orgWe introduce the Clifford Sheaf Neural Network (CSNN), an equivariant sheaf neural network for geometric graphs that places a Clifford algebra on each stalk of a cellular sheaf and transports multivector features along edges. The canonical choice of restriction map for sheaves with algebra-valued stalks is algebra homomorphism. Adding the constraint of equivariance, the naive choice becomes versor conjugation.
By Kotaro Kamiya · arxiv.org
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