arXiv：cs.LG（机器学习，全量分类）· Kotaro Kamiya, Joel Nicholls·· 15 小时前AI 评分27
Clifford Sheaf 神经网络（CSNN）：面向几何图的等变层论模型
Clifford Sheaf Neural Networks
AI 导读
研究者提出 Clifford Sheaf 神经网络（CSNN），一种面向几何图的等变 sheaf 神经网络，在每个 cellular sheaf 的茎上放置 Clifford 代数并沿边传输多向量特征。
正文
Abstract:We 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. However, versor conjugation is expressively weak, so we drop algebra homomorphism and arrive at the K-term sandwich. The resulting sheaf Laplacian is positive semidefinite by construction, needs no versor constraint, and still mixes grades. Our main contribution characterizes the resulting family of restriction maps along three axes: which grades a map couples, how much of the endomorphism space it reaches, and how well it is conditioned. The K-term sandwich spans half of the endomorphism space, and in Cl(3, 0, 0) it corresponds to the maps that commute with the central pseudoscalar. The number of terms controls expressivity. CSNN is the reversion member, a first-order model by construction and the grade-mixing corner of this family, developed as a sheaf construction for graph-level equivariant regression.
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.01322 [cs.LG] |
| (or arXiv:2610.01322v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.01322 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Kotaro Kamiya [view email]
[v1]
Thu, 1 Oct 2026 08:49:33 UTC (51 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org