The Geometry of Polynomial Group Convolutional Neural Networks
Read the original on arXiv Machine Learning →The paper introduces a new mathematical framework for polynomial group convolutional neural networks (PGCNNs) using graded group algebras. It presents two natural parametrizations of the architecture—based on Hadamard and Kronecker products—that are related by a linear map. The authors compute the dimension of the resulting neuromanifold, show it depends only on the number of layers and group size, and describe the general fiber of the Kronecker parametrization, conjecturing a similar description for the Hadamard case, supported by explicit computations for small groups and shallow networks.
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