Hyperplane Neural Codes and the Polar Complex
Neurons and Cognition
2019-02-05 v3 Combinatorics
Abstract
Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of stable hyperplane codes in terms of the {\it polar complex} of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a stable hyperplane code is shellable and show that most currently known properties of the hyperplane codes follow from the shellability of the appropriate polar complex.
Cite
@article{arxiv.1801.02304,
title = {Hyperplane Neural Codes and the Polar Complex},
author = {Vladimir Itskov and Alex Kunin and Zvi Rosen},
journal= {arXiv preprint arXiv:1801.02304},
year = {2019}
}
Comments
23 pages, 5 figures. To appear in Proceedings of the Abel Symposium