@inproceedings{4802f8263f8b47e5927a72d306e585d2,
title = "Hyperplane Neural Codes and the Polar Complex",
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 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 hyperplane codes follow from the shellability of the appropriate polar complex.",
author = "Vladimir Itskov and Alexander Kunin and Zvi Rosen",
note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; Abel Symposium, 2018 ; Conference date: 04-06-2018 Through 08-06-2018",
year = "2020",
doi = "10.1007/978-3-030-43408-3_13",
language = "English (US)",
isbn = "9783030434076",
series = "Abel Symposia",
publisher = "Springer",
pages = "343--369",
editor = "Baas, {Nils A.} and Gereon Quick and Markus Szymik and Marius Thaule and Carlsson, {Gunnar E.}",
booktitle = "Topological Data Analysis - The Abel Symposium, 2018",
}