Hyperplane Neural Codes and the Polar Complex

Vladimir Itskov, Alexander Kunin, Zvi Rosen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationTopological Data Analysis - The Abel Symposium, 2018
EditorsNils A. Baas, Gereon Quick, Markus Szymik, Marius Thaule, Gunnar E. Carlsson
PublisherSpringer
Pages343-369
Number of pages27
ISBN (Print)9783030434076
DOIs
StatePublished - 2020
EventAbel Symposium, 2018 - Geiranger, Norway
Duration: Jun 4 2018Jun 8 2018

Publication series

NameAbel Symposia
Volume15
ISSN (Print)2193-2808
ISSN (Electronic)2197-8549

Conference

ConferenceAbel Symposium, 2018
CountryNorway
CityGeiranger
Period6/4/186/8/18

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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