2018/01/08 by Itskov, Vladimir, Kunin, Alex, Rosen, Zvi · 1 citation
#Combinatorics (math.CO) #FOS: Biological sciences #FOS: Mathematics #Neurons and Cognition (q-bio.NC)
paper · doi:10.48550/arxiv.1801.02304
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.