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.
CITATION STYLE
Itskov, V., Kunin, A., & Rosen, Z. (2020). Hyperplane Neural Codes and the Polar Complex. In Abel Symposia (Vol. 15, pp. 343–369). Springer. https://doi.org/10.1007/978-3-030-43408-3_13
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