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 non-degenerate hyperplane codes , in terms of the polar complex {\it  of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a non-degenerate hyperplane code is shellable and show that all currently known properties of the hyperplane codes follow from the shellability of the appropriate polar complex.
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.
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non-degenerate hyperplane codes ,
stable hyperplane codes
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polar complex
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polar complex
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non-degenerate
stable
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all
most