# Hyperplane Neural Codes and the Polar Complex

arXiv: https://arxiv.org/abs/1801.02304 · HTML: https://mlsanity.com/paper/1801.02304/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2018.

## Built on by (most cited first, 2 of 2)

- [Algorithmic Determination of the Combinatorial Structure of the Linear Regions of ReLU Neural Networks](https://mlsanity.com/paper/2207.07696/) (2022)
- [Labeled sample compression schemes for complexes of oriented matroids](https://mlsanity.com/paper/2110.15168/) (2021)

## Abstract (arXiv)

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.