# Locally Linear Attributes of ReLU Neural Networks

arXiv: https://arxiv.org/abs/2012.01940 · HTML: https://mlsanity.com/paper/2012.01940/

## Key facts

- Cited by 9 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 9 of 9)

- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [How and When Adversarial Robustness Transfers in Knowledge Distillation?](https://mlsanity.com/paper/2110.12072/) (2021)
- [Polyhedral Complex Extraction from ReLU Networks using Edge Subdivision](https://mlsanity.com/paper/2306.07212/) (2023)
- [ReLU Neural Networks, Polyhedral Decompositions, and Persistent Homolog](https://mlsanity.com/paper/2306.17418/) (2023)
- [On the Local Complexity of Linear Regions in Deep ReLU Networks](https://mlsanity.com/paper/2412.18283/) (2024)
- [Reverse Engineering ℓp attacks: A block-sparse optimization approach with recovery guarantees](https://mlsanity.com/paper/2203.04886/) (2022)
- [Dual Graphs of Polyhedral Decompositions for the Detection of Adversarial Attacks](https://mlsanity.com/paper/2211.13305/) (2022)
- [Weaver: Kronecker Product Approximations of Spatiotemporal Attention for Traffic Network Forecasting](https://mlsanity.com/paper/2511.08888/) (2025)
- [Pathwise Explanation of ReLU Neural Networks](https://mlsanity.com/paper/2506.18037/) (2025)

## Abstract (arXiv)

A ReLU neural network determines/is a continuous piecewise linear map from an input space to an output space. The weights in the neural network determine a decomposition of the input space into convex polytopes and on each of these polytopes the network can be described by a single affine mapping. The structure of the decomposition, together with the affine map attached to each polytope, can be analyzed to investigate the behavior of the associated neural network.