# Analysis of Invariance and Robustness via Invertibility of ReLU-Networks

arXiv: https://arxiv.org/abs/1806.09730 · HTML: https://mlsanity.com/paper/1806.09730/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2018.

## Built on by (most cited first, 5 of 5)

- [Training Invertible Neural Networks as Autoencoders](https://mlsanity.com/paper/2303.11239/) (2023)
- [Certified Invertibility in Neural Networks via Mixed-Integer Programming](https://mlsanity.com/paper/2301.11783/) (2023)
- [Convex Geometry of ReLU-layers, Injectivity on the Ball and Local Reconstruction](https://mlsanity.com/paper/2307.09672/) (2023)
- [Injectivity of ReLU-layers: Tools from Frame Theory](https://mlsanity.com/paper/2406.15856/) (2024)
- [Deep Invertible Autoencoders for Dimensionality Reduction of Dynamical Systems](https://mlsanity.com/paper/2603.13496/) (2026)

## Abstract (arXiv)

Studying the invertibility of deep neural networks (DNNs) provides a principled approach to better understand the behavior of these powerful models. Despite being a promising diagnostic tool, a consistent theory on their invertibility is still lacking. We derive a theoretically motivated approach to explore the preimages of ReLU-layers and mechanisms affecting the stability of the inverse. Using the developed theory, we numerically show how this approach uncovers characteristic properties of the network.