# A Provable Defense for Deep Residual Networks

arXiv: https://arxiv.org/abs/1903.12519 · HTML: https://mlsanity.com/paper/1903.12519/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2019.

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

- [Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neurons](https://mlsanity.com/paper/2102.05363/) (2021)
- [Neural Network Verification with PyRAT](https://mlsanity.com/paper/2410.23903/) (2024)
- [Keep your Distance: Determining Sampling and Distance Thresholds in Machine Learning Monitoring](https://mlsanity.com/paper/2207.05078/) (2022)
- [Scope Compliance Uncertainty Estimate](https://mlsanity.com/paper/2312.10801/) (2023)
- [Certified Training with Branch-and-Bound for Lyapunov-stable Neural Control](https://mlsanity.com/paper/2411.18235/) (2024)

## Abstract (arXiv)

We present a training system, which can provably defend significantly larger neural networks than previously possible, including ResNet-34 and DenseNet-100. Our approach is based on differentiable abstract interpretation and introduces two novel concepts: (i) abstract layers for fine-tuning the precision and scalability of the abstraction, (ii) a flexible domain specific language (DSL) for describing training objectives that combine abstract and concrete losses with arbitrary specifications. Our training method is implemented in the DiffAI system.