# Robust Optimization Framework for Training Shallow Neural Networks Using Reachability Method

arXiv: https://arxiv.org/abs/2107.12801 · HTML: https://mlsanity.com/paper/2107.12801/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 27 Jul 2021.

## Builds on (most cited first, 10 of 10)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [DeepTest: Automated Testing of Deep-Neural-Network-driven Autonomous Cars](https://mlsanity.com/paper/1708.08559/) (2017)
- [Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks](https://mlsanity.com/paper/1708.03322/) (2017)
- [Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach](https://mlsanity.com/paper/2004.12273/) (2020)
- [Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activations](https://mlsanity.com/paper/1712.08163/) (2017)
- [Reachable Set Estimation and Safety Verification for Piecewise Linear Systems with Neural Network Controllers](https://mlsanity.com/paper/1802.06981/) (2018)
- [Reachability Analysis and Safety Verification for Neural Network Control Systems](https://mlsanity.com/paper/1805.09944/) (2018)
- [Learnability and Robustness of Shallow Neural Networks Learned With a Performance-Driven BP and a Variant PSO For Edge Decision-Making](https://mlsanity.com/paper/2008.06135/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Data-Driven Hybrid Automaton Framework to Modeling Complex Dynamical Systems](https://mlsanity.com/paper/2304.13811/) (2023)

## Abstract (arXiv)

In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of interval sets. Interval-based reachability analysis is then performed for the hidden layer. With the reachability analysis results, a robust optimization training method is developed in the framework of robust least-square problems. Then, the developed robust least-square problem is relaxed to a semidefinite programming problem. It has been shown that the developed robust learning method can provide better robustness against perturbations at the price of loss of training accuracy to some extent. At last, the proposed method is evaluated on a robot arm model learning example.