# Local Repair of Neural Networks Using Optimization

arXiv: https://arxiv.org/abs/2109.14041 · HTML: https://mlsanity.com/paper/2109.14041/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 35 references that are in the map.
- First posted on arXiv 28 Sep 2021.

## Builds on (most cited first, 16 of 16)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [DeepTest: Automated Testing of Deep-Neural-Network-driven Autonomous Cars](https://mlsanity.com/paper/1708.08559/) (2017)
- [A Survey of Deep Learning Applications to Autonomous Vehicle Control](https://mlsanity.com/paper/1912.10773/) (2019)
- [Formal Verification of Neural Network Controlled Autonomous Systems](https://mlsanity.com/paper/1810.13072/) (2018)
- [Partition-based formulations for mixed-integer optimization of trained ReLU neural networks](https://mlsanity.com/paper/2102.04373/) (2021)
- [Compositional Falsification of Cyber-Physical Systems with Machine Learning Components](https://mlsanity.com/paper/1703.00978/) (2017)
- [GLAS: Global-to-Local Safe Autonomy Synthesis for Multi-Robot Motion Planning with End-to-End Learning](https://mlsanity.com/paper/2002.11807/) (2020)
- [Requirements-driven Test Generation for Autonomous Vehicles with Machine Learning Components](https://mlsanity.com/paper/1908.01094/) (2019)
- [Deep Predictive Models for Collision Risk Assessment in Autonomous Driving](https://mlsanity.com/paper/1711.10453/) (2017)
- [Semantic Adversarial Deep Learning](https://mlsanity.com/paper/1804.07045/) (2018)
- [Counterexample-Guided Data Augmentation](https://mlsanity.com/paper/1805.06962/) (2018)
- [Towards Repairing Neural Networks Correctly](https://mlsanity.com/paper/2012.01872/) (2020)
- [Training Neural Network Controllers Using Control Barrier Functions in the Presence of Disturbances](https://mlsanity.com/paper/2001.08088/) (2020)
- [Safe-by-Repair: A Convex Optimization Approach for Repairing Unsafe Two-Level Lattice Neural Network Controllers](https://mlsanity.com/paper/2104.02788/) (2021)
- [Clone Swarms: Learning to Predict and Control Multi-Robot Systems by Imitation](https://mlsanity.com/paper/1912.02811/) (2019)
- [Safe Navigation in Human Occupied Environments Using Sampling and Control Barrier Functions](https://mlsanity.com/paper/2105.01204/) (2021)

## Built on by (most cited first, 3 of 3)

- [Repairing Deep Neural Networks Based on Behavior Imitation](https://mlsanity.com/paper/2305.03365/) (2023)
- [Reachability Analysis of Neural Networks with Uncertain Parameters](https://mlsanity.com/paper/2303.07917/) (2023)
- [Causal Repair of Learning-enabled Cyber-physical Systems](https://mlsanity.com/paper/2304.02813/) (2023)

## Abstract (arXiv)

In this paper, we propose a framework to repair a pre-trained feed-forward neural network (NN) to satisfy a set of properties. We formulate the properties as a set of predicates that impose constraints on the output of NN over the target input domain. We define the NN repair problem as a Mixed Integer Quadratic Program (MIQP) to adjust the weights of a single layer subject to the given predicates while minimizing the original loss function over the original training domain. We demonstrate the application of our framework in bounding an affine transformation, correcting an erroneous NN in classification, and bounding the inputs of a NN controller.