Local Repair of Neural Networks Using Optimization

Understand

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.