Local Repair of Neural Networks Using Optimization
This addresses the need for reliable and safe neural networks in domains like classification and control, though it is incremental as it builds on existing optimization and repair methods.
The paper tackles the problem of repairing pre-trained neural networks to satisfy specific output constraints by formulating it as a Mixed Integer Quadratic Program (MIQP) to adjust weights in a single layer, and demonstrates applications in bounding transformations, correcting classification errors, and controlling inputs.
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.