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arXiv · 2301.11342

A Robust Optimisation Perspective on Counterexample-Guided Repair of Neural Networks

David Boetius·Stefan Leue·Tobias Sutter
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Abstract

Counterexample-guided repair aims at creating neural networks with mathematical safety guarantees, facilitating the application of neural networks in safety-critical domains. However, whether counterexample-guided repair is guaranteed to terminate remains an open question. We approach this question by showing that counterexample-guided repair can be viewed as a robust optimisation algorithm. While termination guarantees for neural network repair itself remain beyond our reach, we prove termination for more restrained machine learning models and disprove termination in a general setting. We empirically study the practical implications of our theoretical results, demonstrating the suitability of common verifiers and falsifiers for repair despite a disadvantageous theoretical result. Additionally, we use our theoretical insights to devise a novel algorithm for repairing linear regression models based on quadratic programming, surpassing existing approaches.

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David Boetius, Stefan Leue, Tobias Sutter. 2023-01-26. A Robust Optimisation Perspective on Counterexample-Guided Repair of Neural Networks. https://arxiv.org/abs/2301.11342

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