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

• URL: http://arxiv.org/abs/2301.11342v2
• Date: Mon, 5 Jun 2023 14:13:40 GMT
• Title: A Robust Optimisation Perspective on Counterexample-Guided Repair of Neural Networks
• Authors: David Boetius, Stefan Leue, Tobias Sutter
• Abstract summary: We show that counterexample-guided repair can be viewed as a robust optimisation algorithm. We prove termination for more restrained machine learning models and disprove termination in a general setting.
• Score: 2.82532357999662
• License: http://creativecommons.org/licenses/by/4.0/
• 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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