A Robust Optimisation Perspective on Counterexample-Guided Repair of Neural Networks
This work addresses a critical problem for safety-critical applications of neural networks by providing theoretical insights and practical algorithms, though it is incremental as it builds on existing repair frameworks.
The paper tackles the open question of whether counterexample-guided repair of neural networks is guaranteed to terminate by framing it as a robust optimization problem, proving termination for restrained models and disproving it in general, while empirically showing practical suitability of verifiers and falsifiers and introducing a novel quadratic programming-based algorithm for linear regression repair that outperforms existing methods.
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.