Deep Neural Networks (DNNs) have grown in popularity over the past decade and are now being used in safety-critical domains such as aircraft collision avoidance. This has motivated a large number of techniques for finding unsafe behavior in DNNs. In contrast, this paper tackles the problem of correcting a DNN once unsafe behavior is found. We introduce the provable repair problem, which is the problem of repairing a network N to construct a new network N' that satisfies a given specification. If the safety specification is over a finite set of points, our Provable Point Repair algorithm can find a provably minimal repair satisfying the specification, regardless of the activation functions used. For safety specifications addressing convex polytopes containing infinitely many points, our Provable Polytope Repair algorithm can find a provably minimal repair satisfying the specification for DNNs using piecewise-linear activation functions. The key insight behind both of these algorithms is the introduction of a Decoupled DNN architecture, which allows us to reduce provable repair to a linear programming problem. Our experimental results demonstrate the efficiency and effectiveness of our Provable Repair algorithms on a variety of challenging tasks.

本文提出了可证明修复问题，即在发现不安全行为后修复神经网络(DNN)的问题，并介绍了可用于有限点和凸多面体等安全规范的 Provable Point 和 Provable Polytope 修复算法，以及 Decoupled DNN结构，它允许将可证明修复减少至线性规划问题。实验结果证明了我们的算法在各种具有挑战性的任务中的有效性和效率。

深度神经网络的可证明修复