Deep neural networks (DNNs) are becoming increasingly important components of
software, and are considered the state-of-the-art solution for a number of
problems, such as image recognition. However, DNNs are far from infallible, and
incorrect behavior of DNNs can have disastrous real-world consequences. This
paper addresses the problem of architecture-preserving V-polytope provable
repair of DNNs. A V-polytope defines a convex bounded polytope using its vertex
representation. V-polytope provable repair guarantees that the repaired DNN
satisfies the given specification on the infinite set of points in the given
V-polytope. An architecture-preserving repair only modifies the parameters of
the DNN, without modifying its architecture. The repair has the flexibility to
modify multiple layers of the DNN, and runs in polynomial time. It supports
DNNs with activation functions that have some linear pieces, as well as
fully-connected, convolutional, pooling and residual layers. To the best our
knowledge, this is the first provable repair approach that has all of these
features. We implement our approach in a tool called APRNN. Using MNIST,
ImageNet, and ACAS Xu DNNs, we show that it has better efficiency, scalability,
and generalization compared to PRDNN and REASSURE, prior provable repair
methods that are not architecture preserving.

本文提出了一种基于 V-polytope 的可证明修复方法，该方法可以在不修改架构的情况下修改深度神经网络（DNN）的参数，支持多层修复，运行时间复杂度为多项式级别。使用 MNIST，ImageNet 和 ACAS Xu DNNs 测试显示该方法比以前的 PRDNN 和 REASSURE 方法在效率、可扩展性和泛化性方面更好。