This paper proposes a new algorithmic framework, predictor-verifier training,
to train neural networks that are verifiable, i.e., networks that provably
satisfy some desired input-output properties. The key idea is to simultaneously
train two networks: a predictor network that performs the task at hand,e.g.,
predicting labels given inputs, and a verifier network that computes a bound on
how well the predictor satisfies the properties being verified. Both networks
can be trained simultaneously to optimize a weighted combination of the
standard data-fitting loss and a term that bounds the maximum violation of the
property. Experiments show that not only is the predictor-verifier architecture
able to train networks to achieve state of the art verified robustness to
adversarial examples with much shorter training times (outperforming previous
algorithms on small datasets like MNIST and SVHN), but it can also be scaled to
produce the first known (to the best of our knowledge) verifiably robust
networks for CIFAR-10.

本文提出了一种新的算法框架，predictor-verifier training，用于训练可验证的神经网络，同时训练两个网络：一个预测网络和一个验证网络以达到最大化输出准确性并满足输入输出特定属性的目标。实验表明，predictor-verifier 架构能够训练出鲁棒性强的神经网络并且训练时间显著减短，在像 MNIST 和 SVHN 这样的小数据集上优于以前的算法，同时能够扩展到 CIFAR-10 并产生首个已知的可验证鲁棒网络。