论文标题
警方：可证明对深神经网络的最佳线性约束执法
POLICE: Provably Optimal Linear Constraint Enforcement for Deep Neural Networks
论文作者
论文摘要
深层神经网络（DNNS）在许多设置中都超出了替代功能近似值，这要归功于它们在组成任何所需的可区分运算符方面的模块化。然后对形成的参数化功能进行调整，以从简单梯度下降中求解手头的任务。这种模块化是以严格对DNN的约束执行的代价，例如从对任务的先验知识或所需的物理属性的知识，这是一个开放的挑战。在本文中，我们提出了第一种可证明的DNN的可证明的仿射约束实施方法，该方法仅需要最小化对给定DNN的前向通行，即计算友好型，这使得不受限制的DNN参数的优化是不受限制的，即可以采用基于标准梯度的方法。我们的方法不需要任何采样，并证明可以确保DNN在培训和测试过程中的任何时候都对给定输入空间的区域符合仿射约束。我们造成这种方法警察，代表可证明最佳的线性约束执法。 github：https：//github.com/randallbalestriero/police
Deep Neural Networks (DNNs) outshine alternative function approximators in many settings thanks to their modularity in composing any desired differentiable operator. The formed parametrized functional is then tuned to solve a task at hand from simple gradient descent. This modularity comes at the cost of making strict enforcement of constraints on DNNs, e.g. from a priori knowledge of the task, or from desired physical properties, an open challenge. In this paper we propose the first provable affine constraint enforcement method for DNNs that only requires minimal changes into a given DNN's forward-pass, that is computationally friendly, and that leaves the optimization of the DNN's parameter to be unconstrained, i.e. standard gradient-based method can be employed. Our method does not require any sampling and provably ensures that the DNN fulfills the affine constraint on a given input space's region at any point during training, and testing. We coin this method POLICE, standing for Provably Optimal LInear Constraint Enforcement. Github: https://github.com/RandallBalestriero/POLICE
