Learning Neural Networks under Input-Output Specifications

TL;DR

This paper introduces a convexification approach for learning neural networks that satisfy specific input-output specifications, enabling certifiable guarantees through a novel reparametrization and quadratic constraints.

Contribution

It presents a new convexification method for neural network verification using quadratic constraints and a reparametrization scheme, advancing certifiable neural network learning.

Findings

Convex conditions can be enforced during neural network training.

The approach effectively specifies reachable input-output sets.

Validation demonstrates the method's ability to certify neural network behaviors.

Abstract

In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters, which is convex in a transformed space. To this end, we address the key technical challenge of convexifying the verification condition for neural networks, which is derived by abstracting the nonlinear specifications and activation functions with quadratic constraints. In particular, we propose a reparametrization scheme of the original neural network based on loop transformation, which leads to a convex condition that can be enforced during learning. This theoretical construction is validated in an experiment that specifies reachable sets for different regions of inputs.