Verisig: verifying safety properties of hybrid systems with neural network controllers

TL;DR

Verisig introduces a method to verify safety properties of hybrid systems with neural network controllers by transforming sigmoid-based networks into hybrid systems, enabling the use of reachability tools for verification.

Contribution

The paper presents a novel approach to verify closed-loop hybrid systems with neural network controllers by leveraging the sigmoid's differential equation properties.

Findings

Decidability for networks with one hidden layer

Conditional decidability for general networks under Schanuel's conjecture

Successful case studies demonstrating applicability and scalability

Abstract

This paper presents Verisig, a hybrid system approach to verifying safety properties of closed-loop systems using neural networks as controllers. Although techniques exist for verifying input/output properties of the neural network itself, these methods cannot be used to verify properties of the closed-loop system (since they work with piecewise-linear constraints that do not capture non-linear plant dynamics). To overcome this challenge, we focus on sigmoid-based networks and exploit the fact that the sigmoid is the solution to a quadratic differential equation, which allows us to transform the neural network into an equivalent hybrid system. By composing the network's hybrid system with the plant's, we transform the problem into a hybrid system verification problem which can be solved using state-of-the-art reachability tools. We show that reachability is decidable for networks with one hidden layer and decidable for general networks if Schanuel's conjecture is true. We evaluate the applicability and scalability of Verisig in two case studies, one from reinforcement learning and one in which the neural network is used to approximate a model predictive controller.