Output Reachable Set Estimation and Verification for Multi-Layer Neural Networks

TL;DR

This paper presents a method for estimating the output reachable set and verifying safety in multi-layer neural networks using convex optimization and simulation-based techniques, demonstrated on a robotic arm model.

Contribution

It introduces a novel maximum sensitivity concept and develops automated safety verification methods for neural networks based on reachable set estimation.

Findings

Maximum sensitivity can be computed via convex optimization for certain neural networks.

The proposed methods effectively estimate output reachable sets.

Safety verification is successfully applied to a robotic arm example.

Abstract

In this paper, the output reachable estimation and safety verification problems for multi-layer perceptron neural networks are addressed. First, a conception called maximum sensitivity in introduced and, for a class of multi-layer perceptrons whose activation functions are monotonic functions, the maximum sensitivity can be computed via solving convex optimization problems. Then, using a simulation-based method, the output reachable set estimation problem for neural networks is formulated into a chain of optimization problems. Finally, an automated safety verification is developed based on the output reachable set estimation result. An application to the safety verification for a robotic arm model with two joints is presented to show the effectiveness of proposed approaches.