Output Range Analysis for Deep Neural Networks

TL;DR

This paper introduces an efficient method for verifying deep neural networks by computing guaranteed output ranges over convex input sets, combining local search and linear programming for improved accuracy and efficiency.

Contribution

It presents a novel range estimation algorithm that integrates local gradient descent with mixed integer programming to verify neural networks more effectively.

Findings

Outperforms existing solvers like Reluplex in accuracy and efficiency.

Effective for neural networks in control and classification tasks.

Demonstrates practical applicability in high-assurance systems.

Abstract

Deep neural networks (NN) are extensively used for machine learning tasks such as image classification, perception and control of autonomous systems. Increasingly, these deep NNs are also been deployed in high-assurance applications. Thus, there is a pressing need for developing techniques to verify neural networks to check whether certain user-expected properties are satisfied. In this paper, we study a specific verification problem of computing a guaranteed range for the output of a deep neural network given a set of inputs represented as a convex polyhedron. Range estimation is a key primitive for verifying deep NNs. We present an efficient range estimation algorithm that uses a combination of local search and linear programming problems to efficiently find the maximum and minimum values taken by the outputs of the NN over the given input set. In contrast to recently proposed "monolithic" optimization approaches, we use local gradient descent to repeatedly find and eliminate local minima of the function. The final global optimum is certified using a mixed integer programming instance. We implement our approach and compare it with Reluplex, a recently proposed solver for deep neural networks. We demonstrate the effectiveness of the proposed approach for verification of NNs used in automated control as well as those used in classification.