Abstraction based Output Range Analysis for Neural Networks

TL;DR

This paper introduces an abstraction technique using interval neural networks to efficiently approximate output ranges of feed-forward ReLU neural networks, balancing computational complexity and precision.

Contribution

We propose a novel abstraction method that simplifies neural networks into interval neural networks, enabling more efficient output range analysis.

Findings

The method reduces analysis time compared to existing approaches.

It provides a controllable trade-off between accuracy and computational efficiency.

Experimental results demonstrate effectiveness on various neural network architectures.

Abstract

In this paper, we consider the problem of output range analysis for feed-forward neural networks with ReLU activation functions. The existing approaches reduce the output range analysis problem to satisfiability and optimization solving, which are NP-hard problems, and whose computational complexity increases with the number of neurons in the network. To tackle the computational complexity, we present a novel abstraction technique that constructs a simpler neural network with fewer neurons, albeit with interval weights called interval neural network (INN), which over-approximates the output range of the given neural network. We reduce the output range analysis on the INNs to solving a mixed integer linear programming problem. Our experimental results highlight the trade-off between the computation time and the precision of the computed output range.