DISCO Verification: Division of Input Space into COnvex polytopes for neural network verification

TL;DR

This paper introduces a method for neural network verification by partitioning the input space into convex polytopes, simplifying the analysis of piecewise linear networks, supported by empirical analysis of linear regions.

Contribution

It proposes a novel partitioning approach to facilitate neural network verification and evaluates the number of linear regions in networks, including a training reduction technique.

Findings

Empirical analysis of linear regions in neural networks.

Comparison of observed regions with known bounds.

Impact of training techniques on reducing linear regions.

Abstract

The impressive results of modern neural networks partly come from their non linear behaviour. Unfortunately, this property makes it very difficult to apply formal verification tools, even if we restrict ourselves to networks with a piecewise linear structure. However, such networks yields subregions that are linear and thus simpler to analyse independently. In this paper, we propose a method to simplify the verification problem by operating a partitionning into multiple linear subproblems. To evaluate the feasibility of such an approach, we perform an empirical analysis of neural networks to estimate the number of linear regions, and compare them to the bounds currently known. We also present the impact of a technique aiming at reducing the number of linear regions during training.