Static analysis of ReLU neural networks with tropical polyhedra

TL;DR

This paper introduces a novel method for range analysis of ReLU neural networks using tropical polyhedra, improving precision and efficiency over traditional convex approximations.

Contribution

It presents a set-based, abstract interpretation approach employing tropical polyhedra to analyze ReLU networks, addressing limitations of derivative-based and coarse convex methods.

Findings

Tropical polyhedra efficiently abstract ReLU activations.

The approach controls precision loss in linear computations.

Connection to tropical rational functions enhances range analysis.

Abstract

This paper studies the problem of range analysis for feedforward neural networks, which is a basic primitive for applications such as robustness of neural networks, compliance to specifications and reachability analysis of neural-network feedback systems. Our approach focuses on ReLU (rectified linear unit) feedforward neural nets that present specific difficulties: approaches that exploit derivatives do not apply in general, the number of patterns of neuron activations can be quite large even for small networks, and convex approximations are generally too coarse. In this paper, we employ set-based methods and abstract interpretation that have been very successful in coping with similar difficulties in classical program verification. We present an approach that abstracts ReLU feedforward neural networks using tropical polyhedra. We show that tropical polyhedra can efficiently abstract ReLU activation function, while being able to control the loss of precision due to linear computations. We show how the connection between ReLU networks and tropical rational functions can provide approaches for range analysis of ReLU neural networks.