< Retour au sommaire

Tropical Algebra for Neural Network verification

Eric Goubault and Sylvie Putot le

Lieu: bâtiment 650, LISN

This talk is a joint talk with the Digicosme vrAI working group.

In this talk, we will discuss range analyzes for feedforward neural networks, which are basic primitives 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. We use here set-based methods and abstract interpretation that have been very successful in coping with similar difficulties in classical program verification.

We are going to 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.