SPLASH 2022
Mon 5 - Sat 10 December 2022 Auckland, New Zealand
Wed 7 Dec 2022 14:30 - 15:00 at Lecture Theatre 2 - SAS Papers 1 Chair(s): Roberto Giacobazzi

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. We report on a preliminary evaluation of our approach using a prototype implementation.

Wed 7 Dec

Displayed time zone: Auckland, Wellington change

13:30 - 15:00
SAS Papers 1COVID Time Papers In Person at Lecture Theatre 2
Chair(s): Roberto Giacobazzi University of Verona
13:30
30m
Talk
Abstract Neural Networks
COVID Time Papers In Person
Matthew Sotoudeh Stanford University, Aditya V. Thakur University of California at Davis
Link to publication DOI
14:00
30m
Talk
Reduced Products of Abstract Domains for Fairness Certification of Neural Networks
COVID Time Papers In Person
Denis Mazzucato INRIA & École Normale Supérieure, Caterina Urban Inria & École Normale Supérieure | Université PSL
Link to publication DOI
14:30
30m
Talk
Static analysis of ReLU neural networks with tropical polyhedra
COVID Time Papers In Person
Eric Goubault Ecole Polytechnique, Sebastien Palumby Ecole Polytechnique, Sylvie Putot École Polytechnique, Louis Rustenholz Universidad Politécnica de Madrid (UPM) and IMDEA Software Institute, Sriram Sankaranarayanan University of Colorado, Boulder
Link to publication DOI