Lipschitz constant estimation for 1D convolutional neural networks

arXiv (Cornell University)

Abstract

In this work, we propose a dissipativity-based method for Lipschitz constant estimation of 1D convolutional neural networks (CNNs). In particular, we analyze the dissipativity properties of convolutional, pooling, and fully connected layers making use of incremental quadratic constraints for nonlinear activation functions and pooling operations. The Lipschitz constant of the concatenation of these mappings is then estimated by solving a semidefinite program which we derive from dissipativity theory. To make our method as efficient as possible, we exploit the structure of convolutional layers by realizing these finite impulse response filters as causal dynamical systems in state space and carrying out the dissipativity analysis for the state space realizations. The examples we provide show that our Lipschitz bounds are advantageous in terms of accuracy and scalability.

Authors 3

1. Patricia Pauli Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   RWTH-AACHEN.DE RWTH Aachen , Chair of Intelligent Control Systems , 52074 Aachen , Germany

2. Dennis Gramlich Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   RWTH-AACHEN.DE RWTH Aachen , Chair of Intelligent Control Systems , 52074 Aachen , Germany

3. Frank Allgöwer Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   RWTH-AACHEN.DE RWTH Aachen , Chair of Intelligent Control Systems , 52074 Aachen , Germany