Verification of Continuous Time Recurrent Neural Networks (Benchmark Proposal)

Abstract

This manuscript presents a description and implementation of two benchmark problems for continuous-time recurrent neural network (RNN) verification. The first problem deals with the approximation of a vector field for a fixed point attractor located at the origin, whereas the second problem deals with the system identification of a forced damped pendulum. While the verification of neural networks is complicated and often impenetrable to the majority of verification techniques, continuous-time RNNs represent a class of networks that may be accessible to reachability methods for nonlinear ordinary differential equations (ODEs) derived originally in biology and neuroscience. Thus, an understanding of the behavior of a RNN may be gained by simulating the nonlinear equations from a diverse set of initial conditions and inputs, or considering reachability analysis from a set of initial conditions. The verification of continuous-time RNNs is a research area that has received little attention and if the research community can achieve meaningful results in this domain, then this class of neural networks may prove to be a superior approach in solving complex problems compared to other network architectures.