Excitable networks for finite state computation with continuous time recurrent neural networks

Continuous time recurrent neural networks (CTRNN) are systems of coupled ordinary differential equations that are simple enough to be insightful for describing learning and computation, from both biological and machine learning viewpoints. We describe a direct constructive method of realising finite state input-dependent computations on an arbitrary directed graph. The constructed system has an excitable network attractor whose dynamics we illustrate with a number of examples. The resulting CTRNN has intermittent dynamics: trajectories spend long periods of time close to steady-state, with rapid transitions between states. Depending on parameters, transitions between states can either be excitable (inputs or noise needs to exceed a threshold to induce the transition), or spontaneous (transitions occur without input or noise). In the excitable case, we show the threshold for excitability can be made arbitrarily sensitive.