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Continuous time recurrent neural networks (CTRNN) are systems of coupledordinary differential equations that are simple enough to be insightful fordescribing learning and computation, from both biological and machine learningviewpoints. We describe a direct constructive method of realising finite stateinput-dependent computations on an arbitrary directed graph. The constructedsystem has an excitable network attractor whose dynamics we illustrate with anumber of examples. The resulting CTRNN has intermittent dynamics: trajectoriesspend long periods of time close to steady-state, with rapid transitionsbetween states. Depending on parameters, transitions between states can eitherbe excitable (inputs or noise needs to exceed a threshold to induce thetransition), or spontaneous (transitions occur without input or noise). In theexcitable case, we show the threshold for excitability can be made arbitrarilysensitive.

Excitable Networks for Finite State Computation with Continuous Time Recurrent Neural Networks