Temporal Infomax on Markov Chains with Input Leads to Finite State Automata

Information maximization between stationary input and output activity distributions of neural ensembles has been a guiding principle in the study of neural codes. We have recently extended the approach to the optimization of information measures that capture spatial and temporal signal properties. Unconstrained Markov chains that optimize these measures have been shown to be almost deterministic. In the present work we consider the optimization of stochastic interaction in constrained Markov chains where part of the units are clamped to prescribed processes. Temporal Infomax in that case leads to finite state automata