HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Wennekers, T. Articles by Ay, N. Search for Related Content PubMed PubMed Citation Articles by Wennekers, T. Articles by Ay, N.

Finite State Automata Resulting from Temporal Information Maximization and a Temporal Learning Rule

Thomas.Wennekers{at}plymouth.ac.uk, Centre for Theoretical and Computational Neuroscience, University of Plymouth, Plymouth PL4 8AA, U.K.; Institute for Neuroinformatics, Ruhruniversity Bochum, 44780 Bochum, Germany; and Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany

Nihat Ay

ay{at}mi.uni-erlangen.de, Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany; Mathematics Institute, Friedrich Alexander University Erlangen-Nuremberg, 91054 Erlangen, Germany; and Santa Fe Institute, Santa Fe, NM 87501, U.S.A.

We extend Linkser's Infomax principle for feedforward neural networks to a measure for stochastic interdependence that captures spatial and temporal signal properties in recurrent systems. This measure, stochastic interaction, quantifies the Kullback-Leibler divergence of a Markov chain from a product of split chains for the single unit processes. For unconstrained Markov chains, the maximization of stochastic interaction, also called Temporal Infomax, has been previously shown to result in almost deterministic dynamics. This letter considers Temporal Infomax on constrained Markov chains, where some of the units are clamped to prescribed stochastic processes providing input to the system. Temporal Infomax in that case leads to finite state automata, either completely deterministic or weakly nondeterministic. Transitions between internal states of these systems are almost perfectly predictable given the complete current state and the input, but the activity of each single unit alone is virtually random. The results are demonstrated by means of computer simulations and confirmed analytically. It is furthermore shown numerically that Temporal Infomax leads to a high information flow from the input to internal units and that a simple temporal learning rule can approximately achieve the optimization of temporal interaction. We relate these results to experimental data concerning the correlation dynamics and functional connectivities observed in multiple electrode recordings.

This article has been cited by other articles:

				A. S. Klyubin, D. Polani, and C. L. Nehaniv Representations of space and time in the maximization of information flow in the perception-action loop. Neural Comput., September 1, 2007; 19(9): 2387 - 2432. [Abstract] [Full Text] [PDF]