title: Computation in dynamically bounded asymmetric systems.
abstract: Previous explanations of computations performed by recurrent networks have focused on symmetrically connected saturating neurons and their convergence toward attractors. Here we analyze the behavior of asymmetrical connected networks of linear threshold neurons, whose positive response is unbounded. We show that, for a wide range of parameters, this asymmetry brings interesting and computationally useful dynamical properties. When driven by input, the network explores potential solutions through highly unstable 'expansion' dynamics. This expansion is steered and constrained by negative divergence of the dynamics, which ensures that the dimensionality of the solution space continues to reduce until an acceptable solution manifold is reached. Then the system contracts stably on this manifold towards its final solution trajectory. The unstable positive feedback and cross inhibition that underlie expansion and divergence are common motifs in molecular and neuronal networks. Therefore we propose that very simple organizational constraints that combine these motifs can lead to spontaneous computation and so to the spontaneous modification of entropy that is characteristic of living systems.
authors.affiliation: Computation and Neural Systems, California Institute of Technology, Pasadena, California, United States of America; Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, California, United States of America; Departments of Neurosurgery, Neurology and Biomedical Sciences, Cedars-Sinai Medical Center, Los Angeles, California, United States of America.
authors.forename: Ueli
authors.initials: U
authors.lastname: Rutishauser
authors.affiliation: Nonlinear Systems Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America.
authors.forename: Jean-Jacques
authors.initials: JJ
authors.lastname: Slotine
authors.affiliation: Institute of Neuroinformatics, University and ETH Zurich, Zurich, Switzerland.
authors.forename: Rodney
authors.initials: R
authors.lastname: Douglas
mesh_terms: D019295:Computational Biology; D003198:Computer Simulation; D025461:Feedback, Physiological / Q000502:physiology; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology; D009474:Neurons / Q000502:physiology