Computation in Dynamically Bounded Asymmetric Systems
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.
© 2015 Rutishauser et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Received: September 1, 2014; Accepted: November 12, 2014; Published: January 24, 2015. Editor: Olaf Sporns, Indiana University, UNITED STATES. Data Availability:All data in this manuscript is simulated. The MATLAB source code of the underlying models is available on the webpage http://www.ini.uzh.ch/~urut/DFAWTA/ Funded by EU grants DAISY (FP6-2005-015803) and SECO (FP7-2009-216593) awarded to RJD. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. We thank the participants of the Capo Caccia Cognitive Neuromorphic Engineering workshops of 2009–2014 for discussion. Author Contributions: Conceived and designed the experiments: UR JJS RJD. Performed the experiments: UR. Analyzed the data: UR JJS RJD. Contributed reagents/materials/analysis tools: UR JJS RJD. Wrote the paper: UR JJS RJD. Competing interests: The authors have declared that no competing interests exist.
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