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....
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| Format: | Article |
| Language: | en_US |
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Public Library of Science
2015
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| Online Access: | http://hdl.handle.net/1721.1/94559 https://orcid.org/0000-0002-7161-7812 |
| _version_ | 1826192911312617472 |
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| author | Rutishauser, Ueli Douglas, Rodney J. Slotine, Jean-Jacques E. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Rutishauser, Ueli Douglas, Rodney J. Slotine, Jean-Jacques E. |
| author_sort | Rutishauser, Ueli |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:31:03Z |
| format | Article |
| id | mit-1721.1/94559 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:31:03Z |
| publishDate | 2015 |
| publisher | Public Library of Science |
| record_format | dspace |
| spelling | mit-1721.1/945592022-09-30T14:57:06Z Computation in Dynamically Bounded Asymmetric Systems Rutishauser, Ueli Douglas, Rodney J. Slotine, Jean-Jacques E. Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Nonlinear Systems Laboratory Slotine, Jean-Jacques E. 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. 2015-02-17T16:12:08Z 2015-02-17T16:12:08Z 2015-01 2014-09 Article http://purl.org/eprint/type/JournalArticle 1553-7358 1553-734X http://hdl.handle.net/1721.1/94559 Rutishauser, Ueli, Jean-Jacques Slotine, and Rodney Douglas. “Computation in Dynamically Bounded Asymmetric Systems.” Edited by Olaf Sporns. PLoS Comput Biol 11, no. 1 (January 24, 2015): e1004039. https://orcid.org/0000-0002-7161-7812 en_US http://dx.doi.org/10.1371/journal.pcbi.1004039 PLOS Computational Biology Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ application/pdf Public Library of Science Public Library of Science |
| spellingShingle | Rutishauser, Ueli Douglas, Rodney J. Slotine, Jean-Jacques E. Computation in Dynamically Bounded Asymmetric Systems |
| title | Computation in Dynamically Bounded Asymmetric Systems |
| title_full | Computation in Dynamically Bounded Asymmetric Systems |
| title_fullStr | Computation in Dynamically Bounded Asymmetric Systems |
| title_full_unstemmed | Computation in Dynamically Bounded Asymmetric Systems |
| title_short | Computation in Dynamically Bounded Asymmetric Systems |
| title_sort | computation in dynamically bounded asymmetric systems |
| url | http://hdl.handle.net/1721.1/94559 https://orcid.org/0000-0002-7161-7812 |
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