Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity
Different theoretical models have tried to investigate the feasibility of recurrent neural mechanisms for achieving direction selectivity in the visual cortex. The mathematical analysis of such models has been restricted so far to the case of purely linear networks. We present an exact analyti...
| Main Authors: | , |
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| Language: | en_US |
| Published: |
2004
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| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/7273 |
| _version_ | 1811091161716097024 |
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| author | Giese, M.A. Xie, X. |
| author_facet | Giese, M.A. Xie, X. |
| author_sort | Giese, M.A. |
| collection | MIT |
| description | Different theoretical models have tried to investigate the feasibility of recurrent neural mechanisms for achieving direction selectivity in the visual cortex. The mathematical analysis of such models has been restricted so far to the case of purely linear networks. We present an exact analytical solution of the nonlinear dynamics of a class of direction selective recurrent neural models with threshold nonlinearity. Our mathematical analysis shows that such networks have form-stable stimulus-locked traveling pulse solutions that are appropriate for modeling the responses of direction selective cortical neurons. Our analysis shows also that the stability of such solutions can break down giving raise to a different class of solutions ("lurching activity waves") that are characterized by a specific spatio-temporal periodicity. These solutions cannot arise in models for direction selectivity with purely linear spatio-temporal filtering. |
| first_indexed | 2024-09-23T14:57:59Z |
| id | mit-1721.1/7273 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:57:59Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/72732019-04-15T00:40:26Z Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity Giese, M.A. Xie, X. AI direction visual cortex nonlinear dynamics lurching waves stability recurre Different theoretical models have tried to investigate the feasibility of recurrent neural mechanisms for achieving direction selectivity in the visual cortex. The mathematical analysis of such models has been restricted so far to the case of purely linear networks. We present an exact analytical solution of the nonlinear dynamics of a class of direction selective recurrent neural models with threshold nonlinearity. Our mathematical analysis shows that such networks have form-stable stimulus-locked traveling pulse solutions that are appropriate for modeling the responses of direction selective cortical neurons. Our analysis shows also that the stability of such solutions can break down giving raise to a different class of solutions ("lurching activity waves") that are characterized by a specific spatio-temporal periodicity. These solutions cannot arise in models for direction selectivity with purely linear spatio-temporal filtering. 2004-10-20T21:05:06Z 2004-10-20T21:05:06Z 2002-08-01 AIM-2002-013 CBCL-220 http://hdl.handle.net/1721.1/7273 en_US AIM-2002-013 CBCL-220 7 p. 2554351 bytes 1165357 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | AI direction visual cortex nonlinear dynamics lurching waves stability recurre Giese, M.A. Xie, X. Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity |
| title | Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity |
| title_full | Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity |
| title_fullStr | Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity |
| title_full_unstemmed | Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity |
| title_short | Exact Solution of the Nonlinear Dynamics of Recurrent Neural Mechanisms for Direction Selectivity |
| title_sort | exact solution of the nonlinear dynamics of recurrent neural mechanisms for direction selectivity |
| topic | AI direction visual cortex nonlinear dynamics lurching waves stability recurre |
| url | http://hdl.handle.net/1721.1/7273 |
| work_keys_str_mv | AT giesema exactsolutionofthenonlineardynamicsofrecurrentneuralmechanismsfordirectionselectivity AT xiex exactsolutionofthenonlineardynamicsofrecurrentneuralmechanismsfordirectionselectivity |