Collective stability of networks of winner-take-all circuits
The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual cortex are consistent with the recurrent excitation and inhib...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
MIT Press
2011
|
| Online Access: | http://hdl.handle.net/1721.1/66502 https://orcid.org/0000-0002-7161-7812 |
| _version_ | 1811090870703751168 |
|---|---|
| author | Slotine, Jean-Jacques E. Douglas, Rodney J. Rutishauser, Ueli |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Slotine, Jean-Jacques E. Douglas, Rodney J. Rutishauser, Ueli |
| author_sort | Slotine, Jean-Jacques E. |
| collection | MIT |
| description | The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual cortex are consistent with the recurrent excitation and inhibitory feedback required for cooperative-competitive circuits such as the soft winner-take-all (WTA). WTA circuits offer interesting computational properties such as selective amplification, signal restoration, and decision making. But these properties depend on the signal gain derived from positive feedback, and so there is a critical trade-off between providing feedback strong enough to support the sophisticated computations while maintaining overall circuit stability. The issue of stability is all the more intriguing when one considers that the WTAs are expected to be densely distributed through the superficial layers and that they are at least partially interconnected. We consider how to reason about stability in very large distributed networks of such circuits. We approach this problem by approximating the regular cortical architecture as many interconnected cooperative-competitive modules. We demonstrate that by properly understanding the behavior of this small computational module, one can reason over the stability and convergence of very large networks composed of these modules. We obtain parameter ranges in which the WTA circuit operates in a high-gain regime, is stable, and can be aggregated arbitrarily to form large, stable networks. We use nonlinear contraction theory to establish conditions for stability in the fully nonlinear case and verify these solutions using numerical simulations. The derived bounds allow modes of operation in which the WTA network is multistable and exhibits state-dependent persistent activities. Our approach is sufficiently general to reason systematically about the stability of any network, biological or technological, composed of networks of small modules that express competition through shared inhibition. |
| first_indexed | 2024-09-23T14:53:17Z |
| format | Article |
| id | mit-1721.1/66502 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:53:17Z |
| publishDate | 2011 |
| publisher | MIT Press |
| record_format | dspace |
| spelling | mit-1721.1/665022022-09-29T11:13:17Z Collective stability of networks of winner-take-all circuits Slotine, Jean-Jacques E. Douglas, Rodney J. Rutishauser, Ueli Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Nonlinear Systems Laboratory Slotine, Jean-Jacques E. Slotine, Jean-Jacques E. The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual cortex are consistent with the recurrent excitation and inhibitory feedback required for cooperative-competitive circuits such as the soft winner-take-all (WTA). WTA circuits offer interesting computational properties such as selective amplification, signal restoration, and decision making. But these properties depend on the signal gain derived from positive feedback, and so there is a critical trade-off between providing feedback strong enough to support the sophisticated computations while maintaining overall circuit stability. The issue of stability is all the more intriguing when one considers that the WTAs are expected to be densely distributed through the superficial layers and that they are at least partially interconnected. We consider how to reason about stability in very large distributed networks of such circuits. We approach this problem by approximating the regular cortical architecture as many interconnected cooperative-competitive modules. We demonstrate that by properly understanding the behavior of this small computational module, one can reason over the stability and convergence of very large networks composed of these modules. We obtain parameter ranges in which the WTA circuit operates in a high-gain regime, is stable, and can be aggregated arbitrarily to form large, stable networks. We use nonlinear contraction theory to establish conditions for stability in the fully nonlinear case and verify these solutions using numerical simulations. The derived bounds allow modes of operation in which the WTA network is multistable and exhibits state-dependent persistent activities. Our approach is sufficiently general to reason systematically about the stability of any network, biological or technological, composed of networks of small modules that express competition through shared inhibition. California Institute of Technology Massachussets Institute of Technology Sixth Framework Programme (European Commission) (FP6-2005-015803) Seventh Framework Programme (European Commission) (FP7-2009-216593) 2011-10-19T20:18:04Z 2011-10-19T20:18:04Z 2011-02 Article http://purl.org/eprint/type/JournalArticle 0899-7667 1530-888X http://hdl.handle.net/1721.1/66502 Rutishauser, Ueli, Rodney J. Douglas, and Jean-Jacques Slotine. “Collective Stability of Networks of Winner-Take-All Circuits.” Neural Computation 23 (2011): 735-773. Web. 19 Oct. 2011. https://orcid.org/0000-0002-7161-7812 en_US http://dx.doi.org/10.1162/NECO_a_00091 Neural Computation Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf MIT Press MIT Press |
| spellingShingle | Slotine, Jean-Jacques E. Douglas, Rodney J. Rutishauser, Ueli Collective stability of networks of winner-take-all circuits |
| title | Collective stability of networks of winner-take-all circuits |
| title_full | Collective stability of networks of winner-take-all circuits |
| title_fullStr | Collective stability of networks of winner-take-all circuits |
| title_full_unstemmed | Collective stability of networks of winner-take-all circuits |
| title_short | Collective stability of networks of winner-take-all circuits |
| title_sort | collective stability of networks of winner take all circuits |
| url | http://hdl.handle.net/1721.1/66502 https://orcid.org/0000-0002-7161-7812 |
| work_keys_str_mv | AT slotinejeanjacquese collectivestabilityofnetworksofwinnertakeallcircuits AT douglasrodneyj collectivestabilityofnetworksofwinnertakeallcircuits AT rutishauserueli collectivestabilityofnetworksofwinnertakeallcircuits |