Maass, Wwolfgang and Joshi, Prashant and Sontag, Eduardo D. (2007) Computational Aspects of Feedback in Neural Circuits. PLoS Computational Biology, 3 (1). pp. 15-20. ISSN 1553-734X. http://resolver.caltech.edu/CaltechAUTHORS:20130816-103201527
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It has previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with a rapidly fading memory. We investigate the computational capability of such circuits in the more realistic case where not only readout neurons, but in addition a few neurons within the circuit, have been trained for specific tasks. This is essentially equivalent to the case where the output of trained readout neurons is fed back into the circuit. We show that this new model overcomes the limitation of a rapidly fading memory. In fact, we prove that in the idealized case without noise it can carry out any conceivable digital or analog computation on time-varying inputs. But even with noise, the resulting computational model can perform a large class of biologically relevant real-time computations that require a nonfading memory. We demonstrate these computational implications of feedback both theoretically, and through computer simulations of detailed cortical microcircuit models that are subject to noise and have complex inherent dynamics. We show that the application of simple learning procedures (such as linear regression or perceptron learning) to a few neurons enables such circuits to represent time over behaviorally relevant long time spans, to integrate evidence from incoming spike trains over longer periods of time, and to process new information contained in such spike trains in diverse ways according to the current internal state of the circuit. In particular we show that such generic cortical microcircuits with feedback provide a new model for working memory that is consistent with a large set of biological constraints. Although this article examines primarily the computational role of feedback in circuits of neurons, the mathematical principles on which its analysis is based apply to a variety of dynamical systems. Hence they may also throw new light on the computational role of feedback in other complex biological dynamical systems, such as, for example, genetic regulatory networks.
|Additional Information:||Copyright: � 2007 Maass et al. Received December 1, 2005; Accepted October 24, 2006; Published January 19, 2007. A previous version of this article appeared as an Early Online Release on October 24, 2006 (doi:10.1371/journal.pcbi.0020165.eor). Comments from Wulfram Gerstner, Stefan Haeusler, Herbert Jaeger, Konrad Koerding, Henry Markram, Gordon Pipa, Misha Tsodyks, and Tony Zador are gratefully acknowledged. Our computer simulations used software written by Thomas Natschlaeger, Stefan Haeusler, and Michael Pfeiffer. This research was partially supported by the Austrian Science Fund FWF grants S9102-N04 and P17229-N04, and PASCAL project IST2002–506778 of the European Union. The work of EDS was partially supported by US National Science Foundation grants DMS-0504557 and DMS-0614371.|
|Group:||Koch Laboratory, KLAB|
|Official Citation:||Maass W, Joshi P, Sontag ED (2007) Computational aspects of feedback in neural circuits. PLoS Comput Biol 3(1): e165. doi:10.1371/journal.pcbi.0020165|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||KLAB Import|
|Deposited On:||26 Jan 2008 03:58|
|Last Modified:||15 Nov 2013 00:11|
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