INSTITUTE OF PHYSICS PUBLISHING NETWORK: COMPUTATION IN NEURAL SYSTEMS Network: Comput. Neural Syst. 14 (2003) 1–18 PII: S0954-898X(03)54125-2 Ascii/Word NET/net154125-xsl/SPE Printed 26/5/2003 Focal Image (Ed: STUART ) CRC data File name NE .TEX First page Date req. Last page Issue no. Total pages Artnum Cover date Sensory adaptation as Kalman filtering: theory and illustration with contrast adaptation Norberto M Grzywacz 1 and Joaqu´ ın de Juan 2 1 Department of Biomedical Engineering and Neuroscience Graduate Program, University of Southern California, University Park, OHE 500, 3650 S McClintock Avenue, Los Angeles, CA 90089-1451, USA 2 Departamento de Biotecnolog´ ıa, Facultad de Ciencias, Universidad de Alicante, Apartado de Correos 99, 03080 Alicante, Spain E-mail: nmg@bmsr.usc.edu and jdj@ua.es Received 1 October 2002, in final form 29 March 2003 Published Online at stacks.iop.org/Network/14/1 Abstract Sensory adaptation allows biological systems to adjust to variations in the environment. A recent theoretical work postulated that the goal of adaptation is to minimize errors in the performance of particular tasks. The proposed minimization was Bayesian and required prior knowledge of the environment and of the limitations of the mechanisms processing the information. One problem with that formulation is that the environment changes in time and the theory did not specify how to know what the current state of the environment is. Here, we extend that theory to estimate optimally the environmental state from the temporal stream of responses. We show that such optimal estimation is a generalized form of Kalman filtering. An application of this new Kalman- filtering framework is worked out for retinal contrast adaptation. It is shown that this application can account for surprising features of the data. For example, it accounts for the differences in responses to increases and decreases of mean contrasts in the environment. In addition, it accounts for the two-phase decay of contrast gain when the mean contrast in the environment rises suddenly. The success of this and related theories suggest that sensory adaptation is a form of constrained biological optimization. 1. Introduction Adaptation is an important property of biological sensory systems, as it allows them to adjust to variations in the environment (Thorson and Biederman-Thorson 1974,Laughlin 1989). Several investigators have suggested that this adjustment optimizes the systems in the performance of particular tasks. Some tasks are generic, such as sending as much information as possible to the rest of the brain (Srinivasan et al 1982, Atick and Redlich 1992, Field 1994). Other tasks are 0954-898X/03/000001+18$30.00 © 2003 IOP Publishing Ltd Printed in the UK 1