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Population Coding and Decoding in a Neural Field: A Computational Study

s.wu{at}dcs.ac.uk, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan, and Department of Computer Science, Sheffield University, U.K.

Shun-ichi Amari

amari{at}brain.riken.go.jp, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan

Hiroyuki Nakahara

hiro{at}brain.riken.go.jp, RIKEN Brain Science Institute, Wako-shi, Saitama, Japan, and Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

This study uses a neural field model to investigate computational aspects of population coding and decoding when the stimulus is a single variable. A general prototype model for the encoding process is proposed, in which neural responses are correlated, with strength specified by a gaussian function of their difference in preferred stimuli. Based on the model, we study the effect of correlation on the Fisher information, compare the performances of three decoding methods that differ in the amount of encoding information being used, and investigate the implementation of the three methods by using a recurrent network. This study not only rediscovers main results in existing literatures in a unified way, but also reveals important new features, especially when the neural correlation is strong. As the neural correlation of firing becomes larger, the Fisher information decreases drastically. We confirm that as the width of correlation increases, the Fisher information saturates and no longer increases in proportion to the number of neurons. However, we prove that as the width increases further—wider than times the effective width of the turning function—the Fisher information increases again, and it increases without limit in proportion to the number of neurons. Furthermore, we clarify the asymptotic efficiency of the maximum likelihood inference (MLI) type of decoding methods for correlated neural signals. It shows that when the correlation covers a nonlocal range of population (excepting the uniform correlation and when the noise is extremely small), the MLI type of method, whose decoding error satisfies the Cauchy-type distribution, is not asymptotically efficient. This implies that the variance is no longer adequate to measure decoding accuracy.

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