Fisher-Optimal Neural Population Codes for High-Dimensional Diffeomorphic Stimulus Representations

Zhuo Wang and Alan A Stocker and Dan D Lee
NIPS Advances in Neural Information Processing Systems 26, Lake Tahoe CA, December 2013, MIT Press. In press.

In many neural systems, information about stimulus variables is often represented in a distributed manner by means of a population code. It is generally assumed that the responses of the neural population are tuned to the stimulus statistics, and most prior work has investigated the optimal tuning characteristics of one or a small number of stimulus variables. In this work, we investigate the optimal tuning for diffeomorphic representations of high-dimensional stimuli. We analytically derive the solution that minimizes the L2 reconstruction loss. We compared our solution with other well-known criteria such as maximal mutual information. Our solution suggests that the optimal weights do not necessarily decorrelate the inputs, and the optimal nonlinearity differs from the conventional equalization solution. Results illustrating these optimal representations are shown for some input distributions that may be relevant for understanding the coding of perceptual pathways.

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