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Binary tuning is optimal for neural rate coding with high temporal resolution


Bethge,  M
Research Group Computational Vision and Neuroscience, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Bethge, M., Rotermund, D., & Pawelzik, K. (2003). Binary tuning is optimal for neural rate coding with high temporal resolution. Advances in Neural Information Processing Systems, 189-196.

Here we derive optimal gain functions for minimum mean square reconstruction from neural rate responses subjected to Poisson noise. The shape of these functions strongly depends on the length T of the time window within which spikes are counted in order to estimate the underlying firing rate. A phase transition towards pure binary encoding occurs if the maximum mean spike count becomes smaller than approximately three provided the minimum firing rate is zero. For a particular function class, we were able to prove the existence of a second-order phase transition analytically. The critical decoding time window length obtained from the analytical derivation is in precise agreement with the numerical results. We conclude that under most circumstances relevant to information processing in the brain, rate coding can be better ascribed to a binary (low-entropy) code than to the other extreme of rich analog coding.