Second order phase transition in neural rate coding: binary encoding is optimal for rapid signal transmission.
Here, we derive optimal tuning functions for minimum mean square reconstruction from neural rate responses subjected to Poisson noise. The shape of these tuning functions strongly depends on the length T of the time window within which action potentials (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. For a particular function class, we prove the existence of a second-order phase transition. The analytically derived critical decoding time window length is in precise agreement with numerical results. Our analysis reveals that binary rate encoding should dominate in the brain wherever time is the critical constraint.
Bethge
Matthias
M
Institute of Theoretical Physics, University of Bremen, Otto-Hahn-Allee, D-28334 Bremen, Germany.
Rotermund
David
D
Pawelzik
Klaus
K
D000200:Action Potentials / Q000502:physiology; D000818:Animals; D002490:Central Nervous System / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D016012:Poisson Distribution; D009435:Synaptic Transmission / Q000502:physiology*