Bethge Matthias, Rotermund David, Pawelzik Klaus
Institute of Theoretical Physics, University of Bremen, Otto-Hahn-Allee, D-28334 Bremen, Germany.
Phys Rev Lett. 2003 Feb 28;90(8):088104. doi: 10.1103/PhysRevLett.90.088104. Epub 2003 Feb 27.
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.
在此，我们从受泊松噪声影响的神经放电率响应中推导用于最小均方重构的最优调谐函数。这些调谐函数的形状强烈依赖于时间窗口的长度T，在该时间窗口内对动作电位（尖峰）进行计数以估计潜在的放电率。如果最大平均尖峰计数小于约3，则会发生向纯二进制编码的相变。对于特定的函数类，我们证明了二阶相变的存在。解析推导的临界解码时间窗口长度与数值结果精确吻合。我们的分析表明，只要时间是关键约束，二进制速率编码在大脑中应该占主导地位。
