Where are the most informative neurons?

Reinterpreting experimental observations. (A) A single neuron's performance (expressed as discriminability, d_i^{\prime }) to a discrimination task (± 3° motion discrimination) is typically expressed as a function of a neuron's tuned position (expressed as the offset {\text{Δ}}_ifrom the stimulus). Although the dataset here is synthetic, it is based on empirical values [2, 3]. Notably in both cases, the data are highly variable: the median (red curve) both peaked near 70° but the central tendency is weak. (B) Rescaling a neuron's position by its own tuning width {\stackrel{\sim }{\text{Δ}}}_i:={\text{Δ}}_i/{\sigma }_i reduces variation in two ways: a stronger central tendency along the x-axis, and substantially reduced variability along the y-axis. The red curve is the running average of 20 successive data points. (C) Variability with this same dataset is further reduced if d_i^{\prime } is also scaled as D^{\prime }:=d_i^{\prime }\cdot {\sigma }_i. All plots are based on the same 620 neurons. Offsets {\text{Δ}}_iare uniformly sampled from 0 to 100° in 5° increments with 30 repeats. Tuning widths are sampled from a Gaussian distribution (mean = 47°; standard deviation = 27°). A Poisson random number generator produced the spike count.