Fig. 3.
Performance of Fisher-optimal codes. (A) Optimal tuning width as a function of population size for T = 1,000 ms. (B) MASE of a neural population with independent noise and Fisher-optimal width for 10 different integration times T (values logarithmically spaced between 10 and 1,000; light to dark gray). The width of the tuning functions is optimized for each N separately and chosen such that it minimizes the MASE. (C) IMDE for the same Fisher-optimal populations as in B. (D) Family of neurometric functions for Fisher-optimal population codes at T = 10 ms for n = 10 to n = 190 (right to left). ΔθS is the point of saturation, and P is the pedestal error, also marked by the gray dashed line. (E) The pedestal error P is independent of the population size N (T = 1,000 ms not shown for clarity). (F) The pedestal error P depends on the integration time (black; independent of N) and analytical approximation for P (gray). (G) For each population size, approximately three neurons are activated by each stimulus (red), independent of the population size. (H) For coarse discrimination (red vs. green), the two stimuli activate disjoint sets of neurons determining the pedestal error (red vs. green; error bars show 2 SD). For fine discrimination, the activated populations overlap, determining the initial region (red vs. blue). (I) Dependence of the point of saturation ΔθS on the population size N. (J) Two parts of the neurometric function of Fisher-optimal population codes: the pedestal error P (light gray) and the initial region (dark gray). Together they determine the IMDE. The neurometric function is shown in units of difference in preferred orientation; therefore it does not depend on N. The pedestal error is reached at ΔθS ~ 2Δφ (Fig. S4). As N → ∞, the x axis is rescaled and the area of the initial region AIR goes to zero (SI Text) and the IMDE converges to πP.