Rate model accuracy as a function of input noise.

The response of each rate model is compared to a spiking population receiving an input with fluctuating common term and constant variance. The common input is composed of a baseline level and a fluctuating component composed of equal-amplitude sinusoidal oscillations with random phases and frequencies of 61, 50, 33, 13.1, and 7.9 Hz. A–B. Response of EIF population and both rate models to input with a CV of either 0.1 (A) or 0.8 (B). Top, middle, and bottom panels are as described in Figure 1. C. For each spiking model and each CV value, the maximum of the shifted correlation coefficient is computed between the trial-averaged firing rate of the spiking population and each rate model. The trial-averaged firing rate of a spiking population is computed from 300 repetitions of the same common input and different instantiations of noise. Each point in C represents the mean standard error of 10 different instantiations of the random phase shifts in the common input. In most cases, error bars are smaller than the marker. The maximal shifted correlation coefficient between the complex-valued rate model and the EIF, QIF, and LIF are shown in cyan, green, and blue, respectively. The same comparisons between the EIF and the classic rate model either optimized for each CV value or just to CV = 0.8 are shown in red and dark red, respectively. Classic rate model comparisons to the LIF and QIF produce similar results but are omitted for clarity.