Three decoders have different performances for the responses of excitatory and inhibitory neurons. a–c, Space map decoder for one example FOV (the same as Fig. 2a) and accuracies for all FOVs. a, CoM (color dots) of 70 (seven ILDs with 10 repetitions) population vector and mean CoM (color diamonds) averaged over 10 repetitions. b, Decoded ILDs (color circles) that encircled the ground truth ILDs (color dots). In this FOV, the decoding performance is 30%. c, Gardner–Altman plot for two-sample (excitatory vs inhibitory) effect size. FOVs with less than five ILD-tuned neurons are excluded. The p-value is 0.0019, the effect size is 6.26%, and the 95% confidence interval ranges from 2.44 to 10.07%. d, Schematic of the opponent channel decoder. The population of neurons was divided into two groups: preferred ipsilateral sound (blue circle) and preferred contralateral sound (red circle). In this example, five neurons will be chosen randomly. During each trial, at least one neuron (black-filled dot) was chosen from each group or channel. For example, in the third trial, the responses of two neurons that preferred ipsilateral ILD and three neurons that preferred contralateral ILD were averaged separately (thick blue and red curves, respectively). The tuning curve difference (thick brown curve, contralateral minus ipsilateral responses) was used to predict the most likely ILDs. e, Performance of opponent channel decoder versus the number of neurons. Only those neurons that were significantly tuned to the ILD stimuli (ANOVA, p < 0.01; orange, 268 excitatory neurons; green, 211 inhibitory neurons) were included. From the single repetition response of multiple neurons to the same stimulus, we calculated the probability of each stimulus that could evoke those responses using Bayes’ rule (see Materials and Methods). If the stimulus with the highest probability was the real stimulus, then this stimulus was predicted correctly. The y-axis showed the percent of correctly predicted stimulus (0/7, 1/7, 2/7, …, 7/7; the dashed line was 1/7 chance level). Among each population size, 200 different combinations were chosen from the neural population. Thus, the thick color lines and error bars indicated the mean and standard error of performance. f, Schematic of population pattern decoder. Compared with the opponent channel decoder, it is not required to choose at least one neuron from two channels. Thus, the neural population was not grouped, and every neuron has the same probability to be chosen. Five neural responses from five different neurons (two thin blue and three thin red curves) were used to predict the most likely ILDs. g, Performance of population pattern decoder versus number of neurons.
