Extended Data Fig. 9: Moving grating visual stimuli oriented at ±6° are harder to distinguish on the basis of their evoked neural ensemble responses than gratings oriented at ±30°, but also reveal the saturation of information signalling in large neural populations.
From: Fundamental bounds on the fidelity of sensory cortical coding
a, (d′)2 values determined using an ‘instantaneous’ decoder for the interval [0.70 s, 0.94 s] from visual stimulation onset, plotted as a function of the number of cells, n, in the ensemble in mice presented moving gratings oriented at ±6°. Data points represent mean values determined across 100 different subsets of cells, and the shading represents s.e.m. As in Fig. 3f, g, we fit the (d′)2 values as a function of n using a one-parameter fit, (d′)2 = (d′)2shuffled/(1 + ε × n), where (d′)2shuffled (n) is the empirically determined value of (d′)2 for the same number of cells in the shuffled data, and ε is the fit parameter. For each mouse, for both real and trial-shuffled data we normalized (d′)2 values by the value of (d′shuffled)2 for n = 1,000 neurons. Goodness of fit: R2 = 0.41 ± 0.17 (s.d). N = 5 mice. ε = 0.0021 ± 0.0008 (s.d.), 122–167 trials per stimulus condition for each mouse. b, Same as a, but using the ‘cumulative’ decoding strategy over the [0 s, 0.94 s] time interval. c, Box-and-whisker plots of the asymptotic values of d′ in the limit of many neurons (right) and the number of cells at which (d′)2 attains half its asymptotic value (left) as determined from parametric fits to the data of a and b for the instantaneous (open boxes) and cumulative (filled boxes) decoding strategies. Optimal linear decoders (green data) slightly but significantly outperformed diagonal decoders (black data) (**P < 0.0001; one-tailed Wilcoxon rank sum test; N = 100 different randomly chosen assignments of trials to decoder training and test sets in each mouse; 122–167 trials per stimulus condition for each mouse; open circles denote mean values from N = 5 individual mice). d, e, Histograms for the real (unshuffled) and shuffled datasets of the ensemble neural responses to each of the two visual stimuli, projected onto the direction of the optimal decoding vector determined by PLS analysis, as computed in each mouse viewing moving gratings oriented either at ±30° (d) or ±6° (e), using all imaged neurons and the instantaneous decoding approach. Error bars denote counting errors. Values on the x axes are plotted for each mouse in units of the s.d. of its neural ensemble responses along the decoding vector for the shuffled data. For each mouse, the histograms have approximately equal shapes for the two visual stimuli, are unimodal and approximately symmetric about their mean values, bolstering the use of linear decoding and d′. This analysis involved 217–232 trials per stimulus condition per mouse in d and 122–167 trials per stimulus condition per mouse in e.
