Extended Data Fig. 3: Neural ensemble representations of the visual stimuli were invariant over most of the stimulation period.

(a) Mean time-dependent occurrence rates of Ca²⁺ transient events per time bin (0.1 s duration) across different intervals of the trial-structure (demarcated by vertical lines) for 24 neurons from 8 cortical areas, averaged across 5 sessions in one mouse on Go (blue traces) and No-Go (black) trials. Shading: s.d. across 415 trials of each type. (b) For cells that responded significantly to one of the two stimuli (see Fig. 2c), shown are mean percentages of coding cells responding to the Go stimulus in each of 8 areas. The remainder of coding cells responded to the No-Go stimulus. Error bars: s.d. across N = 6 mice. (c) Procedure for training cross-validated instantaneous or consensus linear decoders. After constructing an unbiased dataset with equal numbers of Go and No-Go trials, we divided the set of trials into 3 equal portions, one for dimensionality reduction, another for decoder training, and the third for decoder testing. Using the first subset, a partial least squares (PLS) analysis identified a low-dimensional subspace of the neural ensemble activity that was informative for stimulus discrimination. Within this subspace, we used the second subset of trials to train a Fisher linear decoder (indicated by the vector W_decoder). We used the third subset to test decoder performance. For training and testing datasets, we computed the fidelity, d’, with which the stimuli could be distinguished. To train decoders for identifying the mouse’s decision, we followed the same procedures, starting with equal numbers of correctly and incorrectly performed trials with a given stimulus. (d) We trained consensus decoders during the stimulus, delay, and response intervals of correctly performed trials. Plots show mean (d’)² values for decoder training (blue) and testing (red) datasets, versus the number of PLS dimensions used. When constructing each decoder, we used the number of PLS dimensions that maximized (d’)² for testing datasets. All plotted (d’)² values are separately normalized for each mouse to the maximum (d’)² determined with the testing data. On average, with >5 PLS dimensions decoders overfit the training data, yielding greater (d’)² values than for testing data. For shuffled datasets, 1 or 2 PLS dimensions yielded maximal (d’)² values (data not shown). Shading: s.d. across N = 6 mice. (e) We determined the similarity of the subspaces defined by the top 3 PLS dimensions for each mouse on different days (1–5) or for its across-day, common decoder (C) (Methods). We used the top 3 dimensions, since these contain most of the information (d). The matrices show mean similarity values for all pairs of subspaces, averaged over N = 6 mice, for real (left) and shuffled (right) datasets. For real datasets, PLS dimensions for common decoders were highly similar to those for single-day decoders. (f) Optimal linear decoders of stimulus-type retained a constant form across stimulus presentation. Plots show Pearson correlation coefficients, r, between all pairs of instantaneous decoders (constructed using all imaged neurons in each mouse), for each time bin. (g) Due to the stationarity of the optimal decoders across stimulus presentation, f, consensus and instantaneous decoders performed nearly equivalently. Plots show mean (d’)² values for consensus decoders of stimulus-type versus those for instantaneous decoders, for correctly performed trials. Each datum shows testing results attained by applying each decoder-type to data from one time bin during stimulus presentation. In some mice, e.g. Mice 5 and 6, the consensus decoder achieved slightly superior performance, presumably due to its larger training dataset. (h) Similar results to those of f, computed for different areas and averaged over 6 mice. (i) Similar results to those of Fig. 3c, computed separately for different areas. (j) To measure the information captured by trial-type decoders about the stimulus (S) or mouse’s response (R) in the stimulus (left), delay (middle) or response (right) periods, we projected neural activity on all 4 trial-types (Hit, Miss, Correct Rejection, and False Alarm) onto the common trial-type decoders trained for each period using correctly performed trials. We then computed (d’)² values using trials in which either the stimulus or response was held constant but the other varied. Information, (d’)², about the stimulus did not vary significantly between Lick and No-Lick trials, so we averaged (d’)² values across both stimuli in each plot’s left column. Response-coding was much stronger on Go trials (see k), so right columns only show (d’)² values from Go trials. Each blue point shows data from one mouse (mean±s.d., N = 100 different subsets of trials, each with equal numbers of trials of the two types). Red points: averages across mice (mean±s.e.m., N = 6). During the stimulus period, common decoders nearly exclusively captured stimulus information, which was 691±315 times greater (mean±s.e.m.; N = 6 mice) than information captured about the mouse’s response. In the delay period, response information rose. During the response period, common decoders captured response information that was comparable or greater to information about the stimulus. (k) The mean Fisher information encoded by neural ensemble activity about the stimulus-type was independent of the mouse’s response (top), as (d’)² values for consensus common stimulus decoders trained and tested on ‘No-Lick’ trials were indistinguishable to those for ‘Lick’ trials (P <0.7; Wilcoxon signed-rank test; N = 6 mice). On ‘Go’ but not ‘No-Go’ trials, the upcoming response could be predicted (P<0.01; permutation test; N = 40–754 trials) from neural activity during stimulus presentation (bottom). For each comparison, we constructed training datasets for the two decoders to have equal numbers of trials, 50% of each type. Blue-shaded points are from individual mice; error bars are s.d. (N = 100 different randomly chosen sets of trials. Red points are means; error bars are s.d. (N = 6 mice). (l) Control analysis for Fig. 3c. Across-day common consensus decoders performed equivalently to single-day consensus decoders when they were trained with equally sized datasets. Here we trained common decoders by sub-sampling trials from each session so the training dataset had the same of number of trials as that of the day with the smallest number of trials. We trained single-day decoders using this same number of trials.