Extended Data Fig. 8: The canonical correlation noise modes before stimulus onset were distinct from those after stimulus onset, which were task-related.

(a) During the inter-trial interval (ITI), there were significantly correlated noise fluctuation modes that were shared between cortical areas. However, these modes were not the same as the shared noise fluctuations that arose at stimulus onset. The plots show the mean (N = 6 mice) time courses of the correlation coefficients for the first- and second-largest noise modes shared between 28 different pairs of brain areas (pairs denoted via the graph titles and the colour legend at far right), as found by applying CCA separately to ITI periods (–2 < t < 0) and visual stimulation periods (2 > t > 0). Dashed traces, with and without open circles, respectively show the correlation coefficients for the first and second shared noise modes as identified during ITI periods. Solid traces, with and without open circles, respectively show the correlation coefficients for the first and second share noise modes as identified during stimulus periods. At stimulus onset (t = 0), correlated fluctuations declined within the CCA noise modes identified during ITI periods, whereas correlated fluctuations within the modes identified during the task substantially increased. (b) CCA noise modes found during stimulus periods differ from those found during ITI periods, as shown by the cross-correlation coefficients between the CCA noise modes found for each pair of brain areas before vs. after stimulus onset. The plots show these cross-correlation coefficient values for the largest 5 modes for each pair of brain areas. To compute these coefficients, for each mouse we created 200 different random assignments of half of the trials into a training set and half of the trials into a validation set. Using 100 of these random assignments, we determined CCA noise modes for the ITI period. Using the other 100 assignments, we determined CCA noise modes for the task period. For each entry in the plots, we plotted the mean value of the cross-correlation coefficient, averaged across all 10,000 pairings of one mode from the ITI period and one from the stimulus period, and across 6 different mice. Within each plot, row labels designate the brain area for which we computed the cross-correlation coefficient; column labels designate the area with which the row area was paired in the CCA. (c) As a control analysis for the results of (b), we examined the variability in our estimates of the largest 5 CCA noise modes during the stimulus period. To do this, we computed for each mouse the correlation coefficients between the CCA modes determined from 100 different random assignments of trials into training and validation sets. This showed that most CCA modes are stable during the stimulus presentation period. For each entry in the plots, we plotted the mean value of the cross-correlation coefficient, averaged across all 9,900 pairings of two different mode determinations from the stimulus period, and across 6 different mice. Within each plot, row labels designate the brain area for which we computed the cross-correlation coefficient; column labels designate the area with which the row area was paired in the CCA. The results show that the relative lack of stability exhibited in (b) between CCA noise modes before versus after stimulus onset is not simply due to the statistical variability in the determination of CCA noise modes. (d) In each imaged brain area, we performed a principal component analysis (PCA) of the noise fluctuations around the mean stimulus-evoked responses, averaged over both stimuli. For each brain area, we then computed the correlation coefficients between the modes identified by PCA and those identified by CCA with each of the other 7 brain areas. The results show that fluctuation modes identified by PCA are highly distinct from those found by CCA, indicating that PCA can be incapable of detecting correlated fluctuations between brain areas. (e) Analogous plots to those in (d), except that we performed the PCA over the aggregated set of all brain areas. (f) Plots analogous to those in Fig. 5e, except that results are shown for all pairs of brain areas, rather than averaged across all pairs of sensory areas.