Extended Data Fig. 5: Information-limiting noise correlations and coding redundancy peaked just after stimulus onset and then declined for the rest of stimulus presentation.

(a) The fidelity with which stimulus identity could be decoded from neural ensemble activity saturated for large (>2000) populations of cells, for real (purple curves) but not trial-shuffled (black curves) datasets. To study ensembles of each size (x-axis), we randomly chose 100 different subsets of cells from the entire pool of neurons imaged across all areas. We then trained and tested optimal linear Fisher decoders using the neural activity within [0.4 s, 0.5 s] after stimulus onset on correctly performed trials. We quantified decoding performance using (d′)², which relates to the Fisher information the neural dynamics conveyed about the trial-type. Each curve shows data from one mouse. Whereas (d′)² saturated for large neural populations in real data, this did not occur for trial-shuffled datasets in which correlated fluctuations were scrambled. Shading: s.d. across all 100 subsets of cells for each ensemble size. Inset: Magnified view near the graph origin for one mouse. (b) Using the methods of a, we assessed how well optimal linear decoders could discriminate Go and No-Go trials. Plots show mean (d′)² values for this discrimination as a function of neural ensemble size and for different time bins, averaged over N = 6 mice. The size of the cell ensemble at which (d′)² saturated rose substantially with time during stimulus presentation but stayed relatively constant during the delay and response periods. (d′)² values are normalized relative to their maximum (saturating) value at each time bin. Ensemble size values are normalized relative to the total number of cells recorded in each mouse. (c) Plots like those of b, for individual mice during stimulus presentation. Data are shown only for time bins in which (d′)² values were significantly greater than for control datasets in which the trial-type labels were randomly shuffled (P<0.01; permutation test; N = 710–1340 trials). (d) Mean±s.e.m. (N = 6 mice) Ca²⁺ event rates per time bin (0.1 s duration) for all neurons on correctly performed Go and No-Go trials. These event rates had near identical time dependencies on trials of the two types, but the temporal variations were distinct from those of decoder score fluctuations (Fig. 4b) or correlated fluctuations in cells’ dynamics (panel f). Dashed vertical lines in d–f demarcate stimulus, delay and response periods of the trial structure. (e) Time dependence of the mean Fano factor, determined for each mouse by computing for each cell the ratio of the variance in the cell’s Ca²⁺ event rate to its mean Ca²⁺ event rate, on correctly performed trials. Shading: s.e.m. values (N = 2236-5292 cells). Legend also applies to f and g. (f) Noise correlations between pairs of cells with similar stimulus tuning rose sharply after stimulus onset, peaked ~0.2 s after stimulus onset, and then decayed to baseline values. Each coloured trace shows the mean absolute value of noise correlation coefficients for all pairs of similarly tuned cells across all imaged areas in each mouse. (g) Cross-correlation functions between the dynamics of absolute noise correlations across pairs of cells, shown in f, and the Fano factor, shown in e, as determined for each mouse over the 2-s-stimulus period. The graph shows that changes in pairwise noise correlation coefficients were negatively correlated with and most predictive of upcoming variations in the Fano factor with a lead time of ~200 ms. Shading: s.e.m. values (N = 10–20 time bins for each abscissa value). (h) Plot of the mean time-dependent rate (blue trace) of Ca²⁺ events in Go-stimulus-tuned neurons on Go trials and No-Go-stimulus-tuned neurons on No-Go trials, averaged over both cell-types and N = 6 mice. Also shown is the mean absolute noise correlation coefficient (red trace) for pairs of similarly tuned neurons, computed as in f for the same 6 mice. Notably, changes in noise correlation coefficient levels peaked sooner after stimulus onset than Ca²⁺ activity rates of tuned cells. After reaching their peak values, noise correlation coefficients declined back to baseline values by stimulus offset, whereas Ca²⁺ activity rates did not. These differences make it hard to explain the dynamics of noise correlation coefficients as resulting simply from changes in neural activity rates. Shading: s.e.m. across 6 mice. (i) Plot showing the change in information encoded by the neural ensemble if one cell were to become silent, assessed using instantaneous decoders. Each dot denotes the result from one time bin. (As shown in c and f, noise correlation coefficients vary with time following stimulus onset). Results for trial-shuffled data, in which correlated fluctuations were scrambled, are denoted with crosses and reveal a greater sensitivity to loss of one neuron. (j) Left, Traces of mean absolute noise correlation coefficients as a function of time during stimulus presentation, determined as in f for cell pairs in primary visual cortex (V1; blue trace), secondary cortical visual areas (areas LV, MV and PPC; red trace) or non-visual cortical areas (areas A, S, M and RSC; black trace). Right, Traces of mean absolute noise correlation coefficients between pairs of coding neurons located in different brain areas. The rise in noise correlations for similarly tuned cells in visual cortex is greater than that for cells outside visual cortex (P<0.03; Wilcoxon signed-rank test; N = 6 mice). Shading: s.e.m. across N = 6 mice. (k) We calculated the covariance in the neurons’ responses on each trial-type and on each day. We then averaged the covariance matrices for the two trial-types and computed the top 3 eigenvectors for each day. Left, A plot showing the similarity between the pairs of different subspaces (Methods), each defined by the top 3 eigenvectors of the noise covariance matrix on each day of experimentation. The matrix row and columns labelled ‘C’ is for the noise covariance matrix computed for the set of all trials across all days. Right, As control, we computed the subspace similarities for trial-shuffled datasets in which each neuron’s responses were permuted across trials with the same stimulus. Overall, noise covariance structure in the real data was significantly similar across days, to a degree much beyond that in shuffled datasets.