Extended Data Fig. 6: Alignment of neural data across animals into a joint subspace.

(a) Specification of time points used for alignment displayed for two example neurons from different subjects that show similar responses during avoid, error and ITI events in task 1 (blue shade) and task 2 (green shade). (b) To align neural population data, the temporally aligned event averages displayed in a are first concatenated for all cells. We then process these event averages (Methods) and concatenate them along the time axis. Next, PCA is used to generate the joint subspace, which is defined by the coefficients of the first n PCs (n is chosen below). Subject-specific projection matrices into the joint subspace can then be computed by splitting the coefficient matrix back into matrices for individual subjects and orthogonalizing them using the QR decomposition. (c) Top: mean projections onto subspace dimensions 1–10 (n = 12 subjects). Shading indicates temporal structure displayed in a. Bottom: projections displayed for individual subjects, highlighting common structure. (d) Variance explained by the first 20 subspace dimensions (mean and 95% CIs for 80 repetitions) for the joint PCA + QR procedure (black). To control how the alignment procedure affects how well the low-dimensional subspace captures neural variability, we performed PCA individually per subject as an upper baseline for the explained variance (orange). The alignment only has a minor effect on the variance explained by the identified subspace. In this work, we use the first 10 dimensions to define the joint subspace. (e) Left: cross-subject correlation of the first subspace dimension calculated for pairs of projections into this dimension (see bottom row of c). Right: similarity of pairs of dimensions, where similarity is computed by averaging the elements of the triangular cross-subject correlation matrix displayed on the left. (f) Average dimension similarity for the first 20 subspace dimensions with alignment (PCA + QR, black) and without alignment (Indv. PCA, orange) (mean and 95% CIs for 80 repetitions). Additionally, we controlled how the dimension alignment quality depends on the temporal alignment of specific activity patterns around the chosen events (rather than general bump-like activity) by shuffling event types between subjects (event shuffle, green). We found that shuffling events led to a marked drop in alignment quality, indicating that the correct alignment of neural subspaces depends on the correct temporal alignment of conceptually similar events. We chose the number n of used dimensions to be 10, as it constitutes a good tradeoff between explained variance (see c) and alignment quality.