Extended Data Fig. 8. Pairwise rate correlation structure in RSC is maintained across LM1 and LM2 states.
(a) Low-dimensional population structure can be probed by pairwise neural relationships30: correlations or offsets in spatial tuning between cell pairs should be preserved across environments if the dynamics across environments is low-dimensional. Example spike rates (6 sec window, low-passed at 1 Hz using a single-pole Butterworth filter) for 3 RSC neuron pairs from one example session. R values for each pair were computed across the LM1 and LM2 condition, as well as in the task-initialization phase where mice had to hunt blinking dots (Extended Data Figs. 1, 4). The latter provides a control condition where no landmark-based navigation was required and mice instead had to walk to randomly appearing targets. (b) Top: pairwise correlation matrices for LM1,2 and dot-hunting conditions. Example pairs are highlighted (i,ii,iii). Bottom: spatial firing rate profiles for example pairs. Same analysis as in Fig. 3a. (c) RSC activity is globally low-dimensional. Proportion of variance of low-pass filtered (0.5 Hz) firing rates explained by first 45 principal components from the LM1 states. Proportion of variance explained (black, 16 sessions) drops to below that of shuffled spike trains (red) after the 6-10th principal component. The inset shows the analysis split by condition (same as in panels a and b), and 95% Cis for the spectra across sessions. The right panel shows zoomed in region of the same plot. We found no relationship between individual PCA components and task variables. (d) Correlation dimension in RSC is also low (same analysis as for the ANN in Extended Data Fig. 5p). This measure typically overestimates manifold dimension66, and thus serves as an upper bound on the true manifold dimension. (e) Grey/black: Summary statistics (median and quartiles) for correlation of correlations (panel b shows one example session, black dots indicate individual sessions, N = 16). Median of R value of R values for LM1 vs. LM2 = 0.74 (corresponding R in ANN = 0.73), for LM1 vs. dot-hunting = 0.51. Green: same analysis but spike rates were computed with a 5 Hz low-pass instead of the 1 Hz used throughout, no systematic changes were observed as function of low-pass settings. (f) Rates of individual RSC neurons can be predicted from other neurons with linear regression. In the LM2 to LM2 condition (black), the linear fit is computed for one held-out neuron’s rate from other concurrent rates, and the same regression weights are then used to predict rates during LM1 (green) and dot-hunting (red) time periods. True rates of predicted neurons are plotted as solid black lines. (g) Summary statistics for the linear regression. Histograms show the proportion of explained variance for all 984 neurons, split by condition. In the LM2 to LM2 condition, the fit is computed from other concurrent rates (40.5% variance explained, median across neurons). In the two other conditions, the regression weights are fit in LM2 and held fixed. The sequential, non-interleaved nature of this train/test split across task phases means that any consistent firing rate drifts across the conditions will lead to poor predictions, and consequently, a small number of neurons exhibit negative R2 values indicating a fit that can, for some cells, be worse than an average rate model (11.3% for LM1, 19.3% median across neurons for dot-hunting, small grey bars). However, 24.3% of variance (median across neurons) can be explained despite significant changes in spatial receptive fields (predict LM1 with LM2 weights) and even for a different task, with 16.2% when predicting dot-hunting activity from LM2 weights (red and green histogram and bars showing 95% CI of median). (h) Pairwise correlations between RSC neurons in another example session, same analysis as in panel b, and associated scatterplots. (i) Low-dimensional activity quantified via participation ratio (PR)68. This analysis does not account for noisy eigenvalue estimates from spiketrains, and consequently the shuffled spike trains where there are no prominent modes that correspond to stable sensory, motor, or latent states, yield values of PR = ~ 45.