Fig. 6: Noise correlation in grid cells increases noise projection onto the manifold and impairs information coding.

A Noise correlation can either enhance (“information‐beneficial”) or impair (“information‐detrimental”) coding relative to a model of independent firing grid cells (IFGC). B IFGC’s GKR is identical to the GKR fitted from the original sampled dataset \({{{\mathscr{D}}}}_{s}\), except that the off-diagonal elements of the covariance matrix are set to zero (see texts and Methods). Total noise is the trace of the covariance matrix. Left: Each dot represents the total noise from one GKR model fitted to a specific \({{{\mathscr{D}}}}_{s}\) at a given speed (fifty sampled \({{{\mathscr{D}}}}_{s}\) with eight speed bins = four hundred data points). The lines and error bands show the best linear fitting and 95% CI using BLEA. Right: We computed the speed-averaged total noise as the average total noise across all speeds (from 5 cm/s to 45 cm/s) per \({{{\mathscr{D}}}}_{s}\). Since fifty \({{{\mathscr{D}}}}_{s}\) were used, we have fifty speed-averaged total noise values per experimental configuration, allowing fitting a normal distribution. Dots and error bars show the mean and 95% CI of the estimated speed-averaged total noise distributions (see Methods). The texts below each x-axis tick label indicate the significance level of whether the speed-averaged total noise fitted from the original GKR differs from that of IFGC GKR (two-sided, Bayesian method, see Methods). ***p < 0.001; **p < 0.01; *p < 0.05; NS not significant. C, D Same as (B), but measuring projected noise and total Fisher. Statistical testing (Bayesian Methods) on projected noise (or total Fisher) is one-sided—whether the projected noise (or total Fisher) obtained from the original GKR is greater (or smaller) than IFGC GKR (see Methods). E The key idea of SCA is to assess classification accuracy between data points drawn from two spatial boxes. To compute IFGC’s SCA, we generated a “trial‐shuffled” dataset by permuting each cell’s firing activity across all data points within the same box, allowing eliminates intercellular noise correlations. Illustrations are the same as panel B, except showing SCA at different speeds. Statistical testing is one-sided (Bayesian method, see Methods), indicating whether the SCA from the original dataset is smaller than IFGC’s SCA. Source data are provided as a Source Data file.