Speed modulations in grid cell information geometry.

Grid cells, with hexagonal spatial firing patterns, are thought critical to the brain's spatial representation. High-speed movement challenges accurate localization as self-location constantly changes. Previous studies of speed modulation focus on individual grid cells, yet population-level noise covariance can significantly impact information coding. Here, we introduce a Gaussian Process with Kernel Regression (GKR) method to study neural population representation geometry. We show that increased running speed dilates the grid cell toroidal-like representational manifold and elevates noise strength, and together they yield higher Fisher information at faster speeds, suggesting improved spatial decoding accuracy. Moreover, we show that noise correlations impair information encoding by projecting excess noise onto the manifold. Overall, our results demonstrate that grid cell spatial coding improves with speed, and GKR provides an intuitive tool for characterizing neural population codes.