Efficient and flexible representation of higher-dimensional cognitive variables with grid cells
For ease of illustration, we consider here the encoding of a variable in three dimensions. (a) Left-most column (M = 1): 3D tuning curves of two grid-cells from different modules using our coding model. Remaining columns (M > 1): 3D tuning curves of two conjunctive cells reading from M different modules using our coding model. (b) 3D tuning curve of a conjunctive cell. The xy-plane shows a projected tuning curve taking the maximum along the z-axis. (c) Realistic tuning curves implemented by simulating multiple continuous attractor grid cell network modules with noisy neural activity. (d) Auto-correlations of grid responses along a vertical plane according to our model. The auto-correlations resemble those recorded from rats climbing a “pegboard” in . (e) Each row shows the 2D responses of 4 co-modular cells over a randomly chosen tilted plane (shown on the left in gray) in 3D space. Different rows correspond to different modules and the modules encode space according to our model.