Spatial Pooling, SDRs, and Grid Cell Dimensionality Phase Transitions

[dmac]

I like that you’re thinking with manifolds. Manifolds are a good way to analyze these problems.

@Charles_Rosenbauer

However, SDRs have some interesting properties that come into play here. Any given landmark has a corresponding coordinate in the space of input SDRs (the center of its RF). Nearby landmarks will have similar SDRs, or else they wouldn’t be nearby

Something to consider about the Spatial Pooler is that the exact size of the Receptive Fields is controlled by the input manifold. This is good if you are trying to represent sensory features, which are locations on the input-space manifold.

However grid cells are not representing locations on the input-space manifold, they are representing locations in the physical world (which is a different manifold: Euclidean space).

Two locations could be far apart on the input-manifold, but very close together in the physical world. One challenge for grid cells is to associate adjacent locations with the same RF, even if the locations look totally different.

I’ve written at length on this forum about how to modify a Spatial Pooler such that it forms receptive fields which respond to physical locations (as opposed to sensory features).

Video Lecture of Kropff & Treves, 2008

Update: I recorded a video lecture on this topic: [Kropff & Treves, 2008 for Numenta and the HTM Forum] The slides are at https://github.com/ctrl-z-9000-times/KropffTreves2008_reproduction/blob/master/grid_cells_presentation.pdf References Kropff & Treves, 2008 HTM Spatial Pooler A Theory of How Columns in the Neocortex Enable Learning the Structure of the World