How do Grid Cell Modules relate to Spatial Pooling / mini-columns?

Can I ask, slightly topic-askew, to speculate where the grid cell input would come in? Would it be an input into the SP, or would it join with the SP output SDR at a later stage?

Could you (anyone who cares to give their opinion) explain what the different consequences would be to inject this information before and after the SP?

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Here is a related discussion: Should grid cell or displacement cell modules include minicolumns?

And here are our two papers that talk about location. The Columns Paper talks about a generic distal location input. It’s not input to the spatial pooler, but is distal instead of the temporal circular feedback we talk about in TM.

The Columns+ Paper gets more specific about how grid-cell-like cells can drive this location.

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I’ve been thinking about this for sometime now. In my own mental model, the grid cells serve as an internal representation of the space of allowable transitions. If one knows all of the states of a system and the allowed transitions between them (e.g. finite state machine, or GPS coordinates) then it might be possible to encode them as grid-cell-like modules and import them directly into the network. However, if the agent must learn the allowable states and transitions, then the behavior of the grid cell modules should emerge as a consequence of the network learning temporal sequences from the streaming inputs.

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It seems to me (on totally insufficient grounds) that a single SDR has to do all the work. A biological SDR for a touch on the skin might have to encode the location (where on the skin), the modality (light/deep, sharp/blunt, hot/cold) and aspects of timing (duration, attack/decay, earlier/later). A musical note SDR carries pitch, attack/decay, timbre, instrument, etc.

IOW an SDR can be ‘similar to’ other SDR’s along more than one dimension. Does that mean allocating (say) 10 bits for this attribute, 12 bits for that, 7 bits for something else, and then ‘recognising’ those attributes by masking operations on other SDR’s? I have no idea, but it sounds kind of plausible.

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