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Flexible representation of higher-dimensional cognitive variables with grid cells

Mirko Klukas, Marcus Lewis, Ila Fiete
doi: https://doi.org/10.1101/578641
Mirko Klukas
MIT, Cambridge, MANumenta, Redwood City, CA
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  • For correspondence: mirko.klukas@gmail.com
Marcus Lewis
Numenta, Redwood City, CA
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Ila Fiete
MIT, Cambridge, MA
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Abstract

We shed light on the theoretical capabilities of entorhinal grid cells to encode variables of dimension greater than two. Our model constructs representations of high-dimensional inputs through a combination of low-dimensional random projections and “classical” low-dimensional hexagonal grid cell responses. Without reconfiguration of the recurrent circuit, the same system can flexibly encode multiple variables of different dimensions while maximizing the coding range (per dimension) by automatically trading-off dimension with an exponentially large coding range. In contrast to previously proposed schemes, the model does not require the formation of higher-dimensional grid responses, a cell-inefficient and rigid mechanism. The firing fields observed in flying bats or climbing rats can be generated by neurons that combine activity from multiple grid modules, each representing higher-dimensional spaces according to our model. The idea expands our understanding of grid cells, suggesting that they could implement a general circuit that generates on-demand coding and memory states for variables in high-dimensional vector spaces.

Footnotes

  • Updated abstract and introduction, adjusting the focus towards flexibility of our model; New Figures illustrating the schematic idea behind the coding scheme.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license.
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Posted August 28, 2019.
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Flexible representation of higher-dimensional cognitive variables with grid cells
Mirko Klukas, Marcus Lewis, Ila Fiete
bioRxiv 578641; doi: https://doi.org/10.1101/578641
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Flexible representation of higher-dimensional cognitive variables with grid cells
Mirko Klukas, Marcus Lewis, Ila Fiete
bioRxiv 578641; doi: https://doi.org/10.1101/578641

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