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Flexible representation and memory of higher-dimensional cognitive variables with grid cells

Mirko Klukas, Marcus Lewis, Ila Fiete
doi: https://doi.org/10.1101/578641
Mirko Klukas
Numenta, Inc., Redwood City, CA 94063
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Marcus Lewis
Numenta, Inc., Redwood City, CA 94063
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Ila Fiete
Department of Brain and Cognitive Sciences, MIT, Cambridge, MA 02139
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Abstract

Grid cell representations are simultaneously flexible and powerful yet rigid and constrained: On one hand, they can encode spatial or a variety of non-spatial cognitive variables (Constantinescu et al., 2016; Killian et al., 2012), with remarkable capacity, integration, and error correction properties (Fiete et al., 2008; Sreenivasan and Fiete, 2011; Mathis et al., 2012). On the other, states within each grid module are confined to a fixed two-dimensional (2D) set across time, environment, encoded variable (Yoon et al., 2013, 2016), behavioral states including sleep (Gardner et al., 2017; Trettel et al., 2017), with the inherent low-dimensionality etched directly into the physical topography of the circuit (Heys et al., 2014; Gu et al., 2018). The restriction to 2D states seemingly imposes a severe limit on the representation of general cognitive variables of dimension greater than two by grid cells. We show here that a set of grid cell modules, each with only 2D responses, can generate unambiguous and high-capacity representations of variables in much higher-dimensional spaces. Specifically, M grid modules can represent variables of arbitrary dimension up to 2M, with a capacity exponential in M. The idea generalizes our understanding of the 2D grid code as capable of flexible reconfiguration to generate unique high-capacity metric codes and memory states for representation and algebra in higher-dimensional vector spaces, without costly higher-dimensional grid-like responses in individual cells.

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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 March 16, 2019.
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Flexible representation and memory 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 and memory 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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