Efficient and flexible representation of higher-dimensional cognitive variables with grid cells.

We shed light on the potential of entorhinal grid cells to efficiently encode variables of dimension greater than two, while remaining faithful to empirical data on their low-dimensional structure. 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. It achieves high efficiency and flexibility by combining two powerful concepts, modularity and mixed selectivity, in what we call "mixed modular coding". 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.

Déclaration de conflit d'intérêts

I have read the journal’s policy and the authors of this manuscript have the following competing interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. ML and MK were employed by Numenta. Numenta has stated that use of its intellectual property, including all the ideas contained in this work, is free for noncommercial research purposes. In addition, Numenta has released all pertinent source code as open source under the AGPL V3 license (which includes a patent peace provision).