A principle of economy predicts the functional architecture of grid cells

Wei, Xue-Xin; Prentice, Jason; Balasubramanian, Vijay

doi:10.7554/elife.08362

Cited by 87 publications

(142 citation statements)

References 58 publications

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“…Note that the ratios were measured only for the first few modules with lowest grid spacings. Hence, the theory is in very good agreement with the existing measurements, and with previous theoretical predictions that were based on optimal coding of a static variable [13, 25]. For the larger grid spacings, we predict that the ratios may vary monotonically with respect to the spacing (Fig 2D, see S1 Text section III for further discussion).…”

Section: Resultssupporting

confidence: 89%

“…We follow a similar line of argumentation as in [13], but take into account the motion of the animal. Our goal is to minimize Δ m , the local root mean square error (local RMSE) of readout from the smallest module, while constraining the largest grid spacing λ 1 and the number of neurons N (equivalently, it is possible to minimize the number of neurons while constraining the readout local RMSE).…”

Section: Resultsmentioning

confidence: 99%

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An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules

et al. 2017

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Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal’s motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing.

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Section: Resultssupporting

confidence: 89%

Section: Resultsmentioning

confidence: 99%

An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules

et al. 2017

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“…Interestingly, when characterizing the firing properties of many such cells in a single animal one finds that the the lattice spacing of all cells belongs (approximately) to a discrete set that forms a geometric series [44]. Much work has been devoted to trying to understand how such a code could be used efficiently to represent the animal's location (see for example [45, 46]) and how such a code could be generated [47]. …”

Section: Discussionmentioning

confidence: 99%

Low-dimensional dynamics of structured random networks

et al. 2016

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Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach, we study the relationship between the network connectivity structure and its low dimensional dynamics. Each connection in the network is a random number with mean 0 and variance that depends on pre- and post-synaptic neurons through a sufficiently smooth function g of their identities. We find that these networks undergo a phase transition from a silent to a chaotic state at a critical point we derive as a function of g. Above the critical point, although unit activation levels are chaotic, their autocorrelation functions are restricted to a low-dimensional subspace. This provides a direct link between the network's structure and some of its functional characteristics. We discuss example applications of the general results to neuroscience where we derive the support of the spectrum of connectivity matrices with heterogeneous and possibly correlated degree distributions, and to ecology where we study the stability of the cascade model for food web structure.

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“…They obtain a scale ratio between grid modules of around 1.5 to minimize the risk of large‐scale spatial localization errors. Wei, Prentice, and Balasubramanian () proposed that the grid cell system minimizes the number of neurons required to encode a location at some resolution, obtaining an optimal idealized ratio of square root of e that lies in the range [1.4, 1.7] for realistic neurons. Both arguments for explaining the observed ratio rely on spatial information.…”

Section: Discussionmentioning

confidence: 99%

A hexagonal Fourier model of grid cells

Rodríguez-Domínguez

Caplan

2018

Hippocampus

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Grid cells in rat medial entorhinal cortex are widely thought to play a major role in spatial behavior. However, the exact computational role of the population of grid cells is not known. Here we provide a descriptive model, which nonetheless considers biologically feasible mechanisms, whereby the grid cells are viewed as a two-dimensional Fourier basis set, in hexagonal coordinates, with restricted availability of basis functions. With known properties imposed in the model parameters, we demonstrate how various empirical benchmark findings are straight-forward to understand in this model. We also explain how complex computations, inherent in a Fourier model, are feasible in the medial entorhinal cortex with simple mechanisms. We further suggest, based on model experiments, that grid cells may support a form of lossy compression of contextual information, enabling its representation in an efficient manner. In sum, this hexagonal Fourier model suggests how the entire population of grid cells may be modeled in a principled way, incorporates biologically feasible mechanisms and provides a potentially powerful interpretation of the relationship between grid-cell activity and contextual information beyond spatial knowledge. This enables various phenomena to be modeled with relatively simple mechanisms, and leads to novel and testable predictions.

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A principle of economy predicts the functional architecture of grid cells

Cited by 87 publications

References 58 publications

An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules

An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules

Low-dimensional dynamics of structured random networks

A hexagonal Fourier model of grid cells

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