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Grid cells generate an analog error-correcting code for singularly precise neural computation

Nature Neuroscience volume 14, pages 1330–1337 (2011)Cite this article

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Abstract

Entorhinal grid cells in mammals fire as a function of animal location, with spatially periodic response patterns. This nonlocal periodic representation of location, a local variable, is unlike other neural codes. There is no theoretical explanation for why such a code should exist. We examined how accurately the grid code with noisy neurons allows an ideal observer to estimate location and found this code to be a previously unknown type of population code with unprecedented robustness to noise. In particular, the representational accuracy attained by grid cells over the coding range was in a qualitatively different class from what is possible with observed sensory and motor population codes. We found that a simple neural network can effectively correct the grid code. To the best of our knowledge, these results are the first demonstration that the brain contains, and may exploit, powerful error-correcting codes for analog variables.

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Figure 1: Coding for location: GPC and CPCs.
Figure 2: Error correction and the structure of the GPC location-phase map.
Figure 3: Scaling of dmin and error correction.
Figure 4: Simple neural network can perform ongoing error correction for accurate path integration.

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Acknowledgements

We are grateful to Y. Burak, S. Seung, A. Kepecs, P. Latham, A. Pouget and P. Dayan for thought-provoking questions and comments, S.H. Lee for helpful conversations, T. Lam for advice on a volume computation, D. Johnston, A. Huk, N. Priebe, A. Tan and members of our laboratory for comments on the manuscript, and A. Preston for useful pointers to the literature. I.F. is a Sloan Foundation Fellow, a Searle Scholar and a McKnight Scholar, and receives funding from the Office of Naval Research through the Multidisciplinary University Research Initiative.

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Authors and Affiliations

  1. Center for Learning and Memory, University of Texas at Austin, Austin, Texas, USA

    Sameet Sreenivasan & Ila Fiete

  2. Department of Computer Science, Rensselaer Polytechnic Institute, Troy, New York, USA

    Sameet Sreenivasan

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  1. Sameet Sreenivasan
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Contributions

I.F. conceived the model. S.S. performed simulations and analyzed the data. I.F. and S.S. performed analytical calculations and wrote the manuscript.

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Correspondence to Ila Fiete.

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Sreenivasan, S., Fiete, I. Grid cells generate an analog error-correcting code for singularly precise neural computation. Nat Neurosci 14, 1330–1337 (2011). https://doi.org/10.1038/nn.2901

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