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

Center for Learning and Memory, University of Texas at Austin, Austin, Texas, USA.
Nature Neuroscience (Impact Factor: 16.1). 09/2011; 14(10):1330-7. DOI: 10.1038/nn.2901
Source: PubMed


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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    • "In engineering, codes are designed to solve this problem by choosing codewords that are far apart in the space of patterns, relative to the typical noise levels. That way, if noise corrupts a message, it would still be easily distinguishable from the noisy variants of other codewords (Cover and Thomas, 1991; Sreenivasan and Fiete, 2011; Curto et al., 2013). It is not clear however, how this issue is resolved in the brain, or how it affects the design of the neural code, where information is carried by the joint activity patterns of large groups of noisy neurons (Nicolelis et al., 1995; Maynard et al., 1999; Mazor and Laurent, 2005; Fujisawa et al., 2008; Pillow et al., 2008; Truccolo et al., 2010; Ganmor et al., 2011a; Harvey et al., 2012). "
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    ABSTRACT: Information is carried in the brain by the joint spiking patterns of large groups of noisy, unreliable neurons. This noise limits the capacity of the neural code and determines how information can be transmitted and read-out. To accurately decode, the brain must overcome this noise and identify which patterns are semantically similar. We use models of network encoding noise to learn a thesaurus for populations of neurons in the vertebrate retina responding to artificial and natural videos, measuring the similarity between population responses to visual stimuli based on the information they carry. This thesaurus reveals that the code is organized in clusters of synonymous activity patterns that are similar in meaning but may differ considerably in their structure. This organization is highly reminiscent of the design of engineered codes. We suggest that the brain may use this structure and show how it allows accurate decoding of novel stimuli from novel spiking patterns.
    eLife Sciences 09/2015; 4. DOI:10.7554/eLife.06134 · 9.32 Impact Factor
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    • "Þg)? as the maximum spatial range within which each combination of phase values {p i } (or phase differences {Dp i }) corresponds to a unique decoded location (or displacement )—i.e., the distance between locations encoded by the same set of grid cell phases or the period of the grid cell system as a whole. Theoretical studies suggest that this capacity is much greater than the typical foraging range of an animal (Gorchetchnikov and Grossberg, 2007; Fiete et al., 2008; Sreenivasan and Fiete, 2011; Mathis et al., 2012; see Supplemental Experimental Procedures). Beyond that capacity, the spatial representation provided by the grid cell network as a whole is periodic. "
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    ABSTRACT: Mammals are able to navigate to hidden goal locations by direct routes that may traverse previously unvisited terrain. Empirical evidence suggests that this "vector navigation" relies on an internal representation of space provided by the hippocampal formation. The periodic spatial firing patterns of grid cells in the hippocampal formation offer a compact combinatorial code for location within large-scale space. Here, we consider the computational problem of how to determine the vector between start and goal locations encoded by the firing of grid cells when this vector may be much longer than the largest grid scale. First, we present an algorithmic solution to the problem, inspired by the Fourier shift theorem. Second, we describe several potential neural network implementations of this solution that combine efficiency of search and biological plausibility. Finally, we discuss the empirical predictions of these implementations and their relationship to the anatomy and electrophysiology of the hippocampal formation. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.
    Neuron 08/2015; 87(3):507-20. DOI:10.1016/j.neuron.2015.07.006 · 15.05 Impact Factor
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    • "However, introducing redundancy by only using a subinterval within this representable range, the modular code becomes highly robust to noise, because the representation of each location x x x within the subinterval maps to highly different location representations L. A representation L in which each phase χ λ is corrupted by independent noise -e.g. interference effects in SDM -can be fully recovered, as long as the difference is smaller than the largest correctable error -see Figure 2A for numerical results of error robustness in our model, and (Sreenivasan & Fiete, 2011) for an analytical treatment of error correction capability of the grid cell code. The second advantage is performance -RNS codes can perform addition, subtraction, and multiplication in linear time. "
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    ABSTRACT: Human spatial representations are known to be remarkably robust and efficient, and to be structured hierarchically. In this paper, we describe a biologically inspired computational model of spatial working memory attempting to account for these properties, based on the LIDA cognitive architecture. We also present preliminary results regarding a virtual reality experiment, which the model is able to account for, and the quantitative properties of the representation.
    The 12th International Conference on Cognitive Modelling; 01/2013
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