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Exponential Scaling of Nested Neuronal Representations

Alexander Mathis1, 2, 3*, Martin B. Stemmler1, 2, 3 and Andreas V. Herz1, 2, 3
  • 1 Ludwig-Maximilians-Universität München, Division of Neurobiology, Germany
  • 2 Bernstein Center for Computational Neuroscience Munich, Germany
  • 3 Ludwig-Maximilians-Universität München, Graduate School for Systemic Neuroscience, Germany

In many neuronal coding schemes, the stimulus resolution grow linearly in the number of encoding neurons [1]. We show that nested codes containing self-similar, periodic modules can achieve a resolution that is exponential in the number of neurons, even though the spiking of individual neurons is noisy. This scaling is independent of the dimension D of the stimulus space and leads to a resolution that is orders of magnitude better than a standard neuronal population code and generalizes an older result [2].

Neurons in the superficial layers of medial entorhinal cortex (mEC) exhibit grid-like firing maps of planar space at different spatial scales, just as required for modular coding. Our theoretical analysis indicates that these grid cell properties endow the brain with a highly accurate representation of space; the same principles could be used for representing other continuous, high-dimensional stimuli.

References

[1] Zhang and Sejnowski. Neural Comput, 11(1): 1999.
[2] Mathis, Stemmler and Herz. Front. Comput. Neurosci. Conference Abstract: Bernstein Conference on Computational Neuroscience: 2010

Keywords: exponential scaling, grid cells, medial entorhinal cortex, neural encoding and decoding, population coding

Conference: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany, 4 Oct - 6 Oct, 2011.

Presentation Type: Abstract

Topic: neural encoding and decoding (please use "neural coding and decoding" as keyword)

Citation: Mathis A, Stemmler MB and Herz AV (2011). Exponential Scaling of Nested Neuronal Representations. Front. Comput. Neurosci. Conference Abstract: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011. doi: 10.3389/conf.fncom.2011.53.00001

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Received: 29 Sep 2011; Published Online: 04 Oct 2011.

* Correspondence: Mr. Alexander Mathis, Ludwig-Maximilians-Universität München, Division of Neurobiology, Munich, Germany, mathis@bio.lmu.de