Resolution of Nested Neuronal Representations Can Be Exponential in the Number of Neurons

Mathis, Alexander; Herz, Andreas V. M.; Stemmler, Martin B.

doi:10.1103/physrevlett.109.018103

Cited by 55 publications

(68 citation statements)

References 26 publications

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“…7c). The scale change across successive grid modules could be described as a geometric progression with a constant scale factor 154 , confirming the prior predictions 91,172 , as well as theoretical analyses pointing to nested and modular organizations as the most efficient code for representing space at the highestpossible resolution with the lowest-possible cell number 173,174 .…”

Section: A Zoo Of Cell Typessupporting

confidence: 61%

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Spatial representation in the hippocampal formation: a history

2017

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Section: A Zoo Of Cell Typessupporting

confidence: 61%

“…Read-out Position can be decoded from grid cells and place cells, with greater accuracy in grid cells than place cells if the population is multimodular and scaled in particular ways 159,173,174,276 . Whether neural circuits decode information in the same way remains to be determined, however.…”

Section: Development Of Spatial Network Architecturesmentioning

confidence: 99%

Spatial representation in the hippocampal formation: a history

2017

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“…6). As in our 1-D example, the firing of neurons at each of these three scales of representation is needed to resolve position unambiguously, but the binary grid scheme achieves the same resolution with fewer neurons than the unary scheme (12 versus 64 in this example), again suggesting that a grid-like multiscale representation of position would be more efficient for the brain [52], [56]- [59]. In general, a grid scheme simply needs diverse tuning curves distributed over modules with different periodicities defined on some lattice, and need not have any particular relation imposed between the different modules.…”

Section: The Sense Of Placementioning

confidence: 93%

Heterogeneity and Efficiency in the Brain

Balasubramanian

2015

Proc. IEEE

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The brain is a remarkable information engine. Its efficiency arises via specialized approaches to the task and a hierarchyVa very non-von-Neumann form. The paper suggests that this computational organization is an architecture of memories of procedures and discusses the mathematical and physical basis for how this approach endows the brain with its efficiency for the different tasks.ABSTRACT | The brain carries out enormously diverse and complex information processing operations to deal with a constantly varying world on a power budget of about 12-20 W.We argue that this efficiency is achieved in part through the dedication of specialized circuit elements and architectures to specific computational tasks, in a hierarchy stretching from the scale of neurons to scale of the entire brain, in sharp contrast to the conventional von Neumann architectures. This paper suggests that the heterogeneous computational repertoires of the brain are architectural memories of efficient computational procedures that are learned via evolutionary selection.

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“…The more general case, for tuning curves that are periodic on arbitrary lattices in more than one dimension, is treated by Mathis, Herz, and Stemmler (2012); Mathis, Stemmler, and Herz (2011). Given that the grid code can be orders of magnitude better than the place code, based on the mean maximum likelihood error (MMLE), why are both codes used?…”

Section: Discussionmentioning

confidence: 99%

Optimal Population Codes for Space: Grid Cells Outperform Place Cells

2012

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Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal's position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial "tuning curves" for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons.

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Resolution of Nested Neuronal Representations Can Be Exponential in the Number of Neurons

Cited by 55 publications

References 26 publications

Spatial representation in the hippocampal formation: a history

Spatial representation in the hippocampal formation: a history

Heterogeneity and Efficiency in the Brain

Optimal Population Codes for Space: Grid Cells Outperform Place Cells

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