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Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

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A computational model for grid maps in neural populations.

Fabio Anselmi^1,2,3, Micah M Murray^4,5,6,7, Benedetta Franceschiello^4,5

¹Center for Brains, Minds, and Machines, MIT, Cambridge, MA, USA. anselmi@mit.edu.

Journal of Computational Neuroscience

|March 4, 2020

Summary

This study presents a new framework explaining hexagonal grid cell patterns in the brain. It shows this optimal coding arises from minimal neural variance, noise robustness, and efficient neuron use.

Keywords:

Computational model Grid cells Hippocampus

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Area of Science:

Neuroscience
Computational Neuroscience
Cognitive Science

Background:

Grid cells in the entorhinal cortex are crucial for spatial representation in the brain.
Existing models for grid cell patterns often rely on oscillatory or attractor mechanisms.

Purpose of the Study:

To introduce a novel theoretical and algorithmic framework explaining the optimality of hexagonal grid cell response patterns.
To provide a simplified cortical-based model for grid cell function.

Main Methods:

Formulating the neural encoding problem using Frame Theory, treating neurons as an overcomplete basis.
Applying principles of minimal variance encoding, noise robustness, and minimal neuron count.
Utilizing Hebbian learning as the underlying mechanism.

Main Results:

Demonstrated that hexagonal patterns result from optimal encoding principles (minimal variance, maximal robustness, minimal neurons).
Showcased how Frame Theory provides insights into the optimality of hexagonal receptive fields.
Explained axis alignment, map shifts, rotations, and scaling of grid cell representations.

Conclusions:

The proposed framework offers a new perspective on grid cell function, rooted in efficient information encoding.
This model simplifies grid cell theory by not requiring velocity-driven oscillations or specific synaptic symmetries.
The framework naturally explains key experimental observations regarding grid cell remapping and environmental cue transformations.