A minimalistic representation model for head direction system

TL;DR

This paper introduces a minimalistic model for the head direction system that captures key properties like Gaussian tuning and circle geometry, enabling accurate path integration.

Contribution

It presents a novel, simple representation model for head direction cells based on the rotation group U(1), demonstrating emergent properties and path integration capabilities.

Findings

Emergence of Gaussian-like tuning profiles.

Representation of 2D circle geometry.

Accurate path integration achieved.

Abstract

We present a minimalistic representation model for the head direction (HD) system, aiming to learn a high-dimensional representation of head direction that captures essential properties of HD cells. Our model is a representation of rotation group $U(1)$, and we study both the fully connected version and convolutional version. We demonstrate the emergence of Gaussian-like tuning profiles and a 2D circle geometry in both versions of the model. We also demonstrate that the learned model is capable of accurate path integration.