A minimalistic representation model for head direction system

2024-11-15

arXiv.org

AI Summary

This work addresses the challenge of learning minimal, interpretable neural representations of head direction (HD) systems in high-dimensional neural activity, without imposing biological priors. Method: We propose two self-supervised architectures—fully connected and convolutional—designed explicitly around the U(1) rotation group symmetry; representation learning is driven solely by a path integration objective, with no biologically inspired constraints. Contribution/Results: To our knowledge, this is the first demonstration of spontaneous emergence of Gaussian-shaped directional tuning curves and a one-dimensional circular latent topology—hallmarks of biological HD cells—in a model devoid of neuroanatomical or functional priors. Both architectures achieve high-fidelity path integration (error < 3°/m), confirming that U(1) symmetry alone suffices as a computational foundation for HD coding. Our results establish group representation learning as a principled, interpretable framework for deriving core functional properties and geometric structure of HD systems from first principles.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Representation Learning
• Computer Vision: Representation Learning for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

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.

Problem

• Model learns high-dimensional head direction representation
• Studies U(1) rotation group in connected/convolutional versions
• Demonstrates Gaussian tuning and path integration capabilities

Innovation

• Minimalistic model for head direction representation
• U(1) rotation group representation
• Gaussian-like tuning and path integration