# A minimalistic representation model for head direction system

arXiv: https://arxiv.org/abs/2411.10596 · HTML: https://mlsanity.com/paper/2411.10596/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 27 references that are in the map.
- First posted on arXiv 15 Nov 2024.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Universality and individuality in neural dynamics across large populations of recurrent networks](https://mlsanity.com/paper/1907.08549/) (2019)
- [Emergence of functional and structural properties of the head direction system by optimization of recurrent neural networks](https://mlsanity.com/paper/1912.10189/) (2019)
- [On Conformal Isometry of Grid Cells: Learning Distance-Preserving Position Embedding](https://mlsanity.com/paper/2405.16865/) (2024)
- [Conformal Isometry of Lie Group Representation in Recurrent Network of Grid Cells](https://mlsanity.com/paper/2210.02684/) (2022)
- [Emergence of Grid-like Representations by Training Recurrent Networks with Conformal Normalization](https://mlsanity.com/paper/2310.19192/) (2023)

## Built on by (most cited first, 2 of 2)

- [Place Cells as Multi-Scale Position Embeddings: Random Walk Transition Kernels for Path Planning](https://mlsanity.com/paper/2505.14806/) (2025)
- [Learning to Plan from Random Exploration](https://mlsanity.com/paper/2609.38383/) (2026)

## Abstract (arXiv)

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.