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.

翻译：本文提出一种头部方向（HD）系统的简约表征模型，旨在学习能够捕捉HD细胞本质特性的头部方向高维表征。该模型是旋转群$U(1)$的一种表征形式，我们研究了其全连接版本与卷积版本。实验表明，两种版本均能自发形成类高斯调谐曲线与二维圆环几何结构。我们进一步证明，学习得到的模型能够实现精确的路径积分。