论文标题
在网格单元的路径积分上：组表示和各向同性缩放
On Path Integration of Grid Cells: Group Representation and Isotropic Scaling
论文作者
论文摘要
了解网格细胞如何执行路径集成计算仍然是一个基本问题。在本文中，我们对网格单元的路径积分的一般表示模型进行了理论分析，其中2D自位被编码为较高的维矢量，并且2D自我运动由向量的一般变换表示。我们确定转换的两个条件。一个是路径积分所需的组表示条件。另一种是一种各向同性缩放条件，可确保局部构型嵌入，因此向量表示中的误差可转化为2D自定义中的误差。然后，我们研究了最简单的转换，即线性变换，发现其显式代数和几何结构作为矩阵旋转组，并探索各向同性缩放条件与特殊类别的六边形网格模式之间的连接。最后，通过基于优化的方法，我们设法学习了六角形网格模式，这些模式具有啮齿动物大脑中网格细胞相似的特性。学到的模型能够准确的长距离路径积分。代码可在https://github.com/ruiqigao/grid-cell-path上找到。
Understanding how grid cells perform path integration calculations remains a fundamental problem. In this paper, we conduct theoretical analysis of a general representation model of path integration by grid cells, where the 2D self-position is encoded as a higher dimensional vector, and the 2D self-motion is represented by a general transformation of the vector. We identify two conditions on the transformation. One is a group representation condition that is necessary for path integration. The other is an isotropic scaling condition that ensures locally conformal embedding, so that the error in the vector representation translates conformally to the error in the 2D self-position. Then we investigate the simplest transformation, i.e., the linear transformation, uncover its explicit algebraic and geometric structure as matrix Lie group of rotation, and explore the connection between the isotropic scaling condition and a special class of hexagon grid patterns. Finally, with our optimization-based approach, we manage to learn hexagon grid patterns that share similar properties of the grid cells in the rodent brain. The learned model is capable of accurate long distance path integration. Code is available at https://github.com/ruiqigao/grid-cell-path.
