Gao, Ruiqi & Xie, Jianwen & Zhu, Song & Wu, Yingnian. Learning Grid Cells as Vector Representation of Self-Position Coupled with Matrix Representation of Self-Motion. ICLR 2019

Abstract

“**This paper proposes a representational model for grid cells. In this model, the 2D self-position of the agent is represented by a high-dimensional vector, and the 2D self-motion or displacement of the agent is represented by a matrix that transforms the vector**. Each component of the vector is a unit or a cell. The model consists of the following three sub-models. (1) **Vector-matrix multiplication**. The movement from the current position to the next position is modeled by matrix-vector multiplication, i.e., the vector of the next position is obtained by multiplying the matrix of the motion to the vector of the current position. (2) **Magnified local isometry**. The angle between two nearby vectors equals the Euclidean distance between the two corresponding positions multiplied by a magnifying factor. (3) **Global adjacency kernel.** The inner product between two vectors measures the adjacency between the two corresponding positions, which is defined by a kernel function of the Euclidean distance between the two positions. **Our representational model has explicit algebra and geometry**. It can learn hexagon patterns of grid cells, and **it is capable of error correction, path integral and path planning**.”

Gao, Ruiqi & Xie, Jianwen & Zhu, Song & Wu, Yingnian. (2018). Learning Grid Cells as Vector Representation of Self-Position Coupled with Matrix Representation of Self-Motion. ICLR 2019

GridCell-3D Code: https://github.com/jianwen-xie/GridCell-3D

GridCell Code: https://github.com/ruiqigao/GridCell

Project: http://www.stat.ucla.edu/~ruiqigao/gridcell/main.html

CogNav Blog

New discovery worth spreading on cognitive navigation in robotics and neuroscience

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3D Grid Cells
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3D SLAM
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Allocentric
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Continuous Attractor Neural Network
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hippocampal
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- Laboratory of Nachum Ulanovsky
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- ……