Learning Grid-like Units with Vector Representation of Self-Position and Matrix Representation of Self-Motion

by   Ruiqi Gao, et al.

This paper proposes a model for learning grid-like units for spatial awareness and navigation. In this model, the self-position of the agent is represented by a vector, and the self-motion of the agent is represented by a block-diagonal matrix. Each component of the vector is a unit (or a cell). The model consists of the following two sub-models. (1) Motion sub-model. The movement from the current position to the next position is modeled by matrix-vector multiplication, i.e., multiplying the matrix representation of the motion to the current vector representation of the position in order to obtain the vector representation of the next position. (2) Localization sub-model. The adjacency between any two positions is a monotone decreasing function of their Euclidean distance, and the adjacency is modeled by the inner product between the vector representations of the two positions. Both sub-models can be implemented by neural networks. The motion sub-model is a recurrent network with dynamic weight matrix, and the localization sub-model is a feedforward network. The model can be learned by minimizing a loss function that combines the loss functions of the two sub-models. The learned units exhibit grid-like patterns (as well as stripe patterns) in all 1D, 2D and 3D environments. The learned model can be used for path integral and path planning. Moreover, the learned representation is capable of error correction.


page 9

page 21

page 22


A Representational Model of Grid Cells Based on Matrix Lie Algebras

The grid cells in the mammalian medial entorhinal cortex exhibit strikin...

Emergence of grid-like representations by training recurrent neural networks to perform spatial localization

Decades of research on the neural code underlying spatial navigation hav...

Path Planning Tolerant to Degraded Locomotion Conditions

Mobile robots, especially those driving outdoors and in unstructured ter...

Learning Vector Representation of Content and Matrix Representation of Change: Towards a Representational Model of V1

This paper entertains the hypothesis that the primary purpose of the cel...

Can the brain use waves to solve planning problems?

A variety of behaviors like spatial navigation or bodily motion can be f...

Explicit Motion Risk Representation

This paper presents a formal definition and explicit representation of r...

Please sign up or login with your details

Forgot password? Click here to reset