
A Representational Model of Grid Cells Based on Matrix Lie Algebras
The grid cells in the mammalian medial entorhinal cortex exhibit strikin...
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Emergence of gridlike representations by training recurrent neural networks to perform spatial localization
Decades of research on the neural code underlying spatial navigation hav...
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Path Planning Tolerant to Degraded Locomotion Conditions
Mobile robots, especially those driving outdoors and in unstructured ter...
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The multilayer random dot product graph
We present an extension of the latent position network model known as th...
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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...
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Can the brain use waves to solve planning problems?
A variety of behaviors like spatial navigation or bodily motion can be f...
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AlphaN: Shortest Path Finder Automated Delivery Robot with Obstacle Detection and Avoiding System
Alpha N A selfpowered, wheel driven Automated Delivery Robot is present...
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Learning Gridlike Units with Vector Representation of SelfPosition and Matrix Representation of SelfMotion
This paper proposes a model for learning gridlike units for spatial awareness and navigation. In this model, the selfposition of the agent is represented by a vector, and the selfmotion of the agent is represented by a blockdiagonal matrix. Each component of the vector is a unit (or a cell). The model consists of the following two submodels. (1) Motion submodel. The movement from the current position to the next position is modeled by matrixvector 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 submodel. 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 submodels can be implemented by neural networks. The motion submodel is a recurrent network with dynamic weight matrix, and the localization submodel is a feedforward network. The model can be learned by minimizing a loss function that combines the loss functions of the two submodels. The learned units exhibit gridlike 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.
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