3D Spatially Embedded Networks: Verifying Coordinate Backpropagation on a Single Neuron

The purpose of this research note is to verify that one can apply backpropagation to a spatially embedded artificial neuron. The author applies the chain rule to obtain loss-coordinate derivatives for a single neuron embedded in 3D Euclidean Space. Mean-squared error loss is used.

Publication Details

Journal
Figshare
Published
2025-01-01
DOI
https://doi.org/10.6084/m9.figshare.29580674.v2
Primary Topic
Neural Networks and Applications
Type
article
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article

3D Spatially Embedded Networks: Verifying Coordinate Backpropagation on a Single Neuron

Figshare
Neural Networks and Applications
article

3D Spatially Embedded Networks: Verifying Coordinate Backpropagation on a Single Neuron

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Abstract

The purpose of this research note is to verify that one can apply backpropagation to a spatially embedded artificial neuron. The author applies the chain rule to obtain loss-coordinate derivatives for a single neuron embedded in 3D Euclidean Space. Mean-squared error loss is used.

Figshare
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Neural Networks and Applications
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3D Spatially Embedded Networks: Verifying Coordinate Backpropagation on a Single Neuron · Figshare (2025) | TGRS Research Map | TGRS