3D Spatially Embedded Networks: Extending the Universal Approximation Theorem

This research note offers a functional equivalence construction proof to show that with ReLU activations and bijective weight-distance kernels, an SE-FFN subgraph can replicate an arbitrary MLP edge-weight. Under these conditions, spatially embedded networks are equivalent to multilayer perceptrons, and thus share universal function approximation properties.

Publication Details

Journal
Figshare
Published
2025-01-01
DOI
https://doi.org/10.6084/m9.figshare.29852168.v1
Primary Topic
Neural Networks and Applications
Type
article
Field-Weighted Citation Impact
0.00
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article

3D Spatially Embedded Networks: Extending the Universal Approximation Theorem

Figshare
Neural Networks and Applications
article

3D Spatially Embedded Networks: Extending the Universal Approximation Theorem

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Abstract

This research note offers a functional equivalence construction proof to show that with ReLU activations and bijective weight-distance kernels, an SE-FFN subgraph can replicate an arbitrary MLP edge-weight. Under these conditions, spatially embedded networks are equivalent to multilayer perceptrons, and thus share universal function approximation properties.

Figshare
Openalex Percentile: Top 74%
Neural Networks and Applications
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3D Spatially Embedded Networks: Extending the Universal Approximation Theorem · Figshare (2025) | TGRS Research Map | TGRS