Approximation Rates for Metaplectic Neural Networks
In this paper we develop quantitative approximation results for shallow neural networks constructed using a dictionary based on metaplectic operators. First, we extend the concept of Barron spaces by considering a symplectically motivated extension of the Fourier transform, known as the metaplectic transform. Then, after establishing embedding between metaplectic Barron spaces and Sobolev spaces we consider a neural metaplectic dictionary and we prove Monte-Carlo approximation bounds for metaplectic Barron functions using finite linear combinations of atoms of the dictionary. Finally, we validate the introduction of the neural metaplectic dictionary by devising a deep neural network archi...
| Authors | Ahmed Abdeljawad, Marcello Carioni, Elena Cordero |
|---|---|
| Primary category | cs.LG |
| Published | 9 August 2026 |
| Last updated at source | 9 August 2026 |
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