Universal Approximation of Operators with Transformers and Neural Integral Operators

Emanuele Zappala; Maryam Bagherian

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arXiv · 2409.00841

Universal Approximation of Operators with Transformers and Neural Integral Operators

Emanuele Zappala·Maryam Bagherian

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Abstract

We study the universal approximation properties of transformers and neural integral operators for operators in Banach spaces. In particular, we show that the transformer architecture is a universal approximator of integral operators between H\"older spaces. Moreover, we show that a generalized version of neural integral operators, based on the Gavurin integral, are universal approximators of arbitrary operators between Banach spaces. Lastly, we show that a modified version of transformer, which uses Leray-Schauder mappings, is a universal approximator of operators between arbitrary Banach spaces.

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Emanuele Zappala, Maryam Bagherian. 2024-09-01. Universal Approximation of Operators with Transformers and Neural Integral Operators. https://arxiv.org/abs/2409.00841

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