Universal Approximation of Operators with Transformers and Neural Integral Operators
Year: 2026
Type: article
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 Hölder spaces. Moreover, we show that a generalized version of neural integral operators, based on the Gavurin integral, treats them as universal approximators of arbitrary operators between Banach spaces. Lastly, we show that a modified version of the transformer, which uses Leray–Schauder mappings, is a universal approximator of operators between arbitrary Banach spaces.
Source: Axioms
Authors: Emanuele Zappala, Maryam Bagherian
Institution: Idaho State University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4403160909