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变换器与神经积分算子的通用逼近性研究

Universal Approximation of Operators with Transformers and Neural Integral Operators

Department of Mathematics and Statistics(数学与统计学系);Idaho State University Physical Science Complex(爱达荷州立大学物理科学中心);S. 8th Ave., Stop 8085(921 S. 8th Ave., Stop 8085);Pocatello, ID 83209, USA

Emanuele Zappala, Maryam Bagherian

AI总结:

本文研究变换器和神经积分算子在Banach空间中算子的通用逼近性质,证明变换器可逼近Hölder空间间的积分算子,神经积分算子的推广形式可逼近任意Banach空间间的算子,改进的变换器可逼近任意Banach空间间的算子。

摘要:

我们研究变换器和神经积分算子在Banach空间中算子的通用逼近性质。特别是,我们证明变换器架构是Hölder空间之间积分算子的通用逼近器。此外,我们证明基于Gavurin积分的神经积分算子推广形式是任意Banach空间之间算子的通用逼近器。最后,我们证明改进的变换器,使用Leray-Schauder映射,是任意Banach空间之间算子的通用逼近器。

英文摘要:

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, 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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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