Transformer与神经积分算子可逼近任意算子，理论突破性强。
Universal Approximation of Operators with Transformers and Neural Integral Operators
- 用变换器架构逼近霍尔德空间间的积分算子
- 基于加武林积分的广义神经积分算子可逼近任意巴拿赫空间算子
- 改进版变换器结合勒雷-施劳德映射，实现通用算子逼近
我们研究了变换器与神经积分算子在巴拿赫空间中算子的通用逼近性质。特别地，我们证明变换器架构是霍尔德空间间积分算子的通用逼近器。此外，基于加武林积分的广义神经积分算子是任意巴拿赫空间间算子的通用逼近器。最后，我们证明一种使用勒雷-施劳德映射的改进型变换器，是任意巴拿赫空间间算子的通用逼近器。
原文摘要 · Abstract (English)
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.
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