限制傅立叶神经算子的拉德马赫复杂性

IF 4.3 3区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Taeyoung Kim, Myungjoo Kang
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引用次数: 0

摘要

最近,人们开发了多种类型的神经算子,包括深度算子网络、图神经算子和基于多小波的算子。与这些模型相比,傅立叶神经算子(FNO)作为一种受物理学启发的机器学习方法,计算效率高,可以学习独立于一定有限基础的函数空间之间的非线性算子。本研究基于特定的组规范研究了 FNO 的拉德马赫复杂度边界。利用基于这些规范的容量,我们对模型的泛化误差进行了约束。此外,我们还研究了经验泛化误差与 FNO 拟议容量之间的相关性。我们推断,群体规范的类型决定了存储在容量中的 FNO 模型的权重和结构信息。实验结果让我们深入了解了 FNO 模型中使用的模式数量对泛化误差的影响。结果证实,我们的容量是估算泛化误差的有效指标。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Bounding the Rademacher complexity of Fourier neural operators

Bounding the Rademacher complexity of Fourier neural operators

Recently, several types of neural operators have been developed, including deep operator networks, graph neural operators, and Multiwavelet-based operators. Compared with these models, the Fourier neural operator (FNO), a physics-inspired machine learning method, is computationally efficient and can learn nonlinear operators between function spaces independent of a certain finite basis. This study investigated the bounding of the Rademacher complexity of the FNO based on specific group norms. Using capacity based on these norms, we bound the generalization error of the model. In addition, we investigate the correlation between the empirical generalization error and the proposed capacity of FNO. We infer that the type of group norm determines the information about the weights and architecture of the FNO model stored in capacity. The experimental results offer insight into the impact of the number of modes used in the FNO model on the generalization error. The results confirm that our capacity is an effective index for estimating generalization errors.

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来源期刊
Machine Learning
Machine Learning 工程技术-计算机:人工智能
CiteScore
11.00
自引率
2.70%
发文量
162
审稿时长
3 months
期刊介绍: Machine Learning serves as a global platform dedicated to computational approaches in learning. The journal reports substantial findings on diverse learning methods applied to various problems, offering support through empirical studies, theoretical analysis, or connections to psychological phenomena. It demonstrates the application of learning methods to solve significant problems and aims to enhance the conduct of machine learning research with a focus on verifiable and replicable evidence in published papers.
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