{"title":"限制傅立叶神经算子的拉德马赫复杂性","authors":"Taeyoung Kim, Myungjoo Kang","doi":"10.1007/s10994-024-06533-y","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":49900,"journal":{"name":"Machine Learning","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bounding the Rademacher complexity of Fourier neural operators\",\"authors\":\"Taeyoung Kim, Myungjoo Kang\",\"doi\":\"10.1007/s10994-024-06533-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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.</p>\",\"PeriodicalId\":49900,\"journal\":{\"name\":\"Machine Learning\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Machine Learning\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1007/s10994-024-06533-y\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Machine Learning","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10994-024-06533-y","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
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.
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.