{"title":"Sigmoid网络的复合优化算法","authors":"Huixiong Chen;Qi Ye","doi":"10.1162/neco_a_01603","DOIUrl":null,"url":null,"abstract":"In this letter, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the composite optimization algorithms based on the linearized proximal algorithms and the alternating direction method of multipliers. Under the assumptions of the weak sharp minima and the regularity condition, the algorithm is guaranteed to converge to a globally optimal solution of the objective function even in the case of nonconvex and nonsmooth problems. Furthermore, the convergence results can be directly related to the amount of training data and provide a general guide for setting the size of sigmoid networks. Numerical experiments on Franke’s function fitting and handwritten digit recognition show that the proposed algorithms perform satisfactorily and robustly.","PeriodicalId":54731,"journal":{"name":"Neural Computation","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Composite Optimization Algorithms for Sigmoid Networks\",\"authors\":\"Huixiong Chen;Qi Ye\",\"doi\":\"10.1162/neco_a_01603\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this letter, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the composite optimization algorithms based on the linearized proximal algorithms and the alternating direction method of multipliers. Under the assumptions of the weak sharp minima and the regularity condition, the algorithm is guaranteed to converge to a globally optimal solution of the objective function even in the case of nonconvex and nonsmooth problems. Furthermore, the convergence results can be directly related to the amount of training data and provide a general guide for setting the size of sigmoid networks. Numerical experiments on Franke’s function fitting and handwritten digit recognition show that the proposed algorithms perform satisfactorily and robustly.\",\"PeriodicalId\":54731,\"journal\":{\"name\":\"Neural Computation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2023-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Neural Computation\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10302083/\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Neural Computation","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10302083/","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
Composite Optimization Algorithms for Sigmoid Networks
In this letter, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the composite optimization algorithms based on the linearized proximal algorithms and the alternating direction method of multipliers. Under the assumptions of the weak sharp minima and the regularity condition, the algorithm is guaranteed to converge to a globally optimal solution of the objective function even in the case of nonconvex and nonsmooth problems. Furthermore, the convergence results can be directly related to the amount of training data and provide a general guide for setting the size of sigmoid networks. Numerical experiments on Franke’s function fitting and handwritten digit recognition show that the proposed algorithms perform satisfactorily and robustly.
期刊介绍:
Neural Computation is uniquely positioned at the crossroads between neuroscience and TMCS and welcomes the submission of original papers from all areas of TMCS, including: Advanced experimental design; Analysis of chemical sensor data; Connectomic reconstructions; Analysis of multielectrode and optical recordings; Genetic data for cell identity; Analysis of behavioral data; Multiscale models; Analysis of molecular mechanisms; Neuroinformatics; Analysis of brain imaging data; Neuromorphic engineering; Principles of neural coding, computation, circuit dynamics, and plasticity; Theories of brain function.