Barron Spaces and the Application to Neural Network Approximation

主講人：明平兵 中國科學(xué)院研究員

時(shí)間：2023年10月27日10：00

地點(diǎn)：三號(hào)樓115室

舉辦單位：數(shù)理學(xué)院

主講人介紹：明平兵，中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院研究員并擔(dān)任科學(xué)與工程計(jì)算國家重點(diǎn)實(shí)驗(yàn)室副主任。主要從事固體多尺度建模、多尺度算法以及機(jī)器學(xué)習(xí)的研究。他預(yù)測了石墨烯的理想強(qiáng)度并在Cauchy-Born法則的數(shù)學(xué)理論、擬連續(xù)體方法的穩(wěn)定性方面有較為系統(tǒng)的工作。他在JAMS, CPAM, ARMA, JMPS,PRB等國際著名學(xué)術(shù)期刊上發(fā)表學(xué)術(shù)論文六十余篇。他曾應(yīng)邀在SCADE2009，The SIAM Mathematics Aspects of Materials Science 2016等會(huì)議上作大會(huì)報(bào)告。

內(nèi)容介紹：We shall discuss various Barron type spaces arising from neural network. The relations among them will be clarified, and we also establish the relationship among the spetral Barron space and the classical function spaces such as Besov space, Sobolev space and Bessel potential space, which partly answer the question proposed by Girosi and Anzellotti in 1993. As an application, certain new approximation results for the shallow neural network and deep neural network with the Barron class as the target function space will be proved. This is a joint work with Yulei Liao (AMSS, CAS) and Yan Meng (RUC).