The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of stochastic gradient descent training iterations. Our result describes the neural network's fluctuations around its mean-field limit. The fluctuations have a ...
To further simplify the averaged generating functional (4), we can define a new fieldQ1(t,
文章链接:A mean field view of the landscape of two-layers neural networks 近几年,deep learning theory中mean-field theory不断发展,为我们分析神经网络提供了一套理论框架。相较于之前较流行的NTK理论,mean-field一个很重要的进步是能够分析feature learning的过程,而NTK只能分析在初始点附近的性质,不能解释网...
Various applications of the mean field theory (MFT) technique for obtaining solutions close to optimal minima in feedback networks are reviewed. Using this method in the context of the Boltzmann machine gives rise to a fast deterministic learning algorithm with a performance comparable with that of...
OF TALAGRAND, KKL AND FREIDGUT’S THEOREMS 37:38 FIRST-ORDER CONDITIONS FOR OPTIMIZATION IN THE WASSERSTEIN SPACE 25:38 THE QUANTUM WASSERSTEIN DISTANCE OF ORDER 1 57:09 MEAN-FIELD AND SEMICLASSICAL LIMIT_ WASSERSTEIN VERSUS SCHATTEN 1:01:17 ON THE EXISTENCE OF DERIVATIONS AS SQUARE ROOTS OF ...
Understanding the properties of neural networks trained via stochastic gradient descent (SGD) is at the heart of the theory of deep learning. In this work, we take a mean-field view, and consider a two-layer ReLU network trained via noisy-SGD for a univariate regularized regression problem. ...
A Mean Field View of the Landscape of Two-Layers Neural Networks Multi-layer neural networks are among the most powerful models in machine learning, yet the fundamental reasons for this success defy mathematical understa... S Mei,A Montanari,Phan-Minh Nguyen - 《Proceedings of the National ...
This study analyzes the Fisher information matrix (FIM) by applying mean-field theory to deep neural networks with random weights. We theoretically find novel statistics of the FIM, which are universal among a wide class of deep networks with any number of layers and various activation functions....
链接:A Mean Field View of the Landscape of Two-Layers Neural Networks 前言 之前我们介绍过无限宽网络初始化时候的平均场理论,而这次要介绍缺是另一支不同的理论。为了区分两种理论,我们先做一个总结: 初始化平均场又叫做neural network gaussian process (NNGP),它是NTK的前身 ...
meanfieldviewtwo-layerneuralnetworksSongMeiAndreaMontanariPhan-MinhNguyenMathematicalEngineering,StanfordUniversity,Stanford,CA94305;ElectricalEngineering,StanfordUniversity,Stanford,CA94305;Statistics,StanfordUniversity,Stanford,CA94305EditedBickel,UniversityCalifornia,Berkeley,CA,approvedJune21,2018(receivedreviewApril16...