Nonparametric Classification on Low Dimensional Manifolds using Overparameterized Convolutional Residual Networks
Convolutional residual neural networks (ConvResNets), though overparameterized, can achieve remarkable prediction performance in practice, which cannot be well explained by conventional wisdom. To bridge this gap, we study the performance of ConvResNeXts, which cover ConvResNets as a special case, trained with weight decay from the perspective of nonparametric classification. Our analysis allows for infinitely many building blocks in ConvResNeXts, and shows that weight decay implicitly enforces sparsity on these blocks. Specifically, we consider a smooth target function supported on a low-dimensional manifold, then prove that ConvResNeXts can adapt to the function smoothness and low-dimensional structures and efficiently learn the function without suffering from the curse of dimensionality. Our findings partially justify the advantage of overparameterized ConvResNeXts over conventional machine learning models.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Warped Mixtures for Nonparametric Cluster Shapes
A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussi…
Density EstimationWarped Mixtures for Nonparametric Cluster Shapes
A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussi…
Density EstimationNonparametric Regression on Low-Dimensional Manifolds using Deep ReLU Networks : Function Approximation and Statistical Recovery
Real world data often exhibit low-dimensional geometric structures, and can be viewed as samples near a low-dimensional manifold. This paper studies nonparametric regression of H\"{o}lder functions on low-dimensional man…
regressionDeep Networks and the Multiple Manifold Problem
We study the multiple manifold problem, a binary classification task modeled on applications in machine vision, in which a deep fully-connected neural network is trained to separate two low-dimensional submanifolds of th…
Binary ClassificationIntrinsic Gaussian Processes on Manifolds and Their Accelerations by Symmetry
Amidst the growing interest in nonparametric regression, we address a significant challenge in Gaussian processes(GP) applied to manifold-based predictors. Existing methods primarily focus on low dimensional constrained …
Gaussian Processesregression