When is a convolutional filter easy to learn?

Simon S. Du, Jason D. Lee, Yuandong Tian

Research output: Contribution to conferencePaperpeer-review

Abstract

We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that are restricted to standard Gaussian input. We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches. To the best of our knowledge, this is the first recovery guarantee of gradient-based algorithms for convolutional filter on non-Gaussian input distributions. Our theory also justifies the two-stage learning rate strategy in deep neural networks. While our focus is theoretical, we also present experiments that justify our theoretical findings.

Original languageEnglish (US)
StatePublished - Jan 1 2018
Event6th International Conference on Learning Representations, ICLR 2018 - Vancouver, Canada
Duration: Apr 30 2018May 3 2018

Conference

Conference6th International Conference on Learning Representations, ICLR 2018
CountryCanada
CityVancouver
Period4/30/185/3/18

All Science Journal Classification (ASJC) codes

  • Language and Linguistics
  • Education
  • Computer Science Applications
  • Linguistics and Language

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