Deep Frequency Principle Towards Understanding Why Deeper Learning Is Faster

Authors

  • Zhiqin John Xu Shanghai Jiao Tong University
  • Hanxu Zhou Shanghai Jiao Tong University

Keywords:

Optimization, Learning Theory

Abstract

Understanding the effect of depth in deep learning is a critical problem. In this work, we utilize the Fourier analysis to empirically provide a promising mechanism to understand why feedforward deeper learning is faster. To this end, we separate a deep neural network, trained by normal stochastic gradient descent, into two parts during analysis, i.e., a pre-condition component and a learning component, in which the output of the pre-condition one is the input of the learning one. We use a filtering method to characterize the frequency distribution of a high-dimensional function. Based on experiments of deep networks and real dataset, we propose a deep frequency principle, that is, the effective target function for a deeper hidden layer biases towards lower frequency during the training. Therefore, the learning component effectively learns a lower frequency function if the pre-condition component has more layers. Due to the well-studied frequency principle, i.e., deep neural networks learn lower frequency functions faster, the deep frequency principle provides a reasonable explanation to why deeper learning is faster. We believe these empirical studies would be valuable for future theoretical studies of the effect of depth in deep learning.

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Published

2021-05-18

How to Cite

Xu, Z. J., & Zhou, H. (2021). Deep Frequency Principle Towards Understanding Why Deeper Learning Is Faster. Proceedings of the AAAI Conference on Artificial Intelligence, 35(12), 10541-10550. Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/17261

Issue

Section

AAAI Technical Track on Machine Learning V