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arXiv · 2102.00200

Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks

Yaoyu Zhang·Tao Luo·Zheng Ma·Zhi-Qin John Xu
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Abstract

Why heavily parameterized neural networks (NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency principle (LFP) model accounts for a key dynamical feature of NNs: they learn low frequencies first, irrespective of microscopic details. Theory based on our LFP model shows that low frequency dominance of target functions is the key condition for the non-overfitting of NNs and is verified by experiments. Furthermore, through an ideal two-layer NN, we unravel how detailed microscopic NN training dynamics statistically gives rise to a LFP model with quantitative prediction power.

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Yaoyu Zhang, Tao Luo, Zheng Ma, Zhi-Qin John Xu. 2021-01-30. Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks. https://doi.org/10.1088/0256-307x%2F38%2F3%2F038701

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