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

• URL: http://arxiv.org/abs/2102.00200v1
• Date: Sat, 30 Jan 2021 10:11:37 GMT
• Title: Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks
• Authors: Yaoyu Zhang, Tao Luo, Zheng Ma, and Zhi-Qin John Xu
• Abstract summary: We show that low frequency dominance of target functions is the key condition for the non-overfitting of NNs. 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.
• Score: 4.86119220344659
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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