Learning Over-Parametrized Two-Layer ReLU Neural Networks beyond NTK

• URL: http://arxiv.org/abs/2007.04596v1
• Date: Thu, 9 Jul 2020 07:09:28 GMT
• Title: Learning Over-Parametrized Two-Layer ReLU Neural Networks beyond NTK
• Authors: Yuanzhi Li, Tengyu Ma, Hongyang R. Zhang
• Abstract summary: We consider the dynamic of descent for learning a two-layer neural network. We show that an over-parametrized two-layer neural network can provably learn with gradient loss at most ground with Tangent samples.
• Score: 58.5766737343951
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the dynamic of gradient descent for learning a two-layer neural network. We assume the input $x\in\mathbb{R}^d$ is drawn from a Gaussian distribution and the label of $x$ satisfies $f^{\star}(x) = a^{\top}|W^{\star}x|$, where $a\in\mathbb{R}^d$ is a nonnegative vector and $W^{\star} \in\mathbb{R}^{d\times d}$ is an orthonormal matrix. We show that an over-parametrized two-layer neural network with ReLU activation, trained by gradient descent from random initialization, can provably learn the ground truth network with population loss at most $o(1/d)$ in polynomial time with polynomial samples. On the other hand, we prove that any kernel method, including Neural Tangent Kernel, with a polynomial number of samples in $d$, has population loss at least $\Omega(1 / d)$.

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