A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics-Reference-Cited by-同舟云学术

A comparative analysis of optimization and generalization properties of two-layer neural network and random feature models under gradient descent dynamics

Published:2020-01-08 Issue:7 Volume:63 Page:1235-1258
ISSN:1674-7283
Container-title:Science China Mathematics
language:en
Short-container-title:Sci. China Math.

Author:

E Weinan,Ma Chao,Wu Lei

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

http://link.springer.com/content/pdf/10.1007/s11425-019-1628-5.pdf

Reference32 articles.

1. Allen-Zhu Z, Li Y, Liang Y. Learning and generalization in overparameterized neural networks, going beyond two layers. ArXiv:1811.04918, 2018

2. Allen-Zhu Z, Li Y, Song Z. A convergence theory for deep learning via over-parameterization. ArXiv:1811.03962, 2018

3. Aronszajn N. Theory of reproducing kernels. Trans Amer Math Soc, 1950, 68: 337–404

4. Arora S, Du S S, Hu W, et al. Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks. ArXiv:1901.08584, 2019

5. Barron A R. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans Inform Theory, 1993, 39: 930–945

Cited by 30 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. How many neurons do we need? A refined analysis for shallow networks trained with gradient descent;Journal of Statistical Planning and Inference;2024-12

2. Gradient Descent Provably Escapes Saddle Points in the Training of Shallow ReLU Networks;Journal of Optimization Theory and Applications;2024-09-10

3. Convergence Analysis for Over-Parameterized Deep Learning;Communications in Computational Physics;2024-06

4. Mathematical and Statistical Frameworks Fostering Advances in AI Systems and Computing;Lecture Notes in Computer Science;2024

5. Ridge Function Machines;Applied and Numerical Harmonic Analysis;2024