Understanding Deflation Process in Over-parametrized Tensor Decomposition
Conference Paper
In this paper we study the training dynamics for gradient flow on over-parametrized tensor decomposition problems. Empirically, such training process often first fits larger components and then discovers smaller components, which is similar to a tensor deflation process that is commonly used in tensor decomposition algorithms. We prove that for orthogonally decomposable tensor, a slightly modified version of gradient flow would follow a tensor deflation process and recover all the tensor components. Our proof suggests that for orthogonal tensors, gradient flow dynamics works similarly as greedy low-rank learning in the matrix setting, which is a first step towards understanding the implicit regularization effect of over-parametrized models for low-rank tensors.
Duke Authors
Cited Authors
- Ge, R; Ren, Y; Wang, X; Zhou, M
Published Date
- January 1, 2021
Published In
Volume / Issue
- 2 /
Start / End Page
- 1299 - 1311
International Standard Serial Number (ISSN)
- 1049-5258
International Standard Book Number 13 (ISBN-13)
- 9781713845393
Citation Source
- Scopus