Understanding deflation process in over-parametrized tensor decomposition

R Ge, Y Ren, X Wang, M Zhou - Advances in Neural …, 2021 - proceedings.neurips.cc
Advances in Neural Information Processing Systems, 2021proceedings.neurips.cc
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 …
Abstract
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.
proceedings.neurips.cc
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