Publications [#363832] of Rong Ge

Papers Published

1. Ge, R; Ren, Y; Wang, X; Zhou, M, Understanding Deflation Process in Over-parametrized Tensor Decomposition, Advances in Neural Information Processing Systems, vol. 2 (January, 2021), pp. 1299-1311, ISBN 9781713845393
   (last updated on 2026/01/16)

   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.