Low Dimensional Trajectory Hypothesis is True: DNNs can be Trained in Tiny Subspaces

Abstract

Deep neural networks (DNNs) usually contain massive parameters, but there is redundancy such that it is guessed that they could be trained in low-dimensional subspaces. In this paper, we propose a Dynamic Linear Dimensionality Reduction (DLDR) based on the low-dimensional properties of the training trajectory. The reduction method is efficient, supported by comprehensive experiments: optimizing DNNs in 40-dimensional spaces can achieve comparable performance as regular training over thousands or even millions of parameters. Since there are only a few variables to optimize, we develop an efficient quasi-Newton-based algorithm, obtain robustness to label noise, and improve the performance of well-trained models, which are three follow-up experiments that can show the advantages of finding such low-dimensional subspaces. The code is released (Pytorch: https://github.com/nblt/DLDR and Mindspore: https://gitee.com/mindspore/docs/tree/r1.6/docs/sample_code/dimension_reduce_training).