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).
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