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Deep neural networks (DNNs) usually contain massive parameters, but there isredundancy such that it is guessed that the DNNs could be trained inlow-dimensional subspaces. In this paper, we propose a Dynamic LinearDimensionality Reduction (DLDR) based on low-dimensional properties of thetraining trajectory. The reduction is efficient, which is supported bycomprehensive experiments: optimization in 40 dimensional spaces can achievecomparable performance as regular training over thousands or even millions ofparameters. Since there are only a few optimization variables, we develop aquasi-Newton-based algorithm and also obtain robustness against label noises,which are two follow-up experiments to show the advantages of findinglow-dimensional subspaces.

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