Rethinking Gradient Projection Continual Learning: Stability/Plasticity Feature Space Decoupling

Abstract

Continual learning aims to incrementally learn novel classes over time, while not forgetting the learned knowledge. Recent studies have found that learning would not forget if the updated gradient is orthogonal to the feature space. However, previous approaches require the gradient to be fully orthogonal to the whole feature space, leading to poor plasticity, as the feasible gradient direction becomes narrow when the tasks continually come, i.e., feature space is unlimitedly expanded. In this paper, we propose a space decoupling (SD) algorithm to decouple the feature space into a pair of complementary subspaces, i.e., the stability space <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{I}$</tex> and the plasticity space <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{R}. \mathcal{I}$</tex> is established by conducting space intersection between the historic and current feature space, and thus <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{I}$</tex> contains more task-shared bases. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{R}$</tex> is constructed by seeking the orthogonal complementary subspace of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T$</tex> and thus <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{R}$</tex> mainly contains task-specific bases. By putting distinguishing constraints on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{R}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{I}$</tex> , our method achieves a better balance between stability and plasticity. Extensive experiments are conducted by applying SD to gradient projection baselines, and show SD is model-agnostic and achieves SOTA results on publicly available datasets.