Few-Shot Learning by Dimensionality Reduction in Gradient Space

We introduce SubGD, a novel few-shot learning method which is based on the recent finding that stochastic gradient descent updates tend to live in a low-dimensional parameter subspace. In experimental and theoretical analyses, we show that models confined to a suitable predefined subspace generalize well for few-shot learning. A suitable subspace fulfills three criteria across the given tasks: it (a) allows to reduce the training error by gradient flow, (b) leads to models that generalize well, and (c) can be identified by stochastic gradient descent. SubGD identifies these subspaces from an eigendecomposition of the auto-correlation matrix of update directions across different tasks. Demonstrably, we can identify low-dimensional suitable subspaces for few-shot learning of dynamical systems, which have varying properties described by one or few parameters of the analytical system description. Such systems are ubiquitous among real-world applications in science and engineering. We experimentally corroborate the advantages of SubGD on three distinct dynamical systems problem settings, significantly outperforming popular few-shot learning methods both in terms of sample efficiency and performance.