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 © 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.