  Metric-based meta-learning has attracted a lot of attention due to its
effectiveness and efficiency in few-shot learning. Recent studies show that
metric scaling plays a crucial role in the performance of metric-based
meta-learning algorithms. However, there still lacks a principled method for
learning the metric scaling parameter automatically. In this paper, we recast
metric-based meta-learning from a Bayesian perspective and develop a
variational metric scaling framework for learning a proper metric scaling
parameter. Firstly, we propose a stochastic variational method to learn a
single global scaling parameter. To better fit the embedding space to a given
data distribution, we extend our method to learn a dimensional scaling vector
to transform the embedding space. Furthermore, to learn task-specific
embeddings, we generate task-dependent dimensional scaling vectors with
amortized variational inference. Our method is end-to-end without any
pre-training and can be used as a simple plug-and-play module for existing
metric-based meta-algorithms. Experiments on mini-ImageNet show that our
methods can be used to consistently improve the performance of existing
metric-based meta-algorithms including prototypical networks and TADAM. The
source code can be downloaded from
https://github.com/jiaxinchen666/variational-scaling.
