  Polythetic classifications, based on shared patterns of features that need
neither be universal nor constant among members of a class, are common in the
natural world and greatly outnumber monothetic classifications over a set of
features. We show that threshold meta-learners, such as Prototypical Networks,
require an embedding dimension that is exponential in the number of
task-relevant features to emulate these functions. In contrast, attentional
classifiers, such as Matching Networks, are polythetic by default and able to
solve these problems with a linear embedding dimension. However, we find that
in the presence of task-irrelevant features, inherent to meta-learning
problems, attentional models are susceptible to misclassification. To address
this challenge, we propose a self-attention feature-selection mechanism that
adaptively dilutes non-discriminative features. We demonstrate the
effectiveness of our approach in meta-learning Boolean functions, and synthetic
and real-world few-shot learning tasks.
