  Metric-based meta-learning is one of the de facto standards in few-shot
learning. It composes of representation learning and metrics calculation
designs. Previous works construct class representations in different ways,
varying from mean output embedding to covariance and distributions. However,
using embeddings in space lacks expressivity and cannot capture class
information robustly, while statistical complex modeling poses difficulty to
metric designs. In this work, we use tensor fields (``areas'') to model classes
from the geometrical perspective for few-shot learning. We present a simple and
effective method, dubbed hypersphere prototypes (HyperProto), where class
information is represented by hyperspheres with dynamic sizes with two sets of
learnable parameters: the hypersphere's center and the radius. Extending from
points to areas, hyperspheres are much more expressive than embeddings.
Moreover, it is more convenient to perform metric-based classification with
hypersphere prototypes than statistical modeling, as we only need to calculate
the distance from a data point to the surface of the hypersphere. Following
this idea, we also develop two variants of prototypes under other measurements.
Extensive experiments and analysis on few-shot learning tasks across NLP and CV
and comparison with 20+ competitive baselines demonstrate the effectiveness of
our approach.
