  We propose a novel architecture for $k$-shot classification on the Omniglot
dataset. Building on prototypical networks, we extend their architecture to
what we call Gaussian prototypical networks. Prototypical networks learn a map
between images and embedding vectors, and use their clustering for
classification. In our model, a part of the encoder output is interpreted as a
confidence region estimate about the embedding point, and expressed as a
Gaussian covariance matrix. Our network then constructs a direction and class
dependent distance metric on the embedding space, using uncertainties of
individual data points as weights. We show that Gaussian prototypical networks
are a preferred architecture over vanilla prototypical networks with an
equivalent number of parameters. We report state-of-the-art performance in
1-shot and 5-shot classification both in 5-way and 20-way regime (for 5-shot
5-way, we are comparable to previous state-of-the-art) on the Omniglot dataset.
We explore artificially down-sampling a fraction of images in the training set,
which improves our performance even further. We therefore hypothesize that
Gaussian prototypical networks might perform better in less homogeneous,
noisier datasets, which are commonplace in real world applications.
