# Prototypical Networks for Few-shot Learning

## Summary

This paper proposes *Prototypical Networks* for the problem of few-shot (and zero-shot) classification, where a classifier must generalize to new data given only a small number of examples of each class. Prototypical Networks learn a metric space in which classification can be performed by computing distances to prototype representations of each class. The proposed method is relatively intuitive and surprisingly effective.

## Proposed method

In few-shot classification we are given a small support set of \(N\) labeled examples \(S = {(x_1,y_1), ... ,(x_N, y_N)}\) where each \(x_i \in R^D\) is the D-dimensional feature vector of an example and \(y_i\) is the corresponding label. \(S_k\) denotes the set of examples labeled with class \(k\).

Note that in their implementation, \(f_\phi\) is a four-layer CNN.

Interestingly, when the system uses an Euclidean distance \(d(.)\) the system becomes a linear model as illustrated in Figure 1.

The training algorithm is as follows:

A real illustration of the resulting embedding of a propotype network is shown in Fig.2.

## Results

The method was state of the art on several datasets back in 2017.