  We introduce the isoperimetric loss as a regularization criterion for
learning the map from a visual representation to a semantic embedding, to be
used to transfer knowledge to unknown classes in a zero-shot learning setting.
We use a pre-trained deep neural network model as a visual representation of
image data, a Word2Vec embedding of class labels, and linear maps between the
visual and semantic embedding spaces. However, the spaces themselves are not
linear, and we postulate the sample embedding to be populated by noisy samples
near otherwise smooth manifolds. We exploit the graph structure defined by the
sample points to regularize the estimates of the manifolds by inferring the
graph connectivity using a generalization of the isoperimetric inequalities
from Riemannian geometry to graphs. Surprisingly, this regularization alone,
paired with the simplest baseline model, outperforms the state-of-the-art among
fully automated methods in zero-shot learning benchmarks such as AwA and CUB.
This improvement is achieved solely by learning the structure of the underlying
spaces by imposing regularity.
