  Few-shot learning amounts to learning representations and acquiring knowledge
such that novel tasks may be solved with both supervision and data being
limited. Improved performance is possible by transductive inference, where the
entire test set is available concurrently, and semi-supervised learning, where
more unlabeled data is available. These problems are closely related because
there is little or no adaptation of the representation in novel tasks.
  Focusing on these two settings, we introduce a new algorithm that leverages
the manifold structure of the labeled and unlabeled data distribution to
predict pseudo-labels, while balancing over classes and using the loss value
distribution of a limited-capacity classifier to select the cleanest labels,
iterately improving the quality of pseudo-labels. Our solution sets new state
of the art on four benchmark datasets, namely \emph{mini}ImageNet,
\emph{tiered}ImageNet, CUB and CIFAR-FS, while being robust over feature space
pre-processing and the quantity of available data.
