  We introduce Transductive Infomation Maximization (TIM) for few-shot
learning. Our method maximizes the mutual information between the query
features and their label predictions for a given few-shot task, in conjunction
with a supervision loss based on the support set. We motivate our transductive
loss by deriving a formal relation between the classification accuracy and
mutual-information maximization. Furthermore, we propose a new
alternating-direction solver, which substantially speeds up transductive
inference over gradient-based optimization, while yielding competitive
accuracy. We also provide a convergence analysis of our solver based on
Zangwill's theory and bound-optimization arguments. TIM inference is modular:
it can be used on top of any base-training feature extractor. Following
standard transductive few-shot settings, our comprehensive experiments
demonstrate that TIM outperforms state-of-the-art methods significantly across
various datasets and networks, while used on top of a fixed feature extractor
trained with simple cross-entropy on the base classes, without resorting to
complex meta-learning schemes. It consistently brings between 2 % and 5 %
improvement in accuracy over the best performing method, not only on all the
well-established few-shot benchmarks but also on more challenging scenarios,
with random tasks, domain shift and larger numbers of classes, as in the
recently introduced META-DATASET. Our code is publicly available at
https://github.com/mboudiaf/TIM. We also publicly release a standalone PyTorch
implementation of META-DATASET, along with additional benchmarking results, at
https://github.com/mboudiaf/pytorch-meta-dataset.
