Title: Self-Supervised Prime-Dual Networks for Few-Shot Image Classification. Abstract: We construct a prime-dual network structure for few-shot learning which establishes a commutative relationship between the support set and the query set, as well as a new self- supervision constraint for highly effective few-shot learning. Specifically, the prime network performs the forward label prediction of the query set from the support set, while the dual network performs the reverse label prediction of the support set from the query set. This forward and reserve prediction process with commutated support and query sets forms a label prediction loop and establishes a self-supervision constraint between the ground-truth labels and their predicted values. This unique constraint can be used to significantly improve the training performance of few-shot learning through coupled prime and dual network training. It can be also used as an objective function for optimization during the testing stage to refine the query label prediction results. Our extensive experimental results demonstrate that the proposed self-supervised commutative learning and optimization outperforms existing state-of the-art few-shot learning methods by large margins on various benchmark datasets.