One shot learning is such an active area of research there's a long Wikipedia page[1] about it.

I think the SOTA is probably [2], which came out of DeepMind. There's still a way to go before it matches ResNet performance on ImageNet (or even human performance on any real task) though.

[1] https://en.wikipedia.org/wiki/One-shot_learning

[2] https://arxiv.org/abs/1605.06065