For all the promise of big-data machine learning, what will happen when robots deploy to our homes and workplaces and inevitably encounter new objects, new tasks, and new environments? If a solution to every problem cannot be pre-trained, then robots will need to adapt to this novelty. Can a robot, instead, spend a few seconds to a few minutes gathering information and then accomplish a complex task? Why does it seem that so much data is required, anyway? I will first argue that the hybrid or contact-driven aspects of manipulation clashes with the inductive biases inherent in standard learning methods, driving this current need for large data. I will then show how contact-inspired implicit learning, embedding convex optimization, can reshape the loss landscape and enable more accurate training, better generalization, and ultimately data efficiency. Finally, I will present our latest results on how these learned models can be deployed via real-time multi-contact MPC for robotic manipulation.