An army of more than 4,000 marching doglike robots is a vaguely menacing sight, even in a simulation. But it may point the way for machines to learn new tricks. In the simulation, the machines—called ...

Analysts estimate as-yet unlaunched Apple Robotics could generate about $130 billion a year by 2040, matching the scale of the App Store and greatly exceeding the combined revenue of Mac and iPad.

For that reason, the hardest and perhaps the most promising work of deep learning may lie in the realm of robotics, where the real world introduces constraints that cannot be fully anticipated. That ...