“We met once a week,” Dr. Hinton said in an interview. “Sometimes it ended in a shouting match, sometimes not.”

Neural networks had a brief revival in the late 1980s and early 1990s. After a year of postdoctoral research with Dr. Hinton in Canada, the Paris-born Dr. LeCun moved to AT&T’s Bell Labs in New Jersey, where he designed a neural network that could read handwritten letters and numbers. An AT&T subsidiary sold the system to banks, and at one point it read about 10 percent of all checks written in the United States.

Though a neural network could read handwriting and help with some other tasks, it could not make much headway with big A.I. tasks, like recognizing faces and objects in photos, identifying spoken words, and understanding the natural way people talk.

“They worked well only when you had lots of training data, and there were few areas that had lots of training data,” Dr. LeCun, 58, said.

But some researchers persisted, including the Paris-born Dr. Bengio, 55, who worked alongside Dr. LeCun at Bell Labs before taking a professorship at the University of Montreal.

In 2004, with less than $400,000 in funding from the Canadian Institute for Advanced Research, Dr. Hinton created a research program dedicated to what he called “neural computation and adaptive perception.” He invited Dr. Bengio and Dr. LeCun to join him.