SEATTLE — Ali Farhadi holds a puny $5 computer, called a Raspberry Pi, comfortably in his palm and exults that his team of researchers has managed to squeeze into it a powerful program that can recognize thousands of objects.

Dr. Farhadi, a computer scientist at the Allen Institute for Artificial Intelligence here, calls his advance “artificial intelligence at your fingertips.” The experimental program could drastically lower the cost of artificial intelligence and improve privacy because you wouldn’t need to share information over the internet.

But the A.I. system is emblematic of something even more significant for the microelectronics industry as it inches closer to the physical limits of semiconductors made with silicon: It uses 1/ 32 of the memory and operates 58 times as fast as rival programs.

There is a growing sense of urgency feeding this sort of research into alternative computing methods. For decades, computer designers have been able to count on cheaper and faster chips every two years. As transistors have shrunk in size, at regular intervals, computing has become both more powerful and cheaper at an accelerating rate — a concept known as Moore’s Law.