multiplication – Quanta Magazine

AI Needs Enormous Computing Power. Could Light-Based Chips Help?

Amos Zeeberg — Mon, 20 May 2024 14:40:50 +0000

Moore’s law is already pretty fast. It holds that computer chips pack in twice as many transistors every two years or so, producing major jumps in speed and efficiency. But the computing demands of the deep learning era are growing even faster than that — at a pace that is likely not sustainable. The International Energy Agency predicts that artificial intelligence will consume 10 times as much...

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New Breakthrough Brings Matrix Multiplication Closer to Ideal

Steve Nadis — Thu, 07 Mar 2024 15:30:13 +0000

Computer scientists are a demanding bunch. For them, it’s not enough to get the right answer to a problem — the goal, almost always, is to get the answer as efficiently as possible. Take the act of multiplying matrices, or arrays of numbers. In 1812, the French mathematician Jacques Philippe Marie Binet came up with the basic set of rules we still teach students. It works perfectly well...

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AI Reveals New Possibilities in Matrix Multiplication

Ben Brubaker — Wed, 23 Nov 2022 14:57:13 +0000

Mathematicians love a good puzzle. Even something as abstract as multiplying matrices (two-dimensional tables of numbers) can feel like a game when you try to find the most efficient way to do it. It’s a little like trying to solve a Rubik’s Cube in as few moves as possible — challenging, but alluring. Except that for a Rubik’s Cube, the number of possible moves at each step is 18...

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Computer Scientists Prove That Certain Problems Are Truly Hard

Mordechai Rorvig — Wed, 11 May 2022 05:52:38 +0000

Last summer, three researchers took a small step toward answering one of the most important questions in theoretical computer science. To paraphrase Avi Wigderson of the Institute for Advanced Study, that question asks something simple but profound: Can we solve all the problems we hope to solve? More precisely, computer scientists want to know whether all the problems we hope to solve can be...

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Researchers Identify ‘Master Problem’ Underlying All Cryptography

Erica Klarreich — Wed, 06 Apr 2022 16:58:20 +0000

In 1868, the mathematician Charles Dodgson (better known as Lewis Carroll) proclaimed that an encryption scheme called the Vigenère cipher was “unbreakable.” He had no proof, but he had compelling reasons for his belief, since mathematicians had been trying unsuccessfully to break the cipher for more than three centuries. There was just one small problem: A German infantry officer named Friedrich...

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