We further showcase the flexibility of AlphaTensor through different use-cases: algorithms with state-of-the-art complexity for structured matrix multiplication and improved practical efficiency by ...

An artificial-intelligence approach known as AlphaTensor found exact matrix-multiplication algorithms that are more efficient than those previously known for many matrix sizes.

Matrix multiplication is a fundamental operation in machine learning, and is one of the most time-consuming, due to the extensive use of multiply-add instructions.

To help you understand the algorithm, the video shows a simple two-digit by two-digit multiplication. You can see that the first and last digits are essentially the result of one multiplication.

Completing the tensor decomposition not only allows the AI system to win the game, but also generates a new matrix multiplication algorithm in the process.

By transforming operands into a Montgomery domain, these algorithms enable efficient modular multiplication and exponentiation, which are crucial for public-key cryptosystems.

Karatsuba’s divide-and-conquer multiplication algorithm takes advantage of this saving. Consider a multiplication algorithm that parallels the way multiplication of complex numbers works.

Complexity theorists sort problems into categories, called complexity classes, based on the resource demands of the best algorithms for solving them—that is, the algorithms that run fastest or ...

Computer Scientists Discover Limits of Major Research Algorithm The most widely used technique for finding the largest or smallest values of a math function turns out to be a fundamentally difficult ...