Technology

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Computer scientists have discovered a new way to multiply large matrices faster than ever before by eliminating a previously unknown inefficiency, reports Quanta Magazine.

In October 2022, we covered a new technique discovered by a Google DeepMind AI model called AlphaTensor, focusing on practical algorithmic improvements for specific matrix sizes, such as 4x4 matrices.

By contrast, the new research, conducted by Ran Duan and Renfei Zhou of Tsinghua University, Hongxun Wu of the University of California, Berkeley, and by Virginia Vassilevska Williams, Yinzhan Xu, and Zixuan Xu of the Massachusetts Institute of Technology (in a second paper), seeks theoretical enhancements by aiming to lower the complexity exponent, ω, for a broad efficiency gain across all sizes of matrices.

However, the new technique, which improves upon the "laser method" introduced by Volker Strassen in 1986, has reduced the upper bound of the exponent (denoted as the aforementioned ω), bringing it closer to the ideal value of 2, which represents the theoretical minimum number of operations needed.

In 2020, Josh Alman and Williams introduced a significant improvement in matrix multiplication efficiency by establishing a new upper bound for ω at approximately 2.3728596.

While the reduction of the omega constant might appear minor at first glance—reducing the 2020 record value by 0.0013076—the cumulative work of Duan, Zhou, and Williams represents the most substantial progress in the field observed since 2010.

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