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Matrix Multiplication Record

Manuel Kauers and Jakob Moosbauer showed that 5x5 matrices mod 2 can be multiplied with only 95 multiplications.

Manuel Kauers and Jakob Moosbauer

Despite its central role in all areas of computing, it is still not known what is the most efficient way to multiply matrices. For 5x5 matrices, the standard method requires 125 multiplications, and a better way using only 100 multiplications was found in the 1980s. Since then, there was little progress until Sedoglavic and Smirnov reduced the bound to 98 two years ago. The next step forward happened a few weeks ago, when a team of AI researchers announced a way to do the job with 96 multiplications for ground rings of characteristic 2. This resulted not only in a significant media echo but also attracted the attention of Kauers and Moosbauer from the Institute for Algebra, who succeeded in eliminating one more multiplication from this method, thus obtaining a multiplication scheme that only needs 95 multiplications. This scheme is also restricted to ground rings of characteristic 2. It remains to be seen how long this new record will stand. The new result was covered by several national and international media.

Link: https://arxiv.org/abs/2210.04045, opens an external URL in a new window

Link: https://www.derstandard.at/story/2000140099593/linzer-mathematiker-uebertrumpfen-kuenstliche-intelligenz, opens an external URL in a new window

Link: https://arstechnica.com/information-technology/2022/10/deepmind-breaks-50-year-math-record-using-ai-new-record-falls-a-week-later/, opens an external URL in a new window