DeepMind Breaks 50-Year Math Record Using AI; New Record Falls a Week Later

Last week, DeepMind announced it discovered a more efficient way to perform matrix multiplication, conquering a 50-year-old record. This week, two Austrian researchers at Johannes Kepler University Linz claim they have bested that new record by one step. Ars Technica reports: In 1969, a German mathematician named Volker Strassen discovered the previous-best algorithm for multiplying 4x4 matrices, which reduces the number of steps necessary to perform a matrix calculation. For example, multiplying two 4x4 matrices together using a traditional schoolroom method would take 64 multiplications, while Strassen's algorithm can perform the same feat in 49 multiplications. Using a neural network called AlphaTensor, DeepMind discovered a way to reduce that count to 47 multiplications, and its researchers published a paper about the achievement in Nature last week. To discover more efficient matrix math algorithms, DeepMind set up the problem like a single-player game. The company wrote about the process in more detail in a blog post last week. DeepMind then trained AlphaTensor using reinforcement learning to play this fictional math game -- similar to how AlphaGo learned to play Go -- and it gradually improved over time. Eventually, it rediscovered Strassen's work and those of other human mathematicians, then it surpassed them, according to DeepMind. In a more complicated example, AlphaTensor discovered a new way to perform 5x5 matrix multiplication in 96 steps (versus 98 for the older method). This week, Manuel Kauers and Jakob Moosbauer of Johannes Kepler University in Linz, Austria, published a paper claiming they have reduced that count by one, down to 95 multiplications. It's no coincidence that this apparently record-breaking new algorithm came so quickly because it built off of DeepMind's work. In their paper, Kauers and Moosbauer write, "This solution was obtained from the scheme of [DeepMind's researchers] by applying a sequence of transformations leading to a scheme from which one multiplication could be eliminated."

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