An efficient calculation method means: fewer steps to the same solution
Matrix multiplication is used in thousands of everyday computing tasks, from representing pixels on a computer screen to computing possible motion options in games. A record has remained for more than 50 years: in 1969, the German mathematician Volker Strassen developed the most efficient method of multiplying two 4 x 4 matrices. Since then no one has been able to fix it. as technical explorer Reportedly, a team of researchers from Google’s DeepMind in London has finally broken this record – and with ease, so to say.
The approach taken by the team in the expert journal Nature The description is based on results from the AlphaZero project – an AI that has been trained with great success to master complex board games like chess and Go. Simple principle: each move in the game represents the next step in solving the problem, an algorithm representing the sequence of moves required. The researchers call to transfer this approach to the matrix problem AlphaTensor.
technology review finds a very apt description of the team’s idea in its report: “Instead of learning the best move order in Go or chess, the alpha tensor learned the best step order in multiplying matrices. Play it in as few moves as possible.” was rewarded for winning.” Result: AI could, among other things, break the 50-year efficiency limit when multiplying two 4 x 4 matrices – Strassen’s method required 49 steps, AlphaTensor found a way to achieve the solution in 47 steps. Similar success can be achieved in other matrix problems as well. The best algorithm so far was able to solve the multiplication of 45 matrices with 5 matrices with 80 individual multiplications, with Alphatensor requiring 76.
In the end, progress is always teamwork between humans and computers.
As complex as the subject may seem, such breakthroughs can have a major impact on many people’s daily lives. Because the calculation is simple: If the calculation can be done with fewer steps, you can reduce costs and save energy for the whole process. The next step is exciting here as well: Theoretical researchers who are now analyzing the new algorithm may look for clues to further breakthroughs.
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