Good news! This could be a breakthrough! Accelerating the speed of discovery!
"... Today, in a paper published in Nature, DeepMind unveiled AlphaTensor, the “first artificial intelligence system for discovering novel, efficient and provably correct algorithms.” The Google-owned lab said the research “sheds light” on a 50-year-old open question in mathematics about finding the fastest way to multiply two matrices.
Ever since the Strassen algorithm was published in 1969, computer science has been on a quest to surpass its speed of multiplying two matrices. ..."
"... During the Islamic Golden Age, Persian mathematician Muhammad ibn Musa al-Khwarizmi designed new algorithms to solve linear and quadratic equations. In fact, al-Khwarizmi’s name, translated into Latin as Algoritmi, led to the term algorithm. But, despite the familiarity with algorithms today – used throughout society from classroom algebra to cutting edge scientific research – the process of discovering new algorithms is incredibly difficult, and an example of the amazing reasoning abilities of the human mind. ..."
"... Through learning, AlphaTensor gradually improves over time, rediscovering historical fast matrix multiplication algorithms such as Strassen’s ...
Moreover, AlphaTensor also discovers a diverse set of algorithms with state-of-the-art complexity – up to thousands of matrix multiplication algorithms for each size, showing that the space of matrix multiplication algorithms is richer than previously thought. ..."
Moreover, AlphaTensor also discovers a diverse set of algorithms with state-of-the-art complexity – up to thousands of matrix multiplication algorithms for each size, showing that the space of matrix multiplication algorithms is richer than previously thought. ..."
From the abstract:
"Improving the efficiency of algorithms for fundamental computations can have a widespread impact, as it can affect the overall speed of a large amount of computations. Matrix multiplication is one such primitive task, occurring in many systems—from neural networks to scientific computing routines. The automatic discovery of algorithms using machine learning offers the prospect of reaching beyond human intuition and outperforming the current best human-designed algorithms. However, automating the algorithm discovery procedure is intricate, as the space of possible algorithms is enormous. Here we report a deep reinforcement learning approach based on AlphaZero for discovering efficient and provably correct algorithms for the multiplication of arbitrary matrices. Our agent, AlphaTensor, is trained to play a single-player game where the objective is finding tensor decompositions within a finite factor space. AlphaTensor discovered algorithms that outperform the state-of-the-art complexity for many matrix sizes. Particularly relevant is the case of 4 × 4 matrices in a finite field, where AlphaTensor’s algorithm improves on Strassen’s two-level algorithm for the first time, to our knowledge, since its discovery 50 years ago. 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 optimizing matrix multiplication for runtime on specific hardware. Our results highlight AlphaTensor’s ability to accelerate the process of algorithmic discovery on a range of problems, and to optimize for different criteria."
Single-player game played by AlphaTensor, where the goal is to find a correct matrix multiplication algorithm. The state of the game is a cubic array of numbers (shown as grey for 0, blue for 1, and green for -1), representing the remaining work to be done.
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