How AI Discovered a Faster Matrix Multiplication Algorithm
Quanta Magazine・9 minutes read
Matrix multiplication is a crucial operation in various fields, with Strassen's algorithm reducing steps for two by two matrices and AI algorithms like AlphaTensor surpassing it for specific matrix sizes, highlighting the potential of collaboration between AI and humans.
Insights
- Strassen's algorithm revolutionized matrix multiplication by reducing steps for two by two matrices, inspiring further advancements in computational efficiency.
- The collaboration between AI technology, exemplified by AlphaTensor, and mathematicians showcases the potential for groundbreaking discoveries that enhance human capabilities, emphasizing a symbiotic relationship rather than one of replacement.
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Recent questions
What is matrix multiplication?
Matrix multiplication is a fundamental mathematical operation used in various fields like computer graphics and physics. It involves multiplying two matrices to produce a new matrix by combining the rows of the first matrix with the columns of the second matrix.
Who developed the algorithm to reduce matrix multiplication steps?
Volker Strassen developed an algorithm in 1969 that reduced the multiplication steps for two by two matrices from eight to seven. This algorithm breaks down large matrices into smaller ones, resulting in significant computational savings.
How did DeepMind improve matrix multiplication?
DeepMind, a Google AI research lab, developed a new algorithm that outperformed Strassen's for multiplying four by four matrices with only zero or one elements. This algorithm, called AlphaTensor, uses reinforcement learning to decompose 3D tensors efficiently for matrix multiplication.
What did AlphaTensor discover about Strassen's algorithm?
AlphaTensor, based on DeepMind's AlphaZero, rediscovered Strassen's algorithm within minutes and then surpassed it by finding faster algorithms for specific matrix sizes. This collaboration between AI technology and mathematicians can lead to groundbreaking discoveries in enhancing human capabilities.
How can AI technology enhance human capabilities in mathematics?
Collaboration between AI technology like AlphaTensor and mathematicians can lead to groundbreaking discoveries, enhancing human capabilities rather than replacing them. By leveraging AI algorithms to optimize mathematical operations like matrix multiplication, researchers can achieve faster and more efficient solutions, pushing the boundaries of what is possible in the field of mathematics.
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Summary
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AI and Math: Advancements in Matrix Multiplication
- Matrix multiplication is a fundamental mathematical operation used in various fields like computer graphics and physics.
- Traditional matrix multiplication methods involve a standard algorithm that requires N-cubed steps for N by N matrices.
- Volker Strassen developed an algorithm in 1969 that reduced the multiplication steps for two by two matrices from eight to seven.
- Strassen's algorithm breaks down large matrices into smaller ones, resulting in significant computational savings.
- DeepMind, a Google AI research lab, developed a new algorithm that outperformed Strassen's for multiplying four by four matrices with only zero or one elements.
- AlphaTensor, based on DeepMind's AlphaZero, uses reinforcement learning to decompose 3D tensors efficiently for matrix multiplication.
- AlphaTensor rediscovered Strassen's algorithm within minutes and then surpassed it by finding faster algorithms for specific matrix sizes.
- Collaboration between AI technology like AlphaTensor and mathematicians can lead to groundbreaking discoveries, enhancing human capabilities rather than replacing them.
