Neural Learning of Fast Matrix Multiplication Algorithms: A StrassenNet Approach
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915816033746944 |
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| author | Andreini, Paolo Bernardi, Alessandra Bianchini, Monica Corradini, Barbara Toniella Marziali, Sara Nunziati, Giacomo Scarselli, Franco |
| author_facet | Andreini, Paolo Bernardi, Alessandra Bianchini, Monica Corradini, Barbara Toniella Marziali, Sara Nunziati, Giacomo Scarselli, Franco |
| contents | Fast matrix multiplication can be described as searching for low-rank decompositions of the matrix--multiplication tensor. We design a neural architecture, \textsc{StrassenNet}, which reproduces the Strassen algorithm for $2\times 2$ multiplication. Across many independent runs the network always converges to a rank-$7$ tensor, thus numerically recovering Strassen's optimal algorithm. We then train the same architecture on $3\times 3$ multiplication with rank $r\in\{19,\dots,23\}$. Our experiments reveal a clear numerical threshold: models with $r=23$ attain significantly lower validation error than those with $r\le 22$, suggesting that $r=23$ could actually be the smallest effective rank of the matrix multiplication tensor $3\times 3$.
We also sketch an extension of the method to border-rank decompositions via an $\varepsilon$--parametrisation and report preliminary results consistent with the known bounds for the border rank of the $3\times 3$ matrix--multiplication tensor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21797 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neural Learning of Fast Matrix Multiplication Algorithms: A StrassenNet Approach Andreini, Paolo Bernardi, Alessandra Bianchini, Monica Corradini, Barbara Toniella Marziali, Sara Nunziati, Giacomo Scarselli, Franco Algebraic Geometry Machine Learning 15A69, 68Q17, 14N07 Fast matrix multiplication can be described as searching for low-rank decompositions of the matrix--multiplication tensor. We design a neural architecture, \textsc{StrassenNet}, which reproduces the Strassen algorithm for $2\times 2$ multiplication. Across many independent runs the network always converges to a rank-$7$ tensor, thus numerically recovering Strassen's optimal algorithm. We then train the same architecture on $3\times 3$ multiplication with rank $r\in\{19,\dots,23\}$. Our experiments reveal a clear numerical threshold: models with $r=23$ attain significantly lower validation error than those with $r\le 22$, suggesting that $r=23$ could actually be the smallest effective rank of the matrix multiplication tensor $3\times 3$. We also sketch an extension of the method to border-rank decompositions via an $\varepsilon$--parametrisation and report preliminary results consistent with the known bounds for the border rank of the $3\times 3$ matrix--multiplication tensor. |
| title | Neural Learning of Fast Matrix Multiplication Algorithms: A StrassenNet Approach |
| topic | Algebraic Geometry Machine Learning 15A69, 68Q17, 14N07 |
| url | https://arxiv.org/abs/2602.21797 |