Neural Learning of Fast Matrix Multiplication Algorithms: A StrassenNet Approach

• URL: http://arxiv.org/abs/2602.21797v1
• Date: Wed, 25 Feb 2026 11:22:31 GMT
• Title: Neural Learning of Fast Matrix Multiplication Algorithms: A StrassenNet Approach
• Authors: Paolo Andreini, Alessandra Bernardi, Monica Bianchini, Barbara Toniella Corradini, Sara Marziali, Giacomo Nunziati, Franco Scarselli,
• Abstract summary: Fast matrix multiplication can be described as searching for low-rank decompositions of the matrix--multiplication tensor.<n>We design a neural architecture, textscStrassenNet, which reproduces the Strassen algorithm for $2times 2$ multiplication.<n>We then train the same architecture on $3times 3$ multiplication with rank $rin19,dots,23$.
• Score: 36.2561379432247
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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