Fast Matrix Multiplication in fp8: Certified Coefficient Optimization and Measured Error
A Strassen-type algorithm has many realizations with the same exact product and multiplication count yet different fp8 error because basis changes reshape coefficient geometry, posing the question of which to run. No current account settles this: classical stability controls worst-case $\ell_1$ growth, not the expected-error magnitude, and the Dumas--Pernet--Sedoglavic optimizer could only be called probably optimal, its global optimality unproved. To settle this, we attach to each realization a coefficient functional $Φ$, a scalar summary of its coefficient geometry, which we minimize over the change-of-basis orbit. This Kempf--Ness problem on a Hadamard manifold lets us certify the glob...
| Authors | Shuxiao Xie, Shuyang Xie, Yuan Cao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 4 August 2026 |
| Last updated at source | 4 August 2026 |
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