“Recently, OpenAI showed that matrix multiplication algorithms with exponent near 2.25…”

Recently, OpenAI showed that matrix multiplication algorithms with exponent near 2.25 exist, but not what they actually are. We then shared an AI-written paper that builds them explicitly. That first version was really bad: even at exponent 2.67, it needed matrices with about 10^(2.3×10^11) rows.

So we pushed the AI agents further, and they improved it a lot. At the same exponent, the size dropped to about 10^4,650 rows. That’s a huge improvement, but the observable universe has only about 10^80 atoms, so even at one number per atom it couldn’t hold a single row of such a matrix.

For anyone wondering what this new exponent of 2.25 means: so far, it’s a theoretical result only. The algorithms constructed so far are “galactic,” and making such algorithms practical would require another major breakthrough. Still, there’s real new interesting math here: a step-by-step version of OpenAI’s construction that shrinks the sizes dramatically, and proofs of how far these specific constructions can and can’t go.

New paper produced by AI: https://github.com/SECQUOIA/finite-extraction-matrix-multiplication/blob/main/shifted-chains.pdf