Exponent of matrix multiplication
The exponent : the smallest real number such that two matrices can be multiplied in operations for every .
- steps
- 16
- by AI
- 1
- since
- 1969
The line is the frontier over time, falling as the bound comes down: lower is better here. Filled dots are steps that moved it; muted dots are results that did not. Orange dots are catalog entries, results with AI in the loop. Hollow dots are candidates under review and never move the line.Grey dots along the top edge are results from before the quantity had a number, placed at the worst end because they have no value on this axis. Dots that would overlap are nudged sideways a few pixels. Hover a dot for its value and attribution.
About this frontier
Trivially , and the conjecture is . Every step since Strassen in 1969 has been an upper bound, and since Coppersmith and Winograd in 1990 every step has come from analysing higher powers of one tensor with the laser method. The record moves in the fourth decimal place and each move is a paper.
Every step, newest first
| Date | Value | Who | Model | Status | Source |
|---|---|---|---|---|---|
| 17 Aug 2026 | best | AlphaEvolve with Dupont, Eisenberger, Kozlovskii, Mehrabian, Ruiz, See, Zhou, Alman, Vassilevska Williams and Balog | AlphaEvolve | AI step unreviewed | entry |
| 2024 | Alman, Duan, Vassilevska Williams, Xu, Xu and Zhou | – | historical | source ↗ | |
| 2024 | Vassilevska Williams, Xu, Xu and Zhou | – | historical | source ↗ | |
| 2022 | Duan, Wu and Zhou | – | historical | source ↗ | |
| 2020 | Alman and Vassilevska Williams | – | historical | source ↗ | |
| 2014 | Le Gall | – | historical | source ↗ | |
| 2012 | Vassilevska Williams | – | historical | source ↗ | |
| 2010 | Stothers | – | historical | source ↗ | |
| 1990 | Stood for twenty years. | Coppersmith and Winograd | – | historical | source ↗ |
| 1986 | Strassen | – | historical | source ↗ | |
| 1981 | Coppersmith and Winograd | – | historical | source ↗ | |
| 1981 | Romani | – | historical | source ↗ | |
| 1981 | Schönhage | – | historical | source ↗ | |
| 1979 | Bini, Capovani, Lotti and Romani | – | historical | source ↗ | |
| 1978 | Pan | – | historical | source ↗ | |
| 1969 | Strassen | – | historical | source ↗ |
Historical rows are the timeline table in the Wikipedia article on the computational complexity of matrix multiplication, which cites each paper; years are publication years as given there. Where two bounds share a year (1981) the table's order is kept.
Changelog1 change
- Curatoradded this entry