AlphaTensor discovers faster matrix multiplication algorithms, beating Strassen’s 1969 record for 4×4 mod 2
Result confirmed
Importance: major (4 of 5)The takeaway
DeepMind’s AlphaTensor (Nature, Oct 2022) framed matrix multiplication as a tensor-decomposition game.
Status
- Claim
Result confirmed
- Our reporting
- High confidence
- Verification
- Peer-reviewed
- Importance
- Major (4 of 5)
- Last verified
- 29 September 2026
Your AI and this story
- GPT-6 AstraIn its training data
- Claude Opus 5.5In its training data
- Gemini 4 HydrogenIn its training data
- Grok 4.7In its training data
It happened before the cutoffs of all four assistants, so it can be in their training data.
Key facts
- 4×4 matrices in modular (GF(2)) arithmetic: 47 multiplications vs 49 from Strassen’s 1969 method
- 5×5×5: 96 multiplications (from 98); Kauers & Moosbauer improved to 95 days later with a flip-graph method
- Found 14,236 non-equivalent 4×4 algorithms; also hardware-tuned algorithms faster on GPUs/TPUs
What happened
AlphaTensor, an AlphaZero descendant, searched the space of tensor decompositions and found matrix multiplication schemes using fewer scalar multiplications than any known for several sizes.
Why it matters
It was the first AI-found improvement to a famous algorithmic record. It prompted rapid human counter-improvements and led to AlphaEvolve’s 48-multiplication complex 4×4 result in 2025.
Sources
3 sources from 3 sites. Numbers match the chips in the text.
3 sources: 2 primary, 1 reaction
Primary
- Discovering faster matrix multiplication algorithms with reinforcement learning (Nature)nature.com, paper
- GitHub: google-deepmind/alphatensorgithub.com, code
Reactions
- Computational Complexity blog on AlphaTensorblog.computationalcomplexity.org, discussion
Changes
- Filed