{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2022-10-05-alphatensor-matrix-multiplication/","md":"https://postcutoff.com/e/2022-10-05-alphatensor-matrix-multiplication/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2022-10-05-alphatensor-matrix-multiplication","date":"2022-10-05","date_precision":"day","short_title":"AlphaTensor discovers faster matrix multiplication algorithms, beating Strassen's 1969 record for 4×4 mod 2","deck":null,"takeaway":"DeepMind's AlphaTensor (Nature, Oct 2022) framed matrix multiplication as a tensor-decomposition game.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":[{"n":1,"title":"Discovering faster matrix multiplication algorithms with reinforcement learning (Nature)","url":"https://www.nature.com/articles/s41586-022-05172-4","type":"paper","group":"primary","domain":"nature.com"},{"n":2,"title":"GitHub: google-deepmind/alphatensor","url":"https://github.com/google-deepmind/alphatensor","type":"code","group":"primary","domain":"github.com"},{"n":3,"title":"Computational Complexity blog on AlphaTensor","url":"https://blog.computationalcomplexity.org/2022/10/alpha-tensor.html","type":"discussion","group":"reactions","domain":"blog.computationalcomplexity.org"}],"official":2,"filed":"2026-09-29","updated":"2026-09-29","orgs":["DeepMind"],"title":"AlphaTensor discovers faster matrix multiplication algorithms, beating Strassen's 1969 record for 4×4 mod 2","summary":"DeepMind's AlphaTensor (Nature, Oct 2022) framed matrix multiplication as a tensor-decomposition game. It found a 4×4 algorithm over GF(2) with 47 multiplications (Strassen-based: 49) and improved 5×5 to 96. Human researchers cut 5×5 further to 95 within days.","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"],"key_numbers":[],"tags":["math","algorithms","matrix-multiplication","reinforcement-learning"],"science":{"field":"computer-science","subfield":"algebraic complexity","problem":"Minimum number of multiplications for small matrix products (tensor rank)","result":"New lower-rank decompositions: 4×4 over GF(2) with 47 multiplications; improvements for several other sizes.","open_since":"1969","ai_system":["AlphaTensor"],"human_role":"Autonomous search within a human-designed RL game","verification":{"key":"peer-review","label":"Peer-reviewed","text":"Peer-reviewed in Nature; algorithms checkable by direct computation"},"status":"confirmed","shock":"First improvement in over 50 years to a Strassen-era record for a small matrix size."},"body_md":"## What happened\n\nAlphaTensor, an AlphaZero descendant, searched the space of tensor decompositions and found matrix multiplication schemes using fewer scalar multiplications than any known for several sizes.\n\n## Why it matters\n\nIt 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.","disputed":[],"related":[{"id":"2025-05-14-alphaevolve","url":"https://postcutoff.com/e/2025-05-14-alphaevolve/","date":"2025-05-14","date_precision":"day","short_title":"AlphaEvolve: Gemini-powered agent discovers new algorithms","deck":null,"takeaway":"A concrete example of LLM-based systems making novel discoveries and improving the infrastructure that trains them — an early form of recursive improvement.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":4,"official":4,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Google DeepMind"]},{"id":"2023-06-07-alphadev-sorting","url":"https://postcutoff.com/e/2023-06-07-alphadev-sorting/","date":"2023-06-07","date_precision":"day","short_title":"AlphaDev discovers faster small-sort routines, merged into LLVM's C++ standard library","deck":null,"takeaway":"It was AI-discovered code shipping in core infrastructure, though experts argued about how novel the discovery really was.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"disputed","labels":["Disputed"]},"sources":3,"official":2,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Google DeepMind"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-09-29","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-29","run":null,"sources_read":null,"updated":"2026-09-29","human_review":null,"version":{"date":"2026-10-04"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":null,"in_training_data":true},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":null,"in_training_data":true},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":null,"in_training_data":true},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":null,"in_training_data":true}],"short_url":"https://postcutoff.com/s/alphatensor-discovers-faster"}