---
id: "2022-10-05-alphatensor-matrix-multiplication"
url: "https://postcutoff.com/e/2022-10-05-alphatensor-matrix-multiplication/"
as_of: "2026-11-13T13:49:00+01:00"
date: "2022-10-05"
date_precision: day
category: science
importance: 4
confidence: high
status: [Result confirmed]
verification: Peer-reviewed
sources: 3
editor: human editor
human_review: null
version: "2026-10-04"
---

As of: 2026-11-13 13:49 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2022-10-05-alphatensor-matrix-multiplication/

# AlphaTensor discovers faster matrix multiplication algorithms, beating Strassen's 1969 record for 4×4 mod 2

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

## 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.

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): in its training data
- Claude Opus 5.5 (training cutoff June 2026): in its training data
- Gemini 4 Hydrogen (training cutoff March 2026): in its training data
- Grok 4.7 (training cutoff May 2026): in its training data

## Sources

1. [Discovering faster matrix multiplication algorithms with reinforcement learning (Nature)](https://www.nature.com/articles/s41586-022-05172-4) (nature.com, paper)
2. [GitHub: google-deepmind/alphatensor](https://github.com/google-deepmind/alphatensor) (github.com, code)
3. [Computational Complexity blog on AlphaTensor](https://blog.computationalcomplexity.org/2022/10/alpha-tensor.html) (blog.computationalcomplexity.org, discussion)

## Changes

- 2026-09-29 (filed): Created

## Related

- 2025-05-14: [AlphaEvolve: Gemini-powered agent discovers new algorithms](https://postcutoff.com/e/2025-05-14-alphaevolve/index.md)
- 2023-06-07: [AlphaDev discovers faster small-sort routines, merged into LLVM's C++ standard library](https://postcutoff.com/e/2023-06-07-alphadev-sorting/index.md)