{
  "schema_version": 1,
  "id": "evt-2022-alphatensor",
  "slug": "alphatensor-matrix-multiplication-algorithms",
  "title": {
    "en": "AlphaTensor discovers improved matrix multiplication algorithms",
    "zh-CN": "AlphaTensor 发现改进的矩阵乘法算法"
  },
  "dates": {
    "event": "2022-10-05",
    "first_public_claim": "2022-10-05",
    "paper_release": "2022-10-05",
    "artifact_release": null,
    "independently_verified": null,
    "added_to_chronicle": "2026-09-10",
    "last_updated": "2026-09-10"
  },
  "event_types": [
    "discovery",
    "system"
  ],
  "significance": {
    "tier": "H1",
    "rationale": {
      "en": "AlphaTensor provided a prominent example of reinforcement learning discovering exact algorithms that improved long-standing matrix-multiplication records, including a finite-field 4-by-4 result reported as the first improvement over Strassen's two-level construction in that setting.",
      "zh-CN": "AlphaTensor 是强化学习发现精确算法的代表性案例：它改进了长期存在的矩阵乘法记录，其中有限域上的 4×4 结果被论文报告为该设定下首次超过 Strassen 两层构造。"
    }
  },
  "mathematical_novelty": {
    "type": "new_algorithm"
  },
  "interfaces": [
    "symbolic",
    "numeric",
    "hybrid"
  ],
  "claim": {
    "en": "AlphaTensor discovered provably correct matrix multiplication algorithms that improved the best known multiplication counts for multiple matrix sizes, including a 4-by-4 construction over Z2 using 47 scalar multiplications instead of 49 from two-level Strassen.",
    "zh-CN": "AlphaTensor 发现了一批可证明正确的矩阵乘法算法，在多个矩阵尺寸上改进已知最佳乘法次数，其中在 Z2 上的 4×4 构造使用 47 次标量乘法，而两层 Strassen 构造需要 49 次。"
  },
  "summary": {
    "en": "DeepMind represented matrix multiplication as a tensor-decomposition game and trained an AlphaZero-style reinforcement-learning agent to search the enormous space of factorizations. Released artifacts include discovered factorizations, benchmarking code and checks of algorithmic properties.",
    "zh-CN": "DeepMind 将矩阵乘法表示为张量分解游戏，并训练类似 AlphaZero 的强化学习智能体搜索巨大的分解空间。公开产物包括所发现的分解、基准代码以及算法性质检查工具。"
  },
  "why_it_matters": {
    "en": "The work moved AI4Math beyond solving prepared exercises by demonstrating machine search that produced new exact algorithms with mathematical and computational significance.",
    "zh-CN": "该工作超越了求解预设习题的范式，展示了机器搜索能够产生具有数学与计算意义的新精确算法。"
  },
  "ai_role": {
    "level": "ai_primary_human_verified",
    "description": {
      "en": "AlphaTensor searched for tensor decompositions and discovered candidate algorithms; the resulting decompositions admit exact mathematical checking and were analyzed by the research team.",
      "zh-CN": "AlphaTensor 搜索张量分解并发现候选算法；所得分解可以进行精确数学检查，并由研究团队进一步分析。"
    }
  },
  "human_contribution": {
    "description": {
      "en": "Researchers formulated TensorGame, designed the reinforcement-learning system and reward structures, chose target problems, verified outputs and interpreted their algorithmic consequences.",
      "zh-CN": "研究者构造 TensorGame、设计强化学习系统与奖励机制、选择目标问题、验证输出并解释其算法意义。"
    }
  },
  "systems": [
    "alphatensor"
  ],
  "organizations": [
    "deepmind"
  ],
  "people": [
    "alhussein-fawzi",
    "matej-balog",
    "aja-huang",
    "thomas-hubert",
    "pushmeet-kohli"
  ],
  "problems": [
    "matrix-multiplication"
  ],
  "methods": [
    "reinforcement-learning",
    "monte-carlo-tree-search",
    "tensor-decomposition",
    "algorithm-search"
  ],
  "verification": {
    "evidence_level": "E3",
    "status": "paper_released",
    "formal_assurance": "artifact_available",
    "history": [
      {
        "date": "2022-10-05",
        "status": "paper_released",
        "evidence_level": "E2",
        "note": {
          "en": "Nature published the discovery results and their mathematical formulation.",
          "zh-CN": "Nature 发表了相关发现结果及其数学表述。"
        }
      },
      {
        "date": "2022-10-05",
        "status": "paper_released",
        "evidence_level": "E3",
        "note": {
          "en": "DeepMind released discovered algorithms and supporting verification and benchmarking materials.",
          "zh-CN": "DeepMind 公开了所发现的算法以及配套验证与基准材料。"
        }
      }
    ]
  },
  "sources": [
    {
      "id": "nature-alphatensor-2022",
      "tier": "S1",
      "type": "paper",
      "title": "Discovering faster matrix multiplication algorithms with reinforcement learning",
      "url": "https://www.nature.com/articles/s41586-022-05172-4",
      "primary": true,
      "published_date": "2022-10-05",
      "accessed_at": "2026-09-10"
    },
    {
      "id": "github-google-deepmind-alphatensor",
      "tier": "S1",
      "type": "repository",
      "title": "AlphaTensor accompanying repository",
      "url": "https://github.com/google-deepmind/alphatensor",
      "primary": true,
      "published_date": null,
      "accessed_at": "2026-09-10"
    }
  ],
  "artifacts": [
    {
      "id": "alphatensor-results-repository",
      "kind": "code",
      "title": "AlphaTensor algorithms and verification materials",
      "url": "https://github.com/google-deepmind/alphatensor"
    }
  ],
  "relationships": {
    "predecessors": [],
    "successors": [
      "evt-2025-alphaevolve"
    ],
    "related": [
      "evt-2023-funsearch-cap-set"
    ]
  },
  "timeline": {
    "featured": true,
    "significance": "primary"
  },
  "tags": [
    "matrix-multiplication",
    "reinforcement-learning",
    "algorithm-discovery",
    "tensor-decomposition",
    "alphazero"
  ],
  "editorial": {
    "created_at": "2026-09-10",
    "last_reviewed": "2026-09-11",
    "reviewers": [
      "Charlie-Wang-03"
    ]
  },
  "corrections": []
}