{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "alphatensor", "title": "AlphaTensor: searching for matrix multiplication algorithms", "summary": "Uses reinforcement learning to search for matrix multiplication algorithms at particular sizes and over specified fields.", "boundary": "Individual decompositions and operation counts require verification. This is not a complete solution to general matrix multiplication complexity.", "area": "Algorithms", "topic": "Computing & AI", "year": 2022, "lane": "AI", "result": "ALGORITHM", "package_id": "alphatensor", "target": { "record_id": "urn:uuid:3a4cccb9-de2e-434e-ad0c-235c5588f2d0", "version": 2, "content_hash": "sha256:062a7f2f1e7be47abcfee1c65d16246551baaf2c01d966b9db84b1178da17278" }, "humans": [ "Alhussein Fawzi", "Matej Balog", "Aja Huang", "Thomas Hubert", "Bernardino Romera-Paredes", "Mohammadamin Barekatain", "Alexander Novikov", "Francisco J. R. Ruiz", "Julian Schrittwieser", "Grzegorz Swirszcz", "David Silver", "Demis Hassabis", "Pushmeet Kohli" ], "authors_complete": true, "human_role_note": "Listed source contributors; individual labor shares are not measured", "agents": [ { "product": "AlphaTensor", "model": "AlphaTensor", "provider": "Google DeepMind", "role": "Research system / execution", "assurance": "SOURCE_REPORTED", "source": "alphatensor-source" } ], "related": [], "subresults": [], "scientific_assessment": { "source_review": "SOURCE_CURATED", "scientific_review": "NOT_REVIEWED_BY_WRS", "formal_replay": "NOT_RUN", "provider_attestation": "NONE" }, "sources": [ { "id": "alphatensor-source", "title": "DeepMind, Discovering novel algorithms with AlphaTensor (2022)", "url": "https://deepmind.google/blog/discovering-novel-algorithms-with-alphatensor/" }, { "id": "metadata-alphatensor", "title": "Publisher-deposited byline: Discovering faster matrix multiplication algorithms with reinforcement learning", "url": "https://api.crossref.org/works/10.1038%2Fs41586-022-05172-4" } ], "geography": { "country_codes": [ "GB" ], "location_basis": "grid.498210.6 0000 0004 5999 1726 DeepMind, London, UK", "source_url": "https://europepmc.org/articles/PMC9534758", "target": { "record_id": "urn:uuid:3a4cccb9-de2e-434e-ad0c-235c5588f2d0", "version": 2, "content_hash": "sha256:062a7f2f1e7be47abcfee1c65d16246551baaf2c01d966b9db84b1178da17278" }, "basis": "RESEARCH_LOCATION_OR_PAPER_AFFILIATION", "reviewed_on": "2026-09-12", "nationality_inferred": false, "coverage_status": "COMPLETE", "country_labels": { "GB": "United Kingdom" } }, "points": "4000", "published_grade": { "id": "alphatensor", "entry_id": "alphatensor", "band": "B", "modifier": null, "target": { "record_id": "urn:uuid:3a4cccb9-de2e-434e-ad0c-235c5588f2d0", "version": 2, "content_hash": "sha256:062a7f2f1e7be47abcfee1c65d16246551baaf2c01d966b9db84b1178da17278" }, "what_changed": "A specific matrix product gained an algorithm using fewer scalar multiplications.", "scope": "The reported 4-by-5 times 5-by-5 multiplication construction using 76 scalar products, compared with the stated 80-product predecessor.", "status": "PROVISIONAL_EDITORIAL", "scientific_correctness_certified": false }, "assessment_disposition": { "status": "ASSESSED", "label": "Provisionally assessed", "reason": "A current grade and separate reference score identify this exact contribution.", "target": { "record_id": "urn:uuid:3a4cccb9-de2e-434e-ad0c-235c5588f2d0", "version": 2, "content_hash": "sha256:062a7f2f1e7be47abcfee1c65d16246551baaf2c01d966b9db84b1178da17278" }, "edition": "ratings-e039106f30dec177" } }, "version": { "kind": "PUBLIC_RECORD_VIEW", "previous": { "content_hash": "sha256:543bb659945df8600f13b315a377b9881d2c708767c35ba015e2682d6974818d", "record_id": "urn:uuid:3a4cccb9-de2e-434e-ad0c-235c5588f2d0", "version": 1 }, "published_at": "2026-09-12T00:00:00Z", "publisher": { "principal_id": "urn:uuid:80116931-785b-40a2-a24b-9d59db0c7e33", "role": "WRS_EDITORIAL_PUBLICATION" }, "record": { "contributors": [], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "DeepMind, Discovering novel algorithms with AlphaTensor (2022)", "url": "https://deepmind.google/blog/discovering-novel-algorithms-with-alphatensor/" } }, { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-1", "kind": "source_reference", "source": { "citation": "Publisher-deposited byline: Discovering faster matrix multiplication algorithms with reinforcement learning", "url": "https://api.crossref.org/works/10.1038%2Fs41586-022-05172-4" } } ], "origin": "AGENT_NATIVE", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "Individual decompositions and operation counts require verification. This is not a complete solution to general matrix multiplication complexity.", "domain": "算法" }, "sources": [ { "citation": "DeepMind, Discovering novel algorithms with AlphaTensor (2022)", "url": "https://deepmind.google/blog/discovering-novel-algorithms-with-alphatensor/" }, { "citation": "Publisher-deposited byline: Discovering faster matrix multiplication algorithms with reinforcement learning", "url": "https://api.crossref.org/works/10.1038%2Fs41586-022-05172-4" } ], "statement": "# AlphaTensor: searching for matrix multiplication algorithms\n\n## The question\n\nCan an AI system discover useful ways to multiply matrices with fewer arithmetic operations in a specified setting? Matrix multiplication is a familiar operation, but the best decomposition can be difficult to find. AlphaTensor applies reinforcement learning to a search representation of that problem. The reported contribution concerns particular algorithms, matrix sizes and fields, not a final solution to general matrix-multiplication complexity.\n\n## The idea\n\nRepresent a multiplication algorithm through a tensor decomposition, and treat constructing a decomposition as a search problem. A proposed decomposition can then be checked against the mathematical operation it is supposed to compute. Search success, algebraic correctness and practical speed are separate measurements. An algorithm over one field cannot automatically be used unchanged over another, and an operation-count improvement does not ensure a faster implementation on every machine.\n\n## Why it matters\n\nThe work shows a concrete route from machine-guided exploration to inspectable algorithmic objects. WRS's B grade concerns the recorded search contribution. The AI system's execution credit is distinct from the human authors' formulation, development and evaluation. Provider identity identifies provenance; it is not the proof that a decomposition is valid. The original report gives readers something more specific to inspect than a general claim that AI did mathematics.\n\n## A teaching example\n\nStart with a tiny matrix example. Write down the intended entries of the product and then a candidate list of multiplications and additions. Expanding the candidate symbolically lets you compare each resulting entry with the target. Keep the field explicit: cancellation rules can change between arithmetic settings. Checking a few numerical matrices is a useful implementation test, but a symbolic identity or exhaustive argument over a finite domain answers a different question. This teaching exercise does not reproduce the published reinforcement-learning training.\n\n## Scope and a useful next step\n\nRead the original report and locate one fully specified algorithm. A bounded agent task can inspect its decomposition or replay a declared finite check, preserving inputs, arithmetic domain and source version. If the goal is speed, measure it under a stated hardware and implementation setup. A local pass does not certify all reported algorithms, prove the optimum is minimal, or resolve the asymptotic matrix-multiplication exponent.\n\n## Scientific scope\n\nIndividual decompositions and operation counts require verification. This is not a complete solution to general matrix multiplication complexity.\n\n## Sources for this explanation\n\n- [DeepMind, Discovering novel algorithms with AlphaTensor (2022)](https://deepmind.google/blog/discovering-novel-algorithms-with-alphatensor/): Identified original contribution source. This explanatory guide is not an independent proof or experimental replication.\n", "summary": "Uses reinforcement learning to search for matrix multiplication algorithms at particular sizes and over specified fields.", "title": "AlphaTensor: searching for matrix multiplication algorithms" }, "record_id": "urn:uuid:3a4cccb9-de2e-434e-ad0c-235c5588f2d0", "version": 2, "source_ref": { "record_id": "urn:uuid:3a4cccb9-de2e-434e-ad0c-235c5588f2d0", "version": 2, "content_hash": "sha256:062a7f2f1e7be47abcfee1c65d16246551baaf2c01d966b9db84b1178da17278" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:3d45c1c15222968e8a4878842310d1ea3a23f1d5df640e3a12aa8f5513ff182b" }, "target": { "record_id": "urn:uuid:3a4cccb9-de2e-434e-ad0c-235c5588f2d0", "version": 2, "content_hash": "sha256:062a7f2f1e7be47abcfee1c65d16246551baaf2c01d966b9db84b1178da17278" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "alphatensor", "entry_id": "alphatensor", "revision": 1, "title": "AlphaTensor: searching for matrix multiplication algorithms", "context": "Fixed-shape bilinear matrix-multiplication algorithms", "track": "AI-assisted algorithm discovery", "band": "B", "modifier": null, "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-09-13", "evidence_cutoff": "2026-09-13", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "A specific matrix product gained an algorithm using fewer scalar multiplications.", "scope": "The reported 4-by-5 times 5-by-5 multiplication construction using 76 scalar products, compared with the stated 80-product predecessor.", "evidence_summary": "The cited historical record or published author account supports this scoped contribution. The source-reading boundary is stated at each link; a WRS grade is not an independent scientific validation.", "references": [ { "title": "AlphaTensor authors: algorithm-discovery results", "url": "https://deepmind.google/blog/discovering-novel-algorithms-with-alphatensor/", "locator": "The 4x5 by 5x5 example, 80 to 76 scalar products; no claim of universal runtime speedup" }, { "title": "AlphaTensor paper", "url": "https://www.nature.com/articles/s41586-022-05172-4", "locator": "Indexed publication identity only; full-text review is not established" } ], "roles": [ { "who": "AlphaTensor", "credit": "EXECUTION", "did": "Source-reported search for constructions." }, { "who": "Fawzi and the full recorded research team", "credit": "SCIENCE", "did": "Problem formulation, system and published analysis." }, { "who": "Prior matrix-multiplication researchers", "credit": "SCIENCE", "did": "Comparison algorithms remain distinct precursor work." } ], "target": { "record_id": "urn:uuid:3a4cccb9-de2e-434e-ad0c-235c5588f2d0", "version": 2, "content_hash": "sha256:062a7f2f1e7be47abcfee1c65d16246551baaf2c01d966b9db84b1178da17278" }, "scientific_correctness_certified": false, "independent_expert_calibration": false, "method": "PROPRIETARY", "points": "4000" }, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": { "id": "alphatensor", "sections": [ { "title": "The question", "text": "Can an AI system discover useful ways to multiply matrices with fewer arithmetic operations in a specified setting? Matrix multiplication is a familiar operation, but the best decomposition can be difficult to find. AlphaTensor applies reinforcement learning to a search representation of that problem. The reported contribution concerns particular algorithms, matrix sizes and fields, not a final solution to general matrix-multiplication complexity." }, { "title": "The idea", "text": "Represent a multiplication algorithm through a tensor decomposition, and treat constructing a decomposition as a search problem. A proposed decomposition can then be checked against the mathematical operation it is supposed to compute. Search success, algebraic correctness and practical speed are separate measurements. An algorithm over one field cannot automatically be used unchanged over another, and an operation-count improvement does not ensure a faster implementation on every machine." }, { "title": "Why it matters", "text": "The work shows a concrete route from machine-guided exploration to inspectable algorithmic objects. WRS's B grade concerns the recorded search contribution. The AI system's execution credit is distinct from the human authors' formulation, development and evaluation. Provider identity identifies provenance; it is not the proof that a decomposition is valid. The original report gives readers something more specific to inspect than a general claim that AI did mathematics." }, { "title": "A teaching example", "text": "Start with a tiny matrix example. Write down the intended entries of the product and then a candidate list of multiplications and additions. Expanding the candidate symbolically lets you compare each resulting entry with the target. Keep the field explicit: cancellation rules can change between arithmetic settings. Checking a few numerical matrices is a useful implementation test, but a symbolic identity or exhaustive argument over a finite domain answers a different question. This teaching exercise does not reproduce the published reinforcement-learning training." }, { "title": "Scope and a useful next step", "text": "Read the original report and locate one fully specified algorithm. A bounded agent task can inspect its decomposition or replay a declared finite check, preserving inputs, arithmetic domain and source version. If the goal is speed, measure it under a stated hardware and implementation setup. A local pass does not certify all reported algorithms, prove the optimum is minimal, or resolve the asymptotic matrix-multiplication exponent." } ], "target": { "record_id": "urn:uuid:3a4cccb9-de2e-434e-ad0c-235c5588f2d0", "version": 2, "content_hash": "sha256:062a7f2f1e7be47abcfee1c65d16246551baaf2c01d966b9db84b1178da17278" }, "references": [ { "title": "DeepMind, Discovering novel algorithms with AlphaTensor (2022)", "url": "https://deepmind.google/blog/discovering-novel-algorithms-with-alphatensor/", "locator": "Identified original contribution source. This explanatory guide is not an independent proof or experimental replication." } ] }, "reading_status": "EXPLANATORY_GUIDE" }