AlphaTensor finds a 47-multiplication 4x4 scheme over GF(2)

AI system

System: AlphaTensor (AlphaZero-derived reinforcement learning for tensor decomposition)
Model: Not assessed
Release: Not assessed
Application developer: DeepMind
Role: Not assessed
Configuration: Not assessed
Inputs and outputs: Not assessed
Autonomy: Not assessed
Workflow: Formulation of algorithm discovery as a tensor-decomposition game. Neural-network-guided search with exact verification of each decomposition. Publication of explicit decompositions that others can check and extend.
Human oversight: Not assessed
Relation to AI: The reinforcement-learning agent found the decompositions, which are explicit and checkable. The independent preprint treats the 96-multiplication 5x5 result as established and improves it, which corroborates the result's existence. The 47-multiplication 4x4 scheme rests on the vendor paper's published decomposition.
AI contribution: The reinforcement-learning agent found the decompositions, which are explicit and checkable. The independent preprint treats the 96-multiplication 5x5 result as established and improves it, which corroborates the result's existence. The 47-multiplication 4x4 scheme rests on the vendor paper's published decomposition.

Outcome identifiers: Not assessed
Benefit: multiplying two 4x4 matrices over the field with two elements in 47 multiplications
Category: Improved Knowledge Discovery
Status: Not assessed
Beneficiary groups: Society.
Beneficiaries: Not assessed
Reach: Not assessed
Distribution and access: Not assessed
Duration: Not assessed
Expected?: Yes
Costs and harms: Not assessed

Studies: Not assessed
Study design: Not assessed
Measurement: Not assessed
Setting and sample: Not assessed
Measures: multiplying two 4x4 matrices over the field with two elements in 47 multiplications
Comparison: Not assessed
Results: multiplying two 4x4 matrices over the field with two elements in 47 multiplications
Additional value from AI: Not assessed
Limitations: Not assessed
Denominators: Not assessed
Materials for replication: Not assessed

Participants: Developer: DeepMind. Operator: DeepMind.
Jurisdictions: Benefit: London, United Kingdom. Developer: United Kingdom. Operator: United Kingdom.
Ownership and control: Not assessed
Dependencies: Not assessed
Cross-border connections: Not assessed
Geopolitical implications: Not assessed

Conditions for replication: Decompositions must be verified exactly over the stated ring or field. Independent reproduction or extension by researchers outside the vendor.
Replication attempts: 1 follow-up entries. Benefit recurred: 1.
Later findings: 8 October 2022. Three days after publication, Kauers and Moosbauer took AlphaTensor's 96-multiplication 5x5 scheme over Z2 as a starting point and improved it to 95, confirming and extending the result.
Availability: Not assessed
Institutional decision: Not assessed
Grounds: Not assessed
Action and result: Not assessed
Success criterion: Not assessed

Assessed benefits: Society.
Depth: Society: 2.
Reasons: Society: Researchers in algebraic complexity gained new explicit decompositions that were improved upon within a week by Kauers and Moosbauer. The gains are field-restricted. Nature reports the 4x4 improvement for matrices “in a finite field” and Kauers and Moosbauer give the 5x5 record of 96 multiplications over Z2.
Observed or intended: Not assessed
Rubric: Not assessed
Assessor and date: Not assessed
Alternative assessments: Not assessed
Fill: Independently reported

Kind: Not assessed
Related entries: Not assessed
Field: Mathematics / algorithmic complexity. Industrial research laboratory.
Purpose: Built to discover matrix multiplication algorithms by searching for low-rank tensor decompositions; the new schemes were that purpose.
Dates: Date basis unassessed: 2022 (precision unassessed). Updated: 21 October 2026.
Stage: Not assessed
Version: SHA-256: 36e53663ce0d…