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arxiv: 2506.13131 · v1 · submitted 2025-06-16 · 💻 cs.AI · cs.LG· cs.NE

Recognition: 2 theorem links

· Lean Theorem

AlphaEvolve: A coding agent for scientific and algorithmic discovery

Alexander Novikov , Ng\^an V\~u , Marvin Eisenberger , Emilien Dupont , Po-Sen Huang , Adam Zsolt Wagner , Sergey Shirobokov , Borislav Kozlovskii
show 10 more authors
Francisco J. R. Ruiz Abbas Mehrabian M. Pawan Kumar Abigail See Swarat Chaudhuri George Holland Alex Davies Sebastian Nowozin Pushmeet Kohli Matej Balog
Authors on Pith no claims yet

Pith reviewed 2026-05-10 21:21 UTC · model grok-4.3

classification 💻 cs.AI cs.LGcs.NE
keywords evolutionary algorithmslarge language modelsmatrix multiplicationalgorithm discoverycode optimizationautomated improvement
0
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The pith

An evolutionary coding agent discovered a new algorithm for multiplying 4x4 complex matrices using 48 multiplications.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents AlphaEvolve as a system that directs large language models to edit code in repeated cycles, using evaluator feedback to keep only changes that are both correct and faster. This process is applied to real infrastructure tasks and to longstanding mathematical questions. One outcome is an algorithm for 4x4 complex matrix multiplication that needs only 48 scalar multiplications. The authors argue this is the first such improvement since Strassen's 1969 method, which required 49. The work claims the same loop can be pointed at many other algorithmic bottlenecks.

Core claim

AlphaEvolve runs an evolutionary loop in which language models propose direct edits to source code; each candidate is tested by one or more evaluator functions that return signals about correctness and runtime cost. When applied to the matrix-multiplication problem, the system located a procedure that multiplies two 4-by-4 complex matrices with 48 scalar multiplications, a reduction from the 49 required by Strassen's algorithm.

What carries the argument

The evolutionary pipeline in which language models generate code edits that are retained only if evaluator functions confirm both functional correctness and measurable performance gains.

If this is right

  • Scheduling algorithms for data centers can be made more efficient by the same code-evolution process.
  • Hardware-accelerator circuit designs can be simplified while preserving function.
  • Training runs of the underlying language model itself can be accelerated through discovered code changes.
  • Other open problems in mathematics and computer science can yield provably better algorithms when the same loop is applied.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If reliable evaluators can be written for proof verification or physical simulation, the approach could be directed at open conjectures or model discovery.
  • Scaling the number of parallel evolutionary runs or pairing the system with stronger base models would likely increase the rate of new findings.
  • The method offers a route for domain experts to supply only an evaluator and a starting code skeleton while the agent handles the search.

Load-bearing premise

The evaluator functions reliably detect both correctness and genuine performance improvements without overlooking subtle errors or accepting superficial code changes.

What would settle it

An independent check that either shows the reported 4-by-4 complex matrix algorithm is incorrect or that it requires more than 48 scalar multiplications.

read the original abstract

In this white paper, we present AlphaEvolve, an evolutionary coding agent that substantially enhances capabilities of state-of-the-art LLMs on highly challenging tasks such as tackling open scientific problems or optimizing critical pieces of computational infrastructure. AlphaEvolve orchestrates an autonomous pipeline of LLMs, whose task is to improve an algorithm by making direct changes to the code. Using an evolutionary approach, continuously receiving feedback from one or more evaluators, AlphaEvolve iteratively improves the algorithm, potentially leading to new scientific and practical discoveries. We demonstrate the broad applicability of this approach by applying it to a number of important computational problems. When applied to optimizing critical components of large-scale computational stacks at Google, AlphaEvolve developed a more efficient scheduling algorithm for data centers, found a functionally equivalent simplification in the circuit design of hardware accelerators, and accelerated the training of the LLM underpinning AlphaEvolve itself. Furthermore, AlphaEvolve discovered novel, provably correct algorithms that surpass state-of-the-art solutions on a spectrum of problems in mathematics and computer science, significantly expanding the scope of prior automated discovery methods (Romera-Paredes et al., 2023). Notably, AlphaEvolve developed a search algorithm that found a procedure to multiply two $4 \times 4$ complex-valued matrices using $48$ scalar multiplications; offering the first improvement, after 56 years, over Strassen's algorithm in this setting. We believe AlphaEvolve and coding agents like it can have a significant impact in improving solutions of problems across many areas of science and computation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper introduces AlphaEvolve, an evolutionary coding agent that orchestrates LLMs to iteratively modify code for algorithm improvement under evaluator feedback. It reports applications to Google-scale infrastructure tasks (data-center scheduling, hardware-accelerator circuit simplification, and acceleration of the underlying LLM training) as well as to open mathematical and algorithmic problems, with the headline result being a search-derived procedure for multiplying two 4×4 complex matrices using only 48 scalar multiplications—the first improvement over Strassen’s 49-multiplication construction in 56 years.

Significance. If the reported infrastructure wins and the new matrix-multiplication algorithm are independently verified, the work would demonstrate that LLM-orchestrated evolutionary search can produce both practical computational gains and novel, non-obvious algorithmic results, thereby extending the scope of automated discovery methods beyond the symbolic and theorem-proving settings explored in prior work.

major comments (2)
  1. [Abstract] Abstract: the central claim that AlphaEvolve produced a 'provably correct' 4×4 complex matrix multiplication algorithm using 48 scalar multiplications is presented without any description of the evaluator’s test suite, symbolic verification method, input coverage over the complex field, or the discovered code itself. Because the evaluator is the sole source of both the correctness label and the performance delta, this omission is load-bearing for the discovery claim.
  2. [Abstract] Abstract: the statements that AlphaEvolve 'developed a more efficient scheduling algorithm,' 'found a functionally equivalent simplification in the circuit design,' and 'accelerated the training of the LLM' are given without quantitative metrics, baselines, statistical significance, or error bars, preventing assessment of whether these constitute genuine, reproducible improvements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on the abstract. We have revised the abstract to include additional details on verification methods and quantitative metrics while preserving its concise nature. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that AlphaEvolve produced a 'provably correct' 4×4 complex matrix multiplication algorithm using 48 scalar multiplications is presented without any description of the evaluator’s test suite, symbolic verification method, input coverage over the complex field, or the discovered code itself. Because the evaluator is the sole source of both the correctness label and the performance delta, this omission is load-bearing for the discovery claim.

    Authors: We agree that the abstract would benefit from more context on verification. The full manuscript describes the evaluator in the section on mathematical discovery tasks, which combines symbolic algebraic verification (using exact equality checks via computer algebra) with dense random sampling over the complex field to confirm correctness for arbitrary inputs. The discovered procedure is presented explicitly in the results. We have revised the abstract to note that the 48-multiplication algorithm was obtained and verified through this symbolic and numerical process, with pointers to the full description. revision: yes

  2. Referee: [Abstract] Abstract: the statements that AlphaEvolve 'developed a more efficient scheduling algorithm,' 'found a functionally equivalent simplification in the circuit design,' and 'accelerated the training of the LLM' are given without quantitative metrics, baselines, statistical significance, or error bars, preventing assessment of whether these constitute genuine, reproducible improvements.

    Authors: We acknowledge that quantitative support strengthens the claims. The manuscript body reports the specific metrics, baselines, and statistical details (including multiple runs and significance tests) for each infrastructure application. We have revised the abstract to include concise summaries of these performance deltas and verification approaches. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical search results independent of inputs

full rationale

The paper presents AlphaEvolve as an evolutionary coding agent that applies LLMs to modify code and uses separate evaluators to score correctness and performance. The headline discovery—a 4×4 complex matrix multiplication algorithm using 48 scalar multiplications—is reported as an output of this search process rather than any algebraic derivation, fitted parameter, or self-referential definition. No equations, uniqueness theorems, or ansatzes are introduced that reduce the claimed result to the method's own inputs by construction. Prior citations (e.g., Romera-Paredes et al. 2023) supply background on automated discovery but do not carry the load of the new empirical finding, which rests on external verification of the discovered code. The derivation chain is therefore self-contained and non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on the assumption that LLMs can generate useful code edits and that evaluators can be trusted to guide evolution toward correct solutions; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption LLMs can produce syntactically valid and semantically useful code modifications when prompted with performance feedback.
    Invoked implicitly by the evolutionary pipeline description.
  • domain assumption Evaluator programs provide accurate and complete signals of correctness and performance.
    Required for the evolutionary selection step to converge on improved algorithms.

pith-pipeline@v0.9.0 · 5658 in / 1365 out tokens · 44442 ms · 2026-05-10T21:21:46.086365+00:00 · methodology

discussion (0)

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