[Paper Review] AlphaEvolve: A coding agent for scientific and algorithmic discovery

Alexander Novikov, Nhat Vu+16 more|ArXiv.org|Jun 16, 2025

Scientific Computing and Data Management5 citations

TL;DR

AlphaEvolve is an evolutionary coding agent that uses a pipeline of LLMs to generate, critique, and evolve code, with automatic evaluation, to discover faster algorithms and new mathematical constructions across science and Google's infrastructure.

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 $4 imes 4$ 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.

Motivation & Objective

• Motivate the need for autonomous, code-based discovery to tackle open scientific and practical problems.
• Present an architecture that combines evolutionary search, LLM-driven code modification, and automated evaluation.
• Demonstrate capabilities across matrix multiplication, mathematical constructions, and Google-scale infrastructure optimization.

Proposed method

• An autonomous pipeline of LLMs generates, critiques, and mutates code to improve a target algorithm.
• Evaluation is automated via a user-provided function h that scores candidate solutions.
• Prompts aggregate past solutions from a program database and instruct LLMs to propose diffs in a diff format.
• A distributed, asynchronous pipeline prioritizes throughput and uses an evolutionary database to balance exploration and exploitation.
• Multiple metrics can be optimized simultaneously to guide evolution.
• The system supports optional evaluation cascades and LLM-generated feedback to refine selection.

Experimental results

Research questions

• RQ1 Can AlphaEvolve discover faster matrix multiplication algorithms via evolution of tensor decompositions?
• RQ2 To what extent can AlphaEvolve find new or improved mathematical constructions across analysis, combinatorics, geometry, and number theory?
• RQ3 Can AlphaEvolve meaningfully improve real-world engineering components in large-scale computing stacks (e.g., data-center scheduling, hardware accelerators, LLM training pipelines)?
• RQ4 How does evolving entire codebases compare to evolving single functions in terms of discovery breadth and solution quality?

Key findings

• AlphaEvolve matched or surpassed the best known tensor decomposition bounds for many matrix multiplication targets, including a 4x4 complex-valued case with 48 multiplications.
• AlphaEvolve rediscovered best-known constructions on about 75% of over 50 mathematical problems and surpassed SOTA on about 20%, across analysis, geometry, combinatorics, and number theory.
• In engineering applications at Google's compute stack, AlphaEvolve yielded improvements in scheduling heuristics, matrix-multiplication kernels, arithmetic circuits, and Transformer attention runtimes.
• The approach enabled discovery of novel, provably correct algorithms that exceed state-of-the-art solutions in mathematics and computer science.
• A notable result is the first known rank-48 algorithm for 4x4 complex-valued matrix multiplication, improving over Strassen’s historical result in this setting.