Google DeepMind open-sources AlphaEvolve

Google DeepMind released an open-source repository accompanying its AlphaEvolve paper, including a minimal implementation of the evolutionary coding agent with local evaluation under /src and verification code for the new upper bound on the matrix multiplication exponent AlphaEvolve discovered. The /omega directory holds a JAX/Haiku gradient-based optimization program that runs gradient descent over 32,000 steps with 32 random seeds at recursion depth 3, plus a NumPy/SciPy verifier and a Colab notebook using rational arithmetic for rigorous proof. The repository also provides initial programs, discovered results and verification notebooks for 16 mathematical problems where AlphaEvolve beat the state of the art, including circle packing, kissing numbers, cap sets and Shannon capacity of cycle graphs, along with matrix multiplication tensor decomposition notebooks for standard tensor rank and support rank.

This repository accompanies the paper TODO franrruiz : Add link to paper. There are the following directories: - /src contains a minimal implementation of AlphaEvolve with local evaluation. - /omega contains code and data related to the new upper bound on the matrix multiplication exponent discovered by AlphaEvolve. It includes a Colab notebook for rigorous verification using rational arithmetic, and a level 3/ subdirectory with the gradient-based optimisation code at recursion depth 3: - level 3/final program.py — the optimisation program evolved by AlphaEvolve. It builds a differentiable upper-bound model in JAX/Haiku, runs gradient descent over 32k steps with 32 random seeds, and converts the best solution into a format suitable for verification. Run it directly with python3 final program.py . - level 3/verification.py — a NumPy/SciPy verifier that takes a flat parameter vector produced by the optimiser and evaluates the proven omega upper bound. It uses floating-point arithmetic for fast hill-climbing; the companion Colab notebook uses rational arithmetic for a rigorous proof. A requirements.txt listing the pinned Python dependencies and a Dockerfile for containerised execution are also provided in level 3/ . - - /maths contains the initial programs, discovered results, and verification code for the mathematical problems on which AlphaEvolve found a solution outperforming the state-of-the-art see the "Results" section of the paper . There is a subfolder for each of such problems, each containing the files needed to run an AlphaEvolve experiment and a Colab notebook to verify the found construction. - /matmul tensor decompositions contains Colab notebooks with the decompositions of matrix multiplication tensors across the matrix sizes for which the gradient-based optimization method from AlphaEvolve found a solution outperforming the state-of-the-art, along with the code to verify their correctness. Specifically, there are two Colabs: one for the standard tensor rank decomposition, and another one for the support rank. For the folders /maths and /matmul tensor decompositions , no installation is required. The provided notebooks can be opened and run in Google Colab. For the folder /src , these are the installation instructions: 1. Install docker required for program evaluation : https://www.docker.com/get-started/ https://www.docker.com/get-started/ 2. optional Create venv: sudo apt-get install virtualenv python3-venv virtualenv -p python3.11 alpha evolve source alpha evolve/bin/activate 1. Install pip dependencies: pip install -r src/requirements.txt 1. Set Gemini API key https://ai.google.dev/gemini-api/docs/api-key : export GEMINI API KEY=<your api key - /omega : The Colab notebook to verify the new upper bound on the matrix multiplication exponent can be opened via: Note: To verify our best omega upper bound, you must download the clean level4.npz.xz file from this repository to your local machine, and then upload it when prompted by the Colab notebook. - /maths : The Colab notebook to verify the found solution for each problem can be opened via: - Circle packing: - Erdös minimum overlap: - First autocorrelation inequality: - Second autocorrelation inequality: - Third autocorrelation inequality: - Heilbronn problem for convex regions: - Heilbronn problem for triangles: - Hexagon packing: - Kissing numbers: - Max to min ratio: - Sums and differences: - Uncertainty principles Hermite polynomials approach : - Uncertainty principles Laguerre polynomials approach : - Extremal girth 5: - Shannon capacity of cycle graphs: - Cap sets: - - /matmul tensor decompositions : There are two Colab notebooks: - /src : We provide an example launch command for the circle packing problem below: python run.py --problem config=./data/problem config/circle packing.yaml DISCLAIMER: AlphaEvolve involves the execution of code generated by Large Language Models LLMs . LLM-generated code is intrinsically unpredictable and should be handled as untrusted code. In this version of AlphaEvolve, this code is run in a Docker sandbox as an isolation measure. However, despite sandboxing, the potential for unintended behavior, resource misuse, or security vulnerabilities cannot be fully eliminated. All users should be aware of these inherent risks and understand that they use this software at their own discretion. Google DeepMind shall not be liable for any claims, damages, or other liability arising from the execution of LLM-generated code. If you use the code or data in this package, please cite: TODO franrruiz : Add citation. Copyright 2026 Google LLC All software is licensed under the Apache License, Version 2.0 Apache 2.0 ; you may not use this file except in compliance with the Apache 2.0 license. You may obtain a copy of the Apache 2.0 license at: https://www.apache.org/licenses/LICENSE-2.0 https://www.apache.org/licenses/LICENSE-2.0 All other materials are licensed under the Creative Commons Attribution 4.0 International License CC-BY . You may obtain a copy of the CC-BY license at: https://creativecommons.org/licenses/by/4.0/legalcode https://creativecommons.org/licenses/by/4.0/legalcode Unless required by applicable law or agreed to in writing, all software and materials distributed here under the Apache 2.0 or CC-BY licenses are distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the licenses for the specific language governing permissions and limitations under those licenses. This is not an official Google product.