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FunSearch

Usage:

You can run FunSearch in container using Podman or Docker

podman build . -t funsearch


# Create a folder to share with the container
mkdir data
podman run -it -v ./data:/workspace/data funsearch

# Set the environment variable OPENAI_API_KEY=sk-xxxx or create .env file.
# "gpt-3.5-turbo-instruct" model is used by default.
# Refer to 'llm' package docs to use other models.

funsearch run examples/cap_set_spec.py 11 --sandbox_type ExternalProcessSandbox

In here we are searching for the algorithm to find maximum cap sets for dimension 11. You should see output something like

root@11c22cd7aeac:/workspace# funsearch run examples/cap_set_spec.py 11 --sandbox_type ExternalProcessSandbox
INFO:root:Writing logs to data/1704956206
INFO:absl:Best score of island 0 increased to 2048
INFO:absl:Best score of island 1 increased to 2048
INFO:absl:Best score of island 2 increased to 2048
INFO:absl:Best score of island 3 increased to 2048
INFO:absl:Best score of island 4 increased to 2048
INFO:absl:Best score of island 5 increased to 2048
INFO:absl:Best score of island 6 increased to 2048
INFO:absl:Best score of island 7 increased to 2048
INFO:absl:Best score of island 8 increased to 2048
INFO:absl:Best score of island 9 increased to 2048
INFO:absl:Best score of island 5 increased to 2053
INFO:absl:Best score of island 1 increased to 2049
INFO:absl:Best score of island 8 increased to 2684
^C^CINFO:root:Keyboard interrupt. Stopping.
INFO:absl:Saving backup to data/backups/program_db_priority_1704956206_0.pickle.

Note that in the last command we use the ExternalProcessSandbox that is not fully safe but makes it a bit less likely that invalid code from LLM would break the search.

Alternatively, you can run the main Python process on a host computer outside of any container and let the process build and run separate sandbox containers (still requires Podman/Docker). This variant could be also used, e.g., in Colab quite safely since the environment is some kind of container itself.

pip install .

funsearch run examples/cap_set_spec.py 11

For more complex input data, you can provide the input also as a .json or .pickle file.

Currently, the search is only using single thread with no asyncio and is somewhat slow for challenging tasks.

Alternative LLMs

The search uses gpt-3.5-turbo-instruct by default, but other models can be used with the --model_name argument and possibly installing extensions to the llm package. As an example of performance, with gpt-3.5-turbo-instruct on dimension 8 it usually around 20 tries to find a few improvements to the naive algorithm.

On the other hand, using orca-mini-3b-gguf2-q4_0 doesn't seem to work quite well. The latest version has a bit improved parsing to find the last priority_vX method from the LLM response even if it contains other content like Markdown formatting. Anyway, the model seems to often use strange indentation of 1 space and thus might require some customization to be useful at all. Lastly, even with correct Python syntax, orca-mini-3b does not seem to find improvements (in 60 runs) and mostly generates code that throws "IndexError: tuple index out of range". The situation changes a bit if the search is started using a database generated by gpt-3.5-turbo prompts.

Overall, all models would probably require some prompt engineering, temperatures tuning, and such for the tool to be useful at all except for very simple problems. Also, the implementation is currently lacking good tools to analyze large amount of responses properly which makes any prompt engineering more difficult.

The repository contains a number of sample problems that can be solved with FunSearch. Currently, only the cap set problem (examples/cap_set_spec.py) has been written in the form that can be directly used with the 'funsearch' executable.

This repository accompanies the publication

Romera-Paredes, B. et al. Mathematical discoveries from program search with large language models. Nature (2023)

There are 6 independent directories:

  • cap_set contains functions discovered by FunSearch that construct large cap sets, and we also provide those cap sets in a numerical format for convenience.

  • admissible_set contains functions discovered by FunSearch that construct large admissible sets, and we also provide those admissible sets in a numerical format for convenience.

  • bin_packing contains heuristics discovered by FunSearch for online 1D bin packing problems, and an evaluation suite to reproduce the results reported in the paper.

  • cyclic_graphs contains functions discovered by FunSearch that construct large independent sets in strong products of cyclic graphs, and we also provide those sets in a numerical format for convenience.

  • corner_free_sets contains the discovered sets of indices, in numerical format, satisfying the combinatorial degeneration constraints described for the corners-free problem in the Supplementary Information.

  • implementation contains an implementation of the evolutionary algorithm, code manipulation routines, and a single-threaded implementation of the FunSearch pipeline. It does not contain language models for generating new programs, the sandbox for executing untrusted code, nor the infrastructure for running FunSearch on our distributed system. This directory is intended to be useful for understanding the details of our method, and for adapting it for use with any available language models, sandboxes, and distributed systems.

Installation

No installation is required. All notebooks can be opened and run in Google Colab.

Usage

  • cap_set: The notebook cap_set.ipynb can be opened via Open In Colab.

  • admissible_set: The notebook admissible_set.ipynb can be opened via Open In Colab.

  • bin_packing: The notebook bin_packing.ipynb can be opened via Open In Colab.

  • cyclic_graphs: The notebook cyclic_graphs.ipynb can be opened via Open In Colab.

Citing this work

If you use the code or data in this package, please cite:

@Article{FunSearch2023,
  author  = {Romera-Paredes, Bernardino and Barekatain, Mohammadamin and Novikov, Alexander and Balog, Matej and Kumar, M. Pawan and Dupont, Emilien and Ruiz, Francisco J. R. and Ellenberg, Jordan and Wang, Pengming and Fawzi, Omar and Kohli, Pushmeet and Fawzi, Alhussein},
  journal = {Nature},
  title   = {Mathematical discoveries from program search with large language models},
  year    = {2023},
  doi     = {10.1038/s41586-023-06924-6}
}

License and disclaimer

Copyright 2023 DeepMind Technologies Limited

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

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

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.