This repository contains the official implementation and numerical experiments for the paper: "From Mean-Field Limits to Semiclassical Concentration: Global Convergence of the Canonical Evolutionary Strategy" (2026).
This project implements the Canonical Evolutionary Strategy (CES), a global optimization framework. We provide the tools to reproduce the theoretical validation and the benchmark results presented in the paper.
- CES Engine: Core implementation of the evolutionary dynamics.
-
Mean-Field Limits: Numerical verification of the
$M^{-1/2}$ convergence rate. - Semiclassical Analysis: Scripts for visualizing the concentration of the ground state.
-
High-Dimensional Benchmarks: Scalability tests in
$d=1$ to$d=30$ for Ackley function at different initialization regimes (Uniform and Shifted).
/ces_engine.py: Main algorithm logic./plot_theory_figures.py: Mathematical validation plots./plot_mass_transport.py: 1D and 2D mass transport visualizations./run_benchmarks.py: High-performance simulation suite./data/: (Stored in Parquet) Raw simulation results.
- Clone the repo:
git clone https://github.com/inria-chile/ces-global-convergence.git - Install dependencies:
pip install numpy pandas matplotlib scipy pyarrow - Run benchmarks:
python run_benchmarks.py
If you use this code in your research, please cite our paper:
@misc{ces2026global,
title={From Mean-Field Limits to Semiclassical Concentration: Global Convergence of the Canonical Evolutionary Strategy},
author={Neto, Mat{\'\i}as and Garay, Nicolas and Mart{\'\i}, Luis and Sanchez-Pi, Nayat},
journal={arXiv preprint},
note={Submitted to PPSN 2026}
year={2026},
}