Replication code for the manuscript "Efficient construction and explicit dimensionality of Lie group-equivariant and permutation-invariant spaces"

Zenodo (CERN European Organization for Nuclear Research)

Abstract

This repository contains the source code and scripts used to generate all results and figures reported in the manuscript: Eloïse Barthelemy, Geneviève Dusson, Camille Hernandez, and Liwei Zhang, "Efficient construction and explicit dimensionality of Lie group-equivariant and permutation-invariant spaces", arxiv.2604.01975, 2026. Contents - `constructing_GE-PI_basis_via_lie_alg.jl` — Implementation of the proposed method on SO3 - Julia code. - `constructing_GE-PI_basis_via_lie_alg_SU2.jl` — Implementation of the proposed method on SU2 - Julia code. - `recursive_construction.jl` - Implementation of the proposed recursive method on SO3 - Julia code. - `dim_utils.jl` — Code for computing dimensions - Julia code. - `cache_dim.jld2` - JLD2 file containing cached dimensionalities to avoid duplicate computations. - `script_plots.jl` — Scripts generating figures shown in the manuscript - Julia code. - `cost_plots.jl` — Part of `script_plots.jl`, containing codes for generating the cost figures shown in the manuscript - Julia code. - `recursive_plots.jl` — Part of `script_plots.jl`, containing codes for generating figures regarding the comparison of recursive and direct constructions shown in the manuscript - Julia code. - `code_for_effciency_comparison/` — Folder of scripts running the benchmark of the proposed method and existing methods - Julia and Python codes. - `Project.toml`, `Manifest.toml` — Exact Julia environment for reproducibility. Requirements - Julia ≥ 1.10 - Python ≥ 3.8

Authors 4

1. Eloïse Barthelemy

   Université Marie et Louis Pasteur

   Affiliation as printed

   Université Marie-et-Louis-Pasteur

2. Geneviève Dusson

   Université Marie et Louis Pasteur

   Affiliation as printed

   Université Marie-et-Louis-Pasteur

3. Camille Hernandez

   Université Marie et Louis Pasteur

   Affiliation as printed

   Université Marie-et-Louis-Pasteur

4. Liwei Zhang Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University