README.md

Description

This repository houses the code used to create the plots used in "A unified framework to enforce, discover, and promote symmetry in machine learning" by Otto et al. A preprint can be found on the arXiv (https://arxiv.org/abs/2311.00212).

Getting started

To run this code, download the repository, and run the following to install symm_ml as a python package in your local environment.

pip install -r requirements.txt
pip install -e .

The code used to generate the data for the numerics examples can be found in symm_ml.numerics.experiment. Simply change the experiment variables at the top of the file and run python experiment.py. NOTE: The code was not optimized to be memory efficient and these optimization problems can quickly grow. Be mindful of this when setting the number of workers and size of the problems.

Numerics Data

The numerics for calculating the recovery (or "statistical") dimension can be found in the form of .csv files under data/. Each file corresponds to the class of function and associated Lie algebra prior that was used ($T(n)$ for translations, or $SE(n)$ for the full special Euclidean group). A description of the columns can be found in the table below:

Column name	Description
$m$	The input dimension
$r$	The number of latent features ($r \leq m$)
$d$	The degree of the polynomial on the $r$ features
seed	The random seed used for the experiment instantiation
n_recover	The number of random samples needed to recover the function
n_lib	The number of terms in the library (i.e. total number of coefficients)
dt	The amount of compute time needed to find the recovery dimension.
tot_iters	The total number of cvxpy iterations needed to find the recovery dimension.