OverparametrisedNet

Code repository for the paper "The Nuclear Route: Sharp Asymptotics of ERM in Overparameterized Quadratic Networks"

Overview of the main files:

• visualise.ipynb: Notebook that produces the figures in the paper starging from the data in data/ and saving them in figs/.
• theory.py: Main file containing all the implementation of the theory except the limit of small rank. An example of how to use it is given in the example_theory.py notebook.
• {ALGO}_code.py: Scripts that run the experiments for different algorithms. We have implementations with GD, LBFGS (both using PyTorch) and CVXPY.
• small_rank_Mathematica.nb: Mathematica notebook that produces data for the limit of small rank. We recommend to run it in a Mathematica 13.0

Dependencies: We used Python 3.10.15 and the following packages:

• cvxpy==1.3.0
• numpy==2.2.6
• pandas==2.2.3
• scipy==1.15.3
• torch==1.12.1
• tqdm==4.67.1