ComputationalDepth

This repository contains the code for the paper "The Computational Advantage of Depth: Learning High-Dimensional Hierarchical Functions with Gradient Descent" arXiv:2502.13961.

The requirements to run the code are contained in the requirements.txt file.

The code is organized as follows:

• Codes/RawHyperparams/ contains the hyperparameters file (Setting.yaml). The user can set it by replacing "..." with the wanted values (See the Example folder for a prototype). The user can run the script Codes/genYaml.py to generate the definitive .yaml file to be used in the experiment.
• Codes/RunExperiment.py contains the code to run the experiments. For convenience, we grouped everything in a single script containing both the lazy/shallow methods and the multi-layer methods and some useful functions and classes are in Codes/utils.py. The results are saved in the Codes/data/ folder.
• According to the different metric to analyze, the codes to generate the plots are: Codes/ErrorPlotting.py and Codes/OverlapPlotting.py.