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Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approach

This is the official repository for the ICLR 2024 paper "Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approach" by Shaopeng Fu and Di Wang.

News

• 01/2024: The paper was accepted to ICLR 2024.
• 10/2023: The paper was released on arXiv.

Installation

Requirements

• Python >= 3.10
• PyTorch == 2.0.1
• jax == 0.4.7 and jaxlib == 0.4.7 ("jax[cuda11_cudnn82]"==0.4.7)
• neural_tangents == 0.6.2

Build experiment environment via Docker

There are two ways to build the Docker experiment environment:

• Build via Dockerfile

  docker build --tag 'advntk' .
  

  Run the above command, and then the built image is advntk:latest.

• Build manually

  Firstly, pull the official PyTorch Docker image:

  docker pull pytorch/pytorch:2.0.1-cuda11.7-cudnn8-devel
  

  Then, run the pulled Docker image and install following packages:

  pip install --upgrade "jax[cuda11_cudnn82]"==0.4.7 -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html
  pip install neural-tangents==0.6.2
  

Quick Start

The scripts for $\ell_\infty$-norm, $\rho=8/255$ experiments are collected in ./scripts.

To run an experiment: for example, execute the following command:

bash ./scripts/c10/mlp/advntk-r8.sh ./

To use different perturbation radius $\rho$: modify the following arguments accordingly:

--pgd-radius       # (float) adversarial perturbation radius
--pgd-steps        # (int) steps number in PGD
--pgd-step-size    # (float) step size in PGD
--save-dir         # (string) the path to the dictionary for saving experiment

Citation

@inproceedings{fu2024theoretical,
  title={Theoretical Analysis of Robust Overfitting for Wide DNNs: An NTK Approach},
  author={Shaopeng Fu and Di Wang},
  booktitle={International Conference on Learning Representations},
  year={2024}
}

Acknowledgment

• Neural tangents: https://github.com/google/neural-tangents