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TRADES-random-smoothing

This is the code for JMLR paper "Random Smoothing Might be Unable to Certify $\ell_\infty$ Robustness for High-Dimensional Images" by Avrim Blum (TTIC), Travis Dick (U. of Pennsylvania), Naren Manoj (TTIC), and Hongyang Zhang (TTIC), ordered alphabetically.

TRADES + Random Smoothing achieves SOTA certified robustness in $\ell_\infty$ norm at radius 2/255.

Prerequisites

Python (3.6.4)
Pytorch (0.4.1)
CUDA
numpy

Install

We suggest to install the dependencies using Anaconda or Miniconda. Here is an exemplary command:

$ wget https://repo.anaconda.com/archive/Anaconda3-5.1.0-Linux-x86_64.sh
$ bash Anaconda3-5.1.0-Linux-x86_64.sh
$ source ~/.bashrc
$ conda install pytorch=0.4.1

TRADES+Random Smooth: A New Training Method for Certifiable Robustness

We used TRADES [paper] to train a soft-random-smoothing classifier by injecting Gaussian noise. The method minimizes empirical risk of a regularized surrogate loss L(.,.) (e.g., the cross-entropy loss) with Gaussian noise: $\min_{f}\mathbb{E}_{X,Y}\mathbb{E}_{\eta\sim\mathcal{N}(0,\sigma^2I)}\left[\mathcal{L}(f(X+\eta),Y)+\beta\max_{X'\in\mathbb{B}_2(X,\epsilon)}\mathcal{L}(f(X+\eta),f(X'+\eta))\right].$

Running Demos

Certified $\ell_\infty$ robustness at radius 2/255:

Train ResNet-110 model on CIFAR10:

  $ python code/train_trades.py --epsilon 0.435 --imagesize 32 --noise_sd 0.12 --model-dir 'checkpoints/model_noise12_size32_l2trades0435_beta6_dir'

Certify ResNet-110 model on CIFAR10:

  $ python code/certify_trades.py cifar10 --imagesize 32 --sigma 0.12 --outfile 'results/output_noise12_size32_l2trades0435_beta6_full' --skip 1 --batch 10000 --load-dir 'checkpoints/model_noise12_size32_l2trades0435_beta6/model-res110-epoch.pt'

Benchmark on certified $\ell_\infty$ robustness at radius 2/255 on CIFAR-10:

Method	Robust Accuracy	Natural Accuracy
TRADES + Random Smoothing	62.6%	78.7%
Salman et al. (2019)	60.8%	82.1%
Zhang et al. (2020)	54.0%	72.0%
Wong et al. (2018)	53.9%	68.3%
Mirman et al. (2018)	52.2%	62.0%
Gowal et al. (2018)	50.0%	70.2%
Xiao et al. (2019)	45.9%	61.1%

Effectiveness of lower bound:

Train ResNet-110 models of varying input sizes (32, 48, 64) on CIFAR10:

  $ python code/train_trades.py --epsilon 0.435 --imagesize 32 --noise_sd 0.12 --model-dir 'checkpoints/model_noise12_size32_l2trades0435_beta6_dir'
  $ python code/train_trades.py --epsilon 0.6525 --imagesize 48 --noise_sd 0.18 --model-dir 'checkpoints/model_noise18_size48_l2trades06525_beta6_dir'
  $ python code/train_trades.py --epsilon 0.87 --imagesize 64 --noise_sd 0.24 --model-dir 'checkpoints/model_noise24_size64_l2trades087_beta6_dir'

Certify ResNet-110 models of varying input sizes (32, 48, 64) on CIFAR10:

  $ python code/certify_trades.py cifar10 --imagesize 32 --sigma 0.12 --outfile 'results/output_noise12_size32_l2trades0435_beta6' --skip 20 --batch 10000 --load-dir 'checkpoints/model_noise12_size32_l2trades0435_beta6_dir/model-res110-epoch.pt'
  $ python code/certify_trades.py cifar10 --imagesize 48 --sigma 0.18 --outfile 'results/output_noise18_size48_l2trades06525_beta6' --skip 20 --batch 10000 --load-dir 'checkpoints/model_noise18_size48_l2trades06525_beta6_dir/model-res110-epoch.pt'
  $ python code/certify_trades.py cifar10 --imagesize 64 --sigma 0.24 --outfile 'results/output_noise24_size64_l2trades087_beta6' --skip 20 --batch 10000 --load-dir 'checkpoints/model_noise24_size64_l2trades087_beta6_dir/model-res110-epoch.pt'

Analyze results:

  $ python code/analyze.py

It shows that the three curves of varying input sizes behave similarly. This empirically supports that the certified $\ell_\infty$ robust radius ε should be proportional to the quantity $\sigma/\sqrt{d}$ .

Reference

For technical details and full experimental results, please check the paper.

@article{blum2020random, 
	author = {Avrim Blum and Travis Dick and Naren Manoj and Hongyang Zhang}, 
	title = {Random Smoothing Might be Unable to Certify $\ell_\infty$ Robustness for High-Dimensional Images}, 
	journal = {Journal of Machine Learning Research},
	year = {2020}
}

Contact

Please contact hongyanz@ttic.edu if you have any question on the codes. Enjoy!