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Interval Bound Propagation for Training Verifiably Robust Models

This repository contains a simple implementation of Interval Bound Propagation (IBP) using TensorFlow: https://arxiv.org/abs/1810.12715. It also contains an implementation of CROWN-IBP: https://arxiv.org/abs/1906.06316. It also contains a sentiment analysis example under examples/language for https://arxiv.org/abs/1909.01492.

This is not an official Google product

Installation

IBP can be installed with the following command:

pip install git+https://github.com/deepmind/interval-bound-propagation

IBP will work with both the CPU and GPU version of tensorflow and dm-sonnet, but to allow for that it does not list Tensorflow as a requirement, so you need to install Tensorflow and Sonnet separately if you haven't already done so.

Usage

The following command trains a small model on MNIST with epsilon set to 0.3:

cd examples
python train.py --model=small --output_dir=/tmp/small_model

Pretrained Models

Models trained using IBP and CROWN-IBP can be downloaded here.

IBP models:

Dataset	Test epsilon	Model path	Clean accuracy	Verified accuracy	Accuracy under attack
MNIST	0.1	ibp/mnist_0.2_medium	98.94%	97.08%	97.99%
MNIST	0.2	ibp/mnist_0.4_large_200	98.34%	95.47%	97.06%
MNIST	0.3	ibp/mnist_0.4_large_200	98.34%	91.79%	96.03%
MNIST	0.4	ibp/mnist_0.4_large_200	98.34%	84.99%	94.56%
CIFAR-10	2/255	ibp/cifar_2-255_large_200	70.21%	44.12%	56.53%
CIFAR-10	8/255	ibp/cifar_8-255_large	49.49%	31.56%	39.53%

CROWN-IBP models:

Dataset	Test epsilon	Model path	Clean accuracy	Verified accuracy	Accuracy under attack
MNIST	0.1	crown-ibp/mnist_0.2_large	99.03%	97.75%	98.34%
MNIST	0.2	crown-ibp/mnist_0.4_large	98.38%	96.13%	97.28%
MNIST	0.3	crown-ibp/mnist_0.4_large	98.38%	93.32%	96.38%
MNIST	0.4	crown-ibp/mnist_0.4_large	98.38%	87.51%	94.95%
CIFAR-10	2/255	crown-ibp/cifar_2-255_large	71.52%	53.97%	59.72%
CIFAR-10	8/255	crown-ibp/cifar_8-255_large	47.14%	33.30%	36.81%
CIFAR-10	16/255	crown-ibp/cifar_16-255_large	34.19%	23.08%	26.55%

In these tables, we evaluated the verified accuracy using IBP only. We evaluted the accuracy under attack using a 20-step untargeted PGD attack. You can evaluate these models yourself using eval.py, for example:

cd examples
python eval.py --model_dir pretrained_models/ibp/mnist_0.4_large_200/ \
  --epsilon 0.3

Note that we evaluated the CIFAR-10 2/255 CROWN-IBP model using CROWN-IBP (instead of pure IBP). You can do so yourself by setting the flag --bound_method=crown-ibp:

python eval.py --model_dir pretrained_models/crown-ibp/cifar_2-255_large/ \
  --epsilon 0.00784313725490196 --bound_method=crown-ibp

Giving credit

If you use this code in your work, we ask that you cite this paper:

Sven Gowal, Krishnamurthy Dvijotham, Robert Stanforth, Rudy Bunel, Chongli Qin, Jonathan Uesato, Relja Arandjelovic, Timothy Mann, and Pushmeet Kohli. "On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models." arXiv preprint arXiv:1810.12715 (2018).

If you use CROWN-IBP, we also ask that you cite:

Huan Zhang, Hongge Chen, Chaowei Xiao, Sven Gowal, Robert Stanforth, Bo Li, Duane Boning, Cho-Jui Hsieh. "Towards Stable and Efficient Training of Verifiably Robust Neural Networks." arXiv preprint arXiv:1906.06316 (2019).

If you use the sentiment analysis example, please cite:

Po-Sen Huang, Robert Stanforth, Johannes Welbl, Chris Dyer, Dani Yogatama, Sven Gowal, Krishnamurthy Dvijotham, Pushmeet Kohli. "Achieving Verified Robustness to Symbol Substitutions via Interval Bound Propagation." EMNLP 2019.

Acknowledgements

In addition to the people involved in the original IBP publication, we would like to thank Huan Zhang, Sumanth Dathathri and Johannes Welbl for their contributions.