Interval Bound Propagation

This is Chainer easy-to-follow implementation of Interval Bound Propagation. The MNIST experiment with small or medium models is implemented.

Paper: Sven Gowal, Krishnamurthy Dvijotham, Robert Stanforth, Rudy Bunel, Chongli Qin, Jonathan Uesato, Relja Arandjelovic, Timothy Mann, Pushmeet Kohli, On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models (Scalable Verified Training for Provably Robust Image Classification), ICCV 2019

Authors' TensorFlow Code: https://github.com/deepmind/interval-bound-propagation

python train_mnist.py -d 0 --model-class small

See layers.py or models.py for understanding the core of the algorithm.

Visualize

The left is by a baseline model while the right is by a IBP-trained model. Each shows the activation feature map of normal, upper- and lower-bounds at each layer. The image of range shows the upper - normal and normal - lower diffs with red and blue respectively. The more red, the more looser the upper bound is. The more blue, the more looser the lower bound is.

We can see the IBP-trained model produces noise-robust features. And, its logit for classification (y), on the bottom, is also robust and consistently predicts 7 as the label while the baseline fails.

Visualization notebook is visualize_interval_bound_propagation.ipynb.