We’ve created images that reliably fool neural network classifiers when viewed from varied scales and perspectives. This challenges a claim from last week that self-driving cars would be hard to trick maliciously since they capture images from multiple scales, angles, perspectives, and the like.

However, we’d suspected that active effort could produce a robust adversarial example, as adversarial examples have been shown to transfer⁠(opens in a new window) to the physical world.

Adversarial examples can be created using an optimization method called projected gradient descent to find small perturbations to the image that arbitrarily fool the classifier.

Instead of optimizing for finding an input that’s adversarial from a single viewpoint, we optimize over a large ensemble⁠(opens in a new window) of stochastic classifiers that randomly rescale the input before classifying it. Optimizing against such an ensemble produces robust adversarial examples that are scale-invariant.

Even when we restrict ourselves to only modifying pixels corresponding to the cat, we can create a single perturbed image that is simultaneously adversarial at all desired scales.

By adding random rotations, translations, scales, noise, and mean shifts to our training perturbations, the same technique produces a single input that remains adversarial under any of these transformations.

Our transformations are sampled randomly at test time, demonstrating that our example is invariant to the whole distribution of transformations.