Adversarial Examples and Metrics

Adversarial examples are a type of attack on ML systems which cause misclassification of inputs. Achieving robustness against adversarial examples is crucial to apply ML in the real world. While most prior work on adversarial examples is empirical, a recent line of work establishes fundamental limitations of robust classification based on cryptographic hardness. Most positive and negative results in this field however assume that there is a fixed target metric which constrains the adversary, and we argue that this is often an unrealistic assumption. In this work we study the limitations of robust classification if the target metric is uncertain. Concretely, we construct a classification problem, which admits robust classification by a small classifier if the target metric is known at the time the model is trained, but for which robust classification is impossible for small classifiers if the target metric is chosen after the fact. In the process, we explore a novel connection between hardness of robust classification and bounded storage model cryptography.