I do a lot of work in the area of adversarial machine learning, which aims to characterize a machine learning model’s predictions for challenging unseen inputs (not to be confused with generative adversarial networks (GANs)). Despite having worked in this area for some time, I still struggle with the basic definition of an adversarial example, as proposed by OpenAI:

Adversarial examples are inputs to machine learning models that an attacker has intentionally designed to cause the model to make a mistake; they’re like optical illusions for machines.

Aside from being informal, my problem with this definition is that it tends to absolve designers of their responsibility to a reasonable standard of care, it doesn’t own the problem. By focusing on the role of the attacker, it makes it seem as though the designer has done their absolute best, and that such unpredictable behaviour at test time is simply beyond one’s control. After all, I am not aware of any fix to make humans immune to optical illusions.

At least this definition is more general than arbitrary constraints that invoke an $L_p$ norm directly on the inputs like $\| x - x_{adv} \|_p \leq \epsilon$, but I believe this fundamental emphasis on security, instead of say, stability or fault tolerance, is limiting. The unfortunate reality is that state-of-the-art deep neural nets for computer vision are overwhelmingly unstable, i.e., a small change in the bounded input may induce a large change in the output. As designers of useful systems, we would like to avoid instability in general, not only in security.

Optical illusions simply do not arise that often in nature, and when they do, humans are generally aware that their visual system is being manipulated, and proceed with caution. One could argue that adversarial examples are similarly rare, given that they might violate the independent and identically distributed (i.i.d) data assumption fundamental to machine learning. Recently, this latter view has been taken for granted, but a dependence between an example and the model’s parameters does not necessarily imply that the example is from a different distribution, we usually don’t know the distribution from which our inputs are drawn, which is why we’re using machine learning. The tendency to question the i.i.d. assumption, a fundamental assumption made by a whole community, rather than assuming user error, demonstrates how the aforementioned security-centric definition can be wielded to absolve the designer of responsibility.

I don’t have a significantly better definition of an adversarial example, recent work is concerned with the design of better methodology for evaluating robustness that would render such definitions somewhat unnecessary. However, I would shorten the previous one by removing the necessary role of an attacker, and stipulate that we’re really concerned with confident mistakes (where a suitable confidence threshold is application specific). Something like:

Adversarial examples are bounded inputs to machine learning models for which the prediction differs with high-confidence from that of an oracle.

I continue to use adversarial examples in relation to the problem of maximizing out-of-sample performance, e.g., max-margin generalization, and ensuring model confidence is calibrated for all legitimate inputs. Naturally, following the gradient is one of the quickest ways to test these things, but I consider myself an ally not an adversary; a designer of stable systems, not defense mechanisms.