First published: 2017/06/19 (5 years ago) Abstract: Recent work has demonstrated that neural networks are vulnerable to
adversarial examples, i.e., inputs that are almost indistinguishable from
natural data and yet classified incorrectly by the network. In fact, some of
the latest findings suggest that the existence of adversarial attacks may be an
inherent weakness of deep learning models. To address this problem, we study
the adversarial robustness of neural networks through the lens of robust
optimization. This approach provides us with a broad and unifying view on much
of the prior work on this topic. Its principled nature also enables us to
identify methods for both training and attacking neural networks that are
reliable and, in a certain sense, universal. In particular, they specify a
concrete security guarantee that would protect against any adversary. These
methods let us train networks with significantly improved resistance to a wide
range of adversarial attacks. They also suggest the notion of security against
a first-order adversary as a natural and broad security guarantee. We believe
that robustness against such well-defined classes of adversaries is an
important stepping stone towards fully resistant deep learning models.
Madry et al. provide an interpretation of training on adversarial examples as sattle-point (i.e. min-max) problem. Based on this formulation, they conduct several experiments on MNIST and CIFAR-10 supporting the following conclusions:
- Projected gradient descent might be “strongest” adversary using first-order information. Here, gradient descent is used to maximize the loss of the classifier directly while always projecting onto the set of “allowed” perturbations (e.g. within an $\epsilon$-ball around the samples). This observation is based on a large number of random restarts used for projected gradient descent. Regarding the number of restarts, the authors also note that an adversary should be bounded regarding the computation resources – similar to polynomially bounded adversaries in cryptography.
- Network capacity plays an important role in training robust neural networks using the min-max formulation (i.e. using adversarial training). In particular, the authors suggest that increased capacity is needed to fit/learn adversarial examples without overfitting. Additionally, increased capacity (in combination with a strong adversary) decreases transferability of adversarial examples.
Also view this summary at [davidstutz.de](https://davidstutz.de/category/reading/).