  Deep equilibrium models (DEQs) refrain from the traditional layer-stacking
paradigm and turn to find the fixed point of a single layer. DEQs have achieved
promising performance on different applications with featured memory
efficiency. At the same time, the adversarial vulnerability of DEQs raises
concerns. Several works propose to certify robustness for monotone DEQs.
However, limited efforts are devoted to studying empirical robustness for
general DEQs. To this end, we observe that an adversarially trained DEQ
requires more forward steps to arrive at the equilibrium state, or even
violates its fixed-point structure. Besides, the forward and backward tracks of
DEQs are misaligned due to the black-box solvers. These facts cause gradient
obfuscation when applying the ready-made attacks to evaluate or adversarially
train DEQs. Given this, we develop approaches to estimate the intermediate
gradients of DEQs and integrate them into the attacking pipelines. Our
approaches facilitate fully white-box evaluations and lead to effective
adversarial defense for DEQs. Extensive experiments on CIFAR-10 validate the
adversarial robustness of DEQs competitive with deep networks of similar sizes.
