We identify three common cases that lead to overestimation of adversarial accuracy against bounded first-order attack methods, which is popularly used as a proxy for adversarial robustness in empirical studies. For each case, we propose compensation methods that either address sources of inaccurate gradient computation, such as numerical instability near zero and non-differentiability, or reduce the total number of back-propagations for iterative attacks by approximating second-order information. These compensation methods can be combined with existing attack methods for a more precise empirical evaluation metric. We illustrate the impact of these three cases with examples of practical interest, such as benchmarking model capacity and regularization techniques for robustness. Overall, our work shows that overestimated adversarial accuracy that is not indicative of robustness is prevalent even for conventionally trained deep neural networks, and highlights cautions of using empirical evaluation without guaranteed bounds.
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