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Huang et al. propose a variant of adversarial training called “learning with a strong adversary”. In spirit the idea is also similar to related work [1]. In particular, the authors consider the minmax objective $\min_g \sum_i \max_{\r^{(i)}\\leq c} l(g(x_i + r^{(i)}), y_i)$ where $g$ ranges over expressible functions and $(x_i, y_i)$ is a training sample. In the remainder of the paper, Huang et al. Address the problem of efficiently computing $r^{(i)}$ – i.e. a strong adversarial example based on the current state of the network – and subsequently updating the weights of the network by computing the gradient of the augmented loss. Details can be found in the paper. [1] T. Miyato, S. Maeda, M. Koyama, K. Nakae, S. Ishii. Distributional Smoothing by Virtual Adversarial Training. ArXiv:1507.00677, 2015. Also see this summary at [davidstutz.de](https://davidstutz.de/category/reading/).
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