Why epsilon can be larger than 1? about mnist_challenge HOT 6 CLOSED

You are right, since valid pixel values are from 0 to 1, we clip the perturbation to that range at every step.

The value 8 that you are referring to corresponds to the CIFAR10 dataset where valid pixel values are from 0 to 255. So 8 is actually quite small.

Let me know if that does not make sense.

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okay, thank you very much!

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So why do you use epsilon=8/255 for CIFAR10 but epsilon=0.3 for MNIST rather than use epsilon=8/255 for both datasets? Does 0.3 for MNIST means 0.3/255? If not, why do you use such large epsilon (0.3>>8/255) on MNIST?

Please forgive me for such a stupid question. I'm a greenhand in this area.

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We do use a different epsilon for each dataset---for MNIST we use 0.3/1 and for CIFAR10 8/255. The reason is that these datasets are quite different so the epsilon values that we can be robust to are also different. Specifically, MNIST consists of black-and-white images, so a perturbation of 0.3 cannot change a white pixel to black and vice-versa (which is why we are able to learn robust classifiers after all). In contrast, for CIFAR10, pixels lie in a wider range of values, while the image is 3-dimensional (RGB). As a result, the perturbation needed to actually change the class of an image is much smaller (in Figure 8 of https://arxiv.org/abs/1805.12152 you can see how perturbations of 0.125/1 on CIFAR10 completely change the content of the image).

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I get it. Thank you very much!

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