Xingjun Ma, Bo Li, Yisen Wang, Sarah M. Erfani, Sudanthi N. R. Wijewickrema, Michael E. Houle, Grant Schoenebeck, Dawn Song, James Bailey. Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality. CoRR abs/1801.02613, 2018.

Ma et al. detect adversarial examples based on their estimated intrinsic dimensionality. I want to note that this work is also similar to [1] – in both publications, local intrinsic dimensionality is used to analyze adversarial examples. Specifically, the intrinsic dimensionality of a sample is estimated based on the radii $r_i(x)$ of the $k$-nearest neighbors around a sample $x$:

$- \left(\frac{1}{k} \sum_{i = 1}^k \log \frac{r_i(x)}{r_k(x)}\right)^{-1}$.

For details regarding the original, theoretical formulation of local intrinsic dimensionality I refer to the paper. In experiments, the authors show that adversarial examples exhibit a significant higher intrinsic dimensionality than training samples or randomly perturbed examples. This observation allows detection of adversarial examples. A proper interpretation of this finding is, however, missing. It would be interesting to investigate what this finding implies about the properties of adversarial examples.

Also find this summary on ShortScience.org.

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