Recently, techniques have been developed to provably guarantee the robustness of a classifier to adversarial perturbations of bounded L1 and L2 magnitudes by using randomized smoothing: the robust classification is a consensus of base classifications on randomly noised samples where the noise is additive. In this paper, we extend this technique to the L0 threat model. We propose an efficient and certifiably robust defense against sparse adversarial attacks by randomly ablating input features, rather than using additive noise. Experimentally, on MNIST, we can certify the classifications of over 50% of images to be robust to any distortion of at most 8 pixels. This is comparable to the observed empirical robustness of unprotected classifiers on MNIST to modern L0 attacks, demonstrating the tightness of the proposed robustness certificate. We also evaluate our certificate on ImageNet and CIFAR-10. Our certificates represent an improvement on those provided in a concurrent work (Lee et al. 2019) which uses random noise rather than ablation (median certificates of 8 pixels versus 4 pixels on MNIST; 16 pixels versus 1 pixel on ImageNet.) Additionally, we empirically demonstrate that our classifier is highly robust to modern sparse adversarial attacks on MNIST. Our classifications are robust, in median, to adversarial perturbations of up to 31 pixels, compared to 22 pixels reported as the state-of-the-art defense, at the cost of a slight decrease (around 2.3%) in the classification accuracy. Code and supplementary material is available at https://github.com/alevine0/randomizedAblation/.

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Twentieth century philosophy of science has been dominated by a view of language with a strong prejudice against psychology, even while empirical psychology has moved away from the nineteenth century philosophical psychology against which the prejudice was originally directed. This legacy is shown to dominate even in recent Kripke-inspired efforts toward new theories of meaning. Its influence is argued to undermine prospects for making sense of such phenomena as scientific progress. Avoiding this consequence requires that we pursue a psychologically informed theory of meaning.

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