  Randomized smoothing has achieved great success for certified robustness
against adversarial perturbations. Given any arbitrary classifier, randomized
smoothing can guarantee the classifier's prediction over the perturbed input
with provable robustness bound by injecting noise into the classifier. However,
all of the existing methods rely on fixed i.i.d. probability distribution to
generate noise for all dimensions of the data (e.g., all the pixels in an
image), which ignores the heterogeneity of inputs and data dimensions. Thus,
existing randomized smoothing methods cannot provide optimal protection for all
the inputs. To address this limitation, we propose a novel anisotropic
randomized smoothing method which ensures provable robustness guarantee based
on pixel-wise noise distributions. Also, we design a novel CNN-based noise
generator to efficiently fine-tune the pixel-wise noise distributions for all
the pixels in each input. Experimental results demonstrate that our method
significantly outperforms the state-of-the-art randomized smoothing methods.
