  Randomized Smoothing (RS), being one of few provable defenses, has been
showing great effectiveness and scalability in terms of defending against
$\ell_2$-norm adversarial perturbations. However, the cost of MC sampling
needed in RS for evaluation is high and computationally expensive. To address
this issue, we investigate the possibility of performing randomized smoothing
and establishing the robust certification in the latent space of a network, so
that the overall dimensionality of tensors involved in computation could be
drastically reduced. To this end, we propose Latent Space Randomized Smoothing.
Another important aspect is that we use orthogonal modules, whose Lipschitz
property is known for free by design, to propagate the certified radius
estimated in the latent space back to the input space, providing valid
certifiable regions for the test samples in the input space. Experiments on
CIFAR10 and ImageNet show that our method achieves competitive certified
robustness but with a significant improvement of efficiency during the test
phase.
