  The use of deep 3D point cloud models in safety-critical applications, such
as autonomous driving, dictates the need to certify the robustness of these
models to semantic transformations. This is technically challenging as it
requires a scalable verifier tailored to point cloud models that handles a wide
range of semantic 3D transformations. In this work, we address this challenge
and introduce 3DCertify, the first verifier able to certify robustness of point
cloud models. 3DCertify is based on two key insights: (i) a generic relaxation
based on first-order Taylor approximations, applicable to any differentiable
transformation, and (ii) a precise relaxation for global feature pooling, which
is more complex than pointwise activations (e.g., ReLU or sigmoid) but commonly
employed in point cloud models. We demonstrate the effectiveness of 3DCertify
by performing an extensive evaluation on a wide range of 3D transformations
(e.g., rotation, twisting) for both classification and part segmentation tasks.
For example, we can certify robustness against rotations by $\pm60^\circ$ for
95.7% of point clouds, and our max pool relaxation increases certification by
up to 15.6%.
