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 real-world 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 the 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 ±60°for 95.7% of point clouds, and our max pool relaxation increases certification by up to 15.6%.* This work was done while the author was at ETH Zurich.ness against these attacks. However, as demonstrated in the image recognition domain, such defenses are usually broken by more powerful attacks [1,49], resulting in an arms race between stronger defenses and even stronger attacks.To break this cycle, one ideally needs a proof that a deep learning model is robust against any adversarial attack, under some threat model. This proof is usually obtained by invoking a neural network verifier on a deep learning model and a model input, where the verifier attempts to provide a certificate that the model is robust to any transformation of this input. While plenty of verifiers have been proposed in the image recognition domain [5,19,42,44,48,56,64], no such verifier exists for 3D point cloud models.