Authors: Ehsan Nezhadarya, Ehsan Taghavi, Ryan Razani, Bingbing Liu, Jun Luo Description: Deterministic down-sampling of an unordered point cloud in a deep neural network has not been rigorously studied so far. Existing methods down-sample the points regardless of their importance for the network output and often address down-sampling the raw point cloud before processing. As a result, some important points in the point cloud may be removed, while less valuable points may be passed to next layers. In contrast, the proposed adaptive down-sampling method samples the points by taking into account the importance of each point, which varies according to application, task and training data. In this paper, we propose a novel deterministic, adaptive, permutation-invariant down-sampling layer, called Critical Points Layer (CPL), which learns to reduce the number of points in an unordered point cloud while retaining the important (critical) ones. Unlike most graph-based point cloud down-sampling methods that use k-NN to find the neighboring points, CPL is a global down-sampling method, rendering it computationally very efficient. The proposed layer can be used along with a graph-based point cloud convolution layer to form a convolutional neural network, dubbed CP-Net in this paper. We introduce a CP-Net for 3D object classification that achieves high accuracy for the ModelNet 40 dataset among point cloud-based methods, which validates the effectiveness of the CPL.