In this paper, we propose GVA-net, a fully-convolutional architecture for point cloud classification and part-segmentation. We prove that the hierarchical of the receptive field among the permutation-constant neighborhood leads to better mean accuracy on the benchmark ModelNet40 dataset by 0.7pp with respect to the best method relying on local context aggregation — PointVGG. We proved that substituting a fully-connected MLP-based classifier with a convolution classifying module, followed by average pooling significantly reduces the complexity of the model without deterioration results. The code used in our study is open-source and publicly available in a repository under the MIT license at https://github.com/jamesWalczak/gva-net.