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Processing 3D data efficiently has always been a challenge. Spatial operations on large-scale point clouds, stored as sparse data, require extra cost. Attracted by the success of transformers, researchers are using multi-head attention for vision tasks. However, attention calculations in transformers come with quadratic complexity in the number of inputs and miss spatial intuition on sets like point clouds. We redesign set transformers in this work and incorporate them into a hierarchical framework for shape classification and part and scene segmentation. We propose our local attention unit, which captures features in a spatial neighborhood. We also compute efficient and dynamic global cross attentions by leveraging sampling and grouping at each iteration. Finally, to mitigate the non-heterogeneity of point clouds, we propose an efficient Multi-Scale Tokenization (MST), which extracts scale-invariant tokens for attention operations. The proposed hierarchical model achieves state-of-the-art shape classification in mean accuracy and yields results on par with the previous segmentation methods while requiring significantly fewer computations. Our proposed architecture predicts segmentation labels with around half the latency and parameter count of the previous most efficient method with comparable performance. The code is available at https://github.com/YigeWang-WHU/CloudAttention.