which selects all points with a radius around the centroid. However, it is difficult for ball query to ensure the information inside local regions, which is sensitive to the sparsity of the input point clouds.

![Self-attention module. The input of this module is a $D_1 \times D_2$ feature map and the output is another $D_1 \times (D_2 + C)$ feature map, where $C$ is a parameter.[]{data-label="fig:c_e"}](CE.pdf){height="4cm" width="8cm"}

Hierarchical Self-attention
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In current work of learning on point clouds, Multi-Layer-Perceptron (MLP) layer is widely applied to integrate multiple features. Traditional MLP layer first abstracts each feature into higher dimension individually and then aggregates these features by a concise max pooling operation. However, these two simple operations can hardly encode the correlation between feature vectors in the feature space. Inspired by the self-attention machanism in [@zhang2018sa], the attention machanism is suitable for improving the traditional MLP by learning the correlation between features. In this work, we propose a self-attention module to make up the defects of the MLP layer with an attention mechanism. Here, self-attention refers to learn the correlation among features in the same level.

Different from the raw self-attention, we enforce a hierarchical feature extraction architecture with hierarchical self-attention in 