[@Deng2018ppffoldnet] also learns local descriptors on point cloud with a folding operation. LGAN [@Achlioptas2017latent] proposes an auto-encoder based on PointNet and extends the decoder module to the point cloud generation application with GAN. In this work, we propose a novel auto-encoder architecture to learn representations for point clouds. On the encoder side, an hierarchical self-attention mechanism is applied to embedding the correlation among features in each level. And on the decoder side, an interpolation layer and a RNN decoding layer are engaged to reconstruct multi-scale areas inside local regions. After building local areas, the global point cloud is generated by a fully-connected (FC) layer which acts as a down sampling function.

Method
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Now we introduce the L2G-AE in detail, where the structure is illustrated in Figure \[fig:architecture\]. The input of the encoder is an unordered point set $\bm{P} = \{p_1, p_2, \cdots, p_N \}$ with $N$ ($N=1024$) points. Each point in the point set is composed of a 3D coordinate $(x,y,z)$. L2G-AE first establishes multi-scale areas $\bm{A}_t$ $(t \in [1,T])$ in each local region around the sampled points. Then, a hierarchical feature abstraction is enforced to obtain the global features of input point clouds with self-attentions. In the decoder, 