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   Acc (%)   93.83   94.38   **95.37**   93.94  

  : The effects of the number of sampled points $M$ under ModelNet10.[]{data-label="table:sampled_points"}

The results are shown in Table \[table:sampled\_points\], where the instance accuracies on the benchmark of ModelNet10 have a tendency to rise first and then fall. This comparison implies that L2G-AE can effectively extract the contextual information in point clouds by multi-level feature propagation and $M=256$ is an optimal choice which can well cover input point clouds without excessive redundant.

![The reconstructed results with different sampled points, where the CD represents the Chamfer distance between ground-truth and the reconstructed point cloud.[]{data-label="fig:sample_re"}](sample.pdf){height="1.5cm" width="8cm"}

To learn the reconstructed results intuitively, Figure \[fig:sample\_re\] shows the reconstructed point clouds with different sampled points. According to Chamfer distances, L2G-AE can also reconstruct the input point cloud with the varying of sampled points.

With keeping the sampled points $M = 384$, we investigate the key parameter dimension $C$ inside the self-attention modules. To unify the parameter in self-attention module, we keep the same dimension $C$ in different semantic levels. We change the default $C = 32$ to 16 and 64, respectively. In Table \[table:c\], L2G-AE achieves the best performance when the feature dimension $C$ is 32.

     $M$      16        