Local pooling layers coarsen the graph via downsampling. We present here several learnable local pooling strategies that have been proposed.[20] For each cases, the input is the initial graph is represented by a matrix X {\displaystyle \mathbf {X} } of node features, and the graph adjacency matrix A {\displaystyle \mathbf {A} } . The output is the new matrix X ′ {\displaystyle \mathbf {X} '} of node features, and the new graph adjacency matrix A ′ {\displaystyle \mathbf {A} '} .