readout layer

[[concept]]

Readout Layer

A readout layer is an additional layer added to a GNN to achieve the desired output type/dimension for graph-level tasks or other learning tasks on graphs that require an output that is not a graph signal.

Example

In node-level tasks (ex source localization, community detection, citation networks, etc), both the input and the output are graph signals $x\in {\mathbb{R}}^{n\times d_0},y\in {\mathbb{R}}^{n\times d_L}$. Thus, the map ${\Phi }_H$ is composed strictly of GNN layers.

• Benefit: convolutional graph filters are local. This ensures a parameterization that is independent of graph size $n$

GNN layer equation

$X_{\ell} = \sigma(U_{\ell}) = \sigma\left( \sum_{k=0}^{K-1} S^k X_{\ell-1} H_{\ell, k} \right)$$

When we learn our GNN layers, we fix $S$ and learn only $H_{\ell ,k}\in {\mathbb{R}}^{}$ which does not depend on the graph size.

Mentions

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