Table 1 Core differences between model architectures
Model | Hidden states | Denotion of neighbourhood | Message aggregation scheme |
|---|---|---|---|
MPNN | \(h_{v}^{\left( t \right)}\) | \(N\left( v \right)\) | \(m_{v}^{\left( t \right)} = \mathop \sum \limits_{w \in N\left( v \right)} M_{t} \left( {h_{v}^{\left( t \right)} ,h_{w}^{\left( t \right)} ,e_{vw} } \right)\) |
AMPNN | \(h_{v}^{\left( t \right)}\) | \(N\left( v \right)\) | \(m_{v}^{\left( t \right)} = A_{t} \left( {h_{v}^{\left( t \right)} ,S_{v}^{\left( t \right)} } \right)\), where \(S_{v}^{\left( t \right)} = \left\{ {\left( {h_{w}^{\left( t \right)} ,e_{vw} } \right) | w \in N\left( v \right)} \right\}\) |
EMNN | \(h_{vw}^{\left( t \right)}\) | \(\left\{ {\left( {k,v} \right) | k \in N\left( v \right),k \ne w} \right\}\) | \(m_{vw}^{\left( t \right)} = A_{t} \left( {e_{vw} ,S_{vw}^{\left( t \right)} } \right)\), where \(S_{vw}^{\left( t \right)} = \left\{ {h_{kv} | k \in N\left( v \right), k \ne w} \right\}\) |