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Table 1 Core differences between model architectures

From: Building attention and edge message passing neural networks for bioactivity and physical–chemical property prediction

ModelHidden statesDenotion of neighbourhoodMessage 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
\(S_{vw}^{\left( t \right)} = \left\{ {h_{kv} | k \in N\left( v \right), k \ne w} \right\}\)