Table 4.

Graph neural network variants used for drug embedding matrix generation.

Model	Message Passing Function	Update Function
GCN	$m_v^{\left(t+1\right)}={\displaystyle \sum }_{\mathrm{w}\in \mathrm{N}\left(\mathrm{v}\right){{\displaystyle \cup }}^{ }\left\{\mathrm{v}\right\}}\frac{1}{{\mathrm{c}}_{\mathrm{wv}}}{\mathrm{h}}_{\mathrm{w}}^{\left(\mathrm{t}\right)}$  ${\mathrm{c}}_{\mathrm{wv}}=\frac{1}{\sqrt{\left|\mathrm{N}\left(\mathrm{v}\right)\right|\left|\mathrm{N}\left(\mathrm{w}\right)\right|}}$	$h_v^{\left(t+1\right)}=\mathsf{\sigma }({\mathrm{m}}_{\mathrm{v}}^{\left(\mathrm{t}+1\right)}{\mathrm{W}}^{\mathrm{t}})$
GAT	$m_v^{t+1}=\mathsf{\sigma }({\displaystyle \sum }_{\mathrm{w}\in \mathrm{N}\left(\mathrm{v}\right){{\displaystyle \cup }}^{ }\left\{\mathrm{v}\right\}}{\mathsf{\alpha }}_{\mathrm{vw}}{\mathrm{W}}^{\left(\mathrm{t}\right)}{\mathrm{h}}_{\mathrm{w}}^{\left(\mathrm{t}\right)})$, ${\mathsf{\alpha }}_{\mathrm{vw}}={ \mathrm{softmax}}_{\mathrm{v}}\left({\mathrm{e}}_{\mathrm{vw}}\right)$, ${\mathrm{e}}_{\mathrm{vw}}=\mathrm{LeakyReLU}\left({\mathrm{Wh}}_{\mathrm{v}},{\mathrm{Wh}}_{\mathrm{w}}\right)$	$h_v^{\left(t+1\right)}={\Vert }_{\mathrm{k}=1}^{\mathrm{K}}{\mathrm{m}}_{\mathrm{v}}^{\mathrm{t}+1}$, where ‖ is concatenation.
GIN	$m_v^{t+1}$ = ${\displaystyle \sum }_{\mathrm{w}\in \mathrm{N}\left(\mathrm{v}\right)}\mathrm{MLP}({\mathrm{h}}_{\mathrm{w}}^{\left(\mathrm{t}\right)})$	$h_v^{\left(t+1\right)}=\mathrm{MLP}({\mathrm{h}}_{\mathrm{v}}^{\left(\mathrm{t}\right)}+{\mathrm{m}}_{\mathrm{v}}^{\mathrm{t}+1})$
MPNN	$m_v^{t+1}$ = ${\displaystyle \sum }_{\mathrm{w}\in \mathrm{N}\left(\mathrm{v}\right)}\mathrm{A}\left({\mathrm{e}}_{\mathrm{vw}}\right){ \mathrm{h}}_{\mathrm{w}}^{\mathrm{t}}$	$h_v^{t+1}=\mathrm{GRU}\left({\mathrm{h}}_{\mathrm{v}}^{\mathrm{t}},{\mathrm{m}}_{\mathrm{v}}^{\mathrm{t}+1}\right)$
DMPNN	$m_{vw}^{t+1}$ = ${\displaystyle \sum }_{\mathrm{k}\in \left\{\mathrm{N}\left(\mathrm{v}\right)\setminus \mathrm{w}\right\}}{\mathrm{h}}_{\mathrm{kv}}^{\mathrm{t}}$	$h_{vw}^{t+1}= \mathsf{\tau }\left({\mathrm{h}}_{\mathrm{vw}}^0+{\mathrm{W}}_{\mathrm{m}}{\mathrm{m}}_{\mathrm{vw}}^{\mathrm{t}+1}\right)$

Notes: DMPNN, directed message-passing neural network; GAT, graph attention network; GCN, graph convolutional neural network; GIN, graph isomorphism network; MPNN, message-passing neural network.