Table 1 Algorithm of ABT-MPNN

1)

Given a molecular graph \(G\), generate atom features \({x}_{v}\) and bond features \({e}_{vw}\)

where \(v\in Atom\left(G\right)\) and \(w\in Neighbor\left(v\right)\); three inter-atomic matrices \({M}_{Adjacency},{M}_{Distance},{M}_{Coulomb}\); molecular descriptors \({h}_{f}\)

2)

for each atom \(v\) in molecule \(G\):

3)

    for each atom \(w\) in molecule \(Neighbor\left(v\right)\):

4)

\(\,\,\,\,\,\,\,\,{h}_{vw}^{0}\leftarrow ReLU({W}_{i}Concat\left({x}_{v},{e}_{vw}\right))\)

1)

Message-passing iteration:\(t=1, 2,\dots ,T\)

2)

while \(1\le t\le T\):

3)

    for each atom \(v\) in molecule \(G\):

4)

        for each atom \(w\) in molecule \(Neighbor\left(v\right)\):

5)

\(\,\,\,\,\,\,\,\,\,\,\,\,{m}_{vw}^{t}\leftarrow \sum_{k\in Neighbor\left(v\right)}{h}_{kv}^{t-1}-{h}_{wv}^{t-1}\)

6)

\(\,\,\,\,\,\,\,\,\,\,\,\,{b}_{vw}^{t}\leftarrow BondAttention\left({m}_{vw}^{t}\right)+{m}_{vw}^{t}\)

7)

\(\,\,\,\,\,\,\,\,\,\,\,\,{h}_{vw}^{t}\leftarrow ReLU({h}_{vw}^{0}+{W}_{h} {b}_{vw}^{t})\)

1)

for each atom \(v\) in molecule \(G\):

2)

\(\,\,\,\,{m}_{v}\leftarrow ReLU({W}_{o}Concat({x}_{v},\sum_{w\in Neighbor\left(v\right)}{h}_{vw}^{T}))\)

3)

\(\,\,\,\,{h}_{v}\leftarrow AtomAttention\left({m}_{v},{M}_{Adjacency},{M}_{Distance},{M}_{Coulomb }\right)+{m}_{v}\)

1)

\(h\leftarrow \sum_{v\in G}{h}_{v}\)

2)

\(\widehat{y}\leftarrow FFN(Concat(h,{h}_{f}))\)