Table 1.

Core differences between model architectures

Model	Hidden states	Denotion of neighbourhood	Message aggregation scheme
MPNN	$h_{v}^{(t)}$	$N (v)$	$m_{v}^{(t)} = \sum_{w \in N (v)} M_{t} (h_{v}^{(t)}, h_{w}^{(t)}, e_{vw})$
AMPNN	$h_{v}^{(t)}$	$N (v)$	$m_{v}^{(t)} = A_{t} (h_{v}^{(t)}, S_{v}^{(t)})$ , where $S_{v}^{(t)} = \{(h_{w}^{(t)}, e_{vw}) \| w \in N (v)\}$
EMNN	$h_{vw}^{(t)}$	$\{(k, v) \| k \in N (v), k \neq w\}$	$m_{vw}^{(t)} = A_{t} (e_{vw}, S_{vw}^{(t)})$ , where $S_{vw}^{(t)} = \{h_{kv} \| k \in N (v), k \neq w\}$

Model

Hidden states

Denotion of neighbourhood

Message aggregation scheme

MPNN

h_{v}^{(t)}

N (v)

m_{v}^{(t)} = \sum_{w \in N (v)} M_{t} (h_{v}^{(t)}, h_{w}^{(t)}, e_{vw})

AMPNN

h_{v}^{(t)}

N (v)

$m_{v}^{(t)} = A_{t} (h_{v}^{(t)}, S_{v}^{(t)})$ , where

$S_{v}^{(t)} = \{(h_{w}^{(t)}, e_{vw}) | w \in N (v)\}$

EMNN

h_{vw}^{(t)}

\{(k, v) | k \in N (v), k \neq w\}

$m_{vw}^{(t)} = A_{t} (e_{vw}, S_{vw}^{(t)})$ , where

$S_{vw}^{(t)} = \{h_{kv} | k \in N (v), k \neq w\}$