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test 18
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nordinbelkacemi committed Jun 3, 2024
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Expand Up @@ -30,7 +30,7 @@ ing, simplicial complexes, equivariant message passing networks and message pass
networks.

### 2.1 Message passing
Let $G = (V,E)$ be a graph consisting of nodes $V$ and edges $E$. Then let each node $v_i \in V$ and edge $e_{ij} \in E$ have an associated node feature $\mathbf{f}_i \in \mathbb{R}^{c_n}$ and edge feature $\mathbf{a}_{ij}$ $\in \mathbb{R}^{c_e}$, with dimensionality $c_n, c_e \in \mathbb{N}_{>0}$. In message passing, nodes have hidden states (features). We update nodes' features iteratively via the following procedure:
Let $G = (V,E)$ be a graph consisting of nodes $V$ and edges $E$. Then let each node $v_i \in V$ and edge $e_{ij} \in E$ have an associated node feature $\mathbf{f}_i \in \mathbb{R}^{c_n}$ and edge feature $a_{ij}$ $\in \mathbb{R}^{c_e}$, with dimensionality $c_n, c_e \in \mathbb{N}_{>0}$. In message passing, nodes have hidden states (features). We update nodes' features iteratively via the following procedure:


$$\mathbf{m}_{ij}=\phi_m\left(\mathbf{f}_i, \mathbf{f}_j, \mathbf{a}_{i j}\right) \tag{1}
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