Graph Attention Network GAT Equation Formula Latex Code and Summary

Graph Attention Network GAT

Tags: #machine learning #graph #GNN

Equation

$$h=\{\vec{h_{1}},\vec{h_{2}},...,\vec{h_{N}}\}, \\ \vec{h_{i}} \in \mathbb{R}^{F} \\ W \in \mathbb{R}^{F \times F^{'}} \\ e_{ij}=a(Wh_{i},Wh_{j}) \\ k \in \mathcal{N}_{i},\text{ neighbourhood nodes}\\ a_{ij}=\text{softmax}_{j}(e_{ij})=\frac{\exp(e_{ij})}{\sum_{k \in \mathcal{N}_{i}} \exp(e_{ik})}$$

Latex Code

                                 h=\{\vec{h_{1}},\vec{h_{2}},...,\vec{h_{N}}\}, \\
            \vec{h_{i}} \in \mathbb{R}^{F} \\
            W \in \mathbb{R}^{F \times F^{'}} \\
            e_{ij}=a(Wh_{i},Wh_{j}) \\
            k \in \mathcal{N}_{i},\text{ neighbourhood nodes}\\
            a_{ij}=\text{softmax}_{j}(e_{ij})=\frac{\exp(e_{ij})}{\sum_{k \in \mathcal{N}_{i}} \exp(e_{ik})}

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Introduction

$h=\{\vec{h_{1}},\vec{h_{2}},...,\vec{h_{N}}\}, \\ \vec{h_{i}} \in \mathbb{R}^{F} \\ W \in \mathbb{R}^{F \times F^{'}} \\ e_{ij}=a(Wh_{i},Wh_{j}) \\ k \in \mathcal{N}_{i},\text{ neighbourhood nodes}\\ a_{ij}=\text{softmax}_{j}(e_{ij})=\frac{\exp(e_{ij})}{\sum_{k \in \mathcal{N}_{i}} \exp(e_{ik})}$

Latex Code

            h=\{\vec{h_{1}},\vec{h_{2}},...,\vec{h_{N}}\}, \\
            \vec{h_{i}} \in \mathbb{R}^{F} \\
            W \in \mathbb{R}^{F \times F^{'}} \\
            e_{ij}=a(Wh_{i},Wh_{j}) \\
            k \in \mathcal{N}_{i},\text{ neighbourhood nodes}\\
            a_{ij}=\text{softmax}_{j}(e_{ij})=\frac{\exp(e_{ij})}{\sum_{k \in \mathcal{N}_{i}} \exp(e_{ik})}

Explanation

GAT applies graph attentional layer to model the graph propagation. In each layer, the node i has attention on all the other nodes j. And the attention coefficient is calculated. For the attention calculation, only the set of neighbours nodes N_{i} of each node i contributes to the final softmax attention calculation. You can check more detailed information in this paper, GRAPH ATTENTION NETWORKS for more details.

Discussion

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Lauren Sanchez

All I'm asking for is to pass this test!

2023-11-17 00:00
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Evelyn Nelson reply to Lauren Sanchez

Best Wishes.

2023-12-15 00:00:00.0
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Hugo Chandler

Keeping my head up and aiming for a pass on this test.

2024-01-22 00:00
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Brian Clark reply to Hugo Chandler

You can make it...

2024-02-11 00:00:00.0
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Tammy Ward

Please let me pass this test.

2023-06-09 00:00
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You can make it...

2023-06-11 00:00:00.0
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