Besides considering the layer-wise node features propagated within the GNN, CAs can additionally incorporate various structural interventions, such as node cluster embedding, and higher-order structural correlations that can be learned outside of GNN, when computing attention scores. The node features that are regarded as significant by the conjoint criteria are therefore more likely to be propagated in the GNN. Given the novel Conjoint Attention strategies, we then propose Graph conjoint attention networks (CATs) that can learn representations embedded with significant latent features deemed by the Conjoint Attentions.

To prove Theorem 1, we need to consider the two directions of the iff conditions. Obviously, the above equation does not hold as the terms in the summation operator are positive. Eq. (4), we have: null However, the RHS of Eq. (10) can be an RHS is an irrational number, while LHS is a rational number. Eq. (9) can be rewritten as: null To prove Theorem 2, we can follow the procedure which is used to prove Theorem 1. As Eq. (20) holds for any Obviously, the above equation does not hold as softmax function is positive.

Graph neural networks (GNNs) have shown much success in the learning of graph structured data.

Besides considering the layer-wise node features propagated within the GNN, CAs can additionally incorporate various structural interventions, such as node cluster embedding, and higher-order structural correlations that can be learned outside of GNN, when computing attention scores. The node features that are regarded as significant by the conjoint criteria are therefore more likely to be propagated in the GNN. Given the novel Conjoint Attention strategies, we then propose Graph conjoint attention networks (CATs) that can learn representations embedded with significant latent features deemed by the Conjoint Attentions. CATs utilizing the proposed Conjoint Attention strategies have been extensively tested in well-established benchmarking datasets and comprehensively compared with state-of-the-art baselines. The obtained notable performance demonstrates the effectiveness of the proposed Conjoint Attentions.