[Paper Review] Multi-hop Attention Graph Neural Network

Guangtao Wang, Zhitao Ying+2 more|arXiv (Cornell University)|Sep 29, 2020

Advanced Graph Neural Networks40 references35 citations

TL;DR

MAGNA introduces a diffusion-based multi-hop attention mechanism in GNNs, enabling context-dependent attention across large graph neighborhoods and achieving state-of-the-art results on node classification and knowledge graph completion.

ABSTRACT

Self-attention mechanism in graph neural networks (GNNs) led to state-of-the-art performance on many graph representation learning tasks. Currently, at every layer, attention is computed between connected pairs of nodes and depends solely on the representation of the two nodes. However, such attention mechanism does not account for nodes that are not directly connected but provide important network context. Here we propose Multi-hop Attention Graph Neural Network (MAGNA), a principled way to incorporate multi-hop context information into every layer of attention computation. MAGNA diffuses the attention scores across the network, which increases the receptive field for every layer of the GNN. Unlike previous approaches, MAGNA uses a diffusion prior on attention values, to efficiently account for all paths between the pair of disconnected nodes. We demonstrate in theory and experiments that MAGNA captures large-scale structural information in every layer, and has a low-pass effect that eliminates noisy high-frequency information from graph data. Experimental results on node classification as well as the knowledge graph completion benchmarks show that MAGNA achieves state-of-the-art results: MAGNA achieves up to 5.7 percent relative error reduction over the previous state-of-the-art on Cora, Citeseer, and Pubmed. MAGNA also obtains the best performance on a large-scale Open Graph Benchmark dataset. On knowledge graph completion MAGNA advances state-of-the-art on WN18RR and FB15k-237 across four different performance metrics.

Motivation & Objective

• Motivate improving GNN attention by incorporating multi-hop contextual information beyond direct neighbors.
• Propose a diffusion-based attention mechanism to compute context-dependent attention between any pair of nodes.
• Enable large-scale structural information processing while maintaining parameter efficiency.
• Demonstrate state-of-the-art performance on standard node classification benchmarks and knowledge graph completion datasets.

Proposed method

• Compute edge-level attention as in GAT but then diffuse attention scores across all paths using a diffusion operator with decaying path weights.
• Voice that diffusion yields a diffusion matrix A combining powers of the one-hop attention matrix, approximated with a stable iterative scheme (Z^(K) convergence).
• Use a multi-head attention diffusion layer with layer normalization and residual connections to stack MAGNA blocks.
• Relate MAGNA to Personalized PageRank, showing that diffused attention corresponds to a PPR prior over node pairs.
• Provide spectral analysis showing MAGNA acts as a graph low-pass filter that emphasizes large-scale structure and reduces high-frequency noise.

Experimental results

Research questions

• RQ1 Does incorporating multi-hop context via attention diffusion improve GNN performance on node classification and knowledge graph completion?
• RQ2 How does MAGNA relate to PPR, and what is its effect on graph spectral properties?
• RQ3 What are the empirical benefits and ablation effects of diffusion, layer normalization, and deep aggregation in MAGNA?

Key findings

• MAGNA achieves up to 5.7% relative error reduction over prior state-of-the-art on Cora, Citeseer, and Pubmed for node classification.
• MAGNA attains state-of-the-art results on Open Graph Benchmark (ogbn-arxiv) and on knowledge graph completion benchmarks (WN18RR and FB15k-237).
• MAGNA with 3 layers and 6-hop width outperforms GAT with 18 layers at equal receptive field, showing enhanced efficiency.
• Ablation studies show diffusion and layer normalization are crucial, with diffusion enabling multi-hop context and layer normalization stabilizing training.
• Spectral analysis indicates MAGNA amplifies smaller Laplacian eigenvalues (large-scale structure) and dampens larger eigenvalues (noise).
• MAGNA learns more diverse attention distributions than GAT, indicating better focus on important nodes.