[Paper Review] LookHops: light multi-order convolution and pooling for graph classification

Zhangyang Gao, Haitao Lin+1 more|arXiv (Cornell University)|Dec 28, 2020

Advanced Graph Neural Networks22 references4 citations

TL;DR

This paper proposes LookHops, a lightweight multi-order graph convolution and pooling framework for graph classification that selects optimal $k$-hop neighborhoods via neighborhood information gain. It achieves state-of-the-art performance with fewer parameters and lower computation cost by combining efficient $k$-order convolutions and a novel $k$-order pooling module that jointly learns node importance and edge structure.

ABSTRACT

Convolution and pooling are the key operations to learn hierarchical representation for graph classification, where more expressive $k$-order($k>1$) method requires more computation cost, limiting the further applications. In this paper, we investigate the strategy of selecting $k$ via neighborhood information gain and propose light $k$-order convolution and pooling requiring fewer parameters while improving the performance. Comprehensive and fair experiments through six graph classification benchmarks show: 1) the performance improvement is consistent to the $k$-order information gain. 2) the proposed convolution requires fewer parameters while providing competitive results. 3) the proposed pooling outperforms SOTA algorithms in terms of efficiency and performance.

Motivation & Objective

• Address the high computational cost of expressive $k$-order graph convolutions ($k>1$) in graph classification.
• Develop a criterion for selecting the optimal $k$-hop neighborhood based on information gain to balance expressiveness and efficiency.
• Design a parameter-efficient $k$-order convolution module that maintains competitive performance with reduced model complexity.
• Propose a novel $k$-order pooling mechanism that jointly learns node importance and edge structure, improving both accuracy and efficiency over SOTA methods.

Proposed method

• Introduce a $k$-hop neighborhood information gain (kInfo) criterion to guide the selection of $k$ for $k$-order convolutions, ensuring effective receptive field expansion.
• Implement a light $k$-order convolution using learnable attention over $k$-hop neighbors, reducing parameters while preserving multi-hop message passing.
• Propose a $k$-order pooling module that combines normalized feature projection (NF), node-level pooling (pN), and edge-level structure learning (pE) for improved representation learning.
• Use LiCheb as the base convolution module, with learnable weights for $k$-hop message passing, enabling efficient approximation of higher-order graph signals.
• Integrate normalized features to improve node score estimation in pooling, replacing simple L2 norm with geometrically meaningful projections.
• Apply edge dropping based on endpoint feature differences to preserve structurally informative edges, enhancing performance through structure-aware compression.

Experimental results

Research questions

• RQ1 How can we effectively select the optimal $k$-hop neighborhood for graph convolution to balance expressiveness and computational cost?
• RQ2 Can a lightweight $k$-order convolution module achieve competitive performance with significantly fewer parameters than existing methods?
• RQ3 Does a $k$$-order pooling mechanism that jointly learns node importance and edge structure outperform existing SOTA pooling methods in both accuracy and efficiency?
• RQ4 To what extent does incorporating normalized features and edge-level structure learning improve the performance of graph pooling layers?
• RQ5 Under what conditions does graph pooling still provide benefits despite the risk of structural degradation in large graphs?

Key findings

• The proposed $k$-order convolution achieves consistent performance gains that correlate with the $k$-hop neighborhood information gain, validating the proposed selection criterion.
• The light $k$-order convolution module reduces parameter count while matching or exceeding the performance of SOTA models on all six benchmarks.
• The proposed pooling method outperforms TopkPool, SAGPool, ASAP, and EdgePool in both accuracy and inference speed, achieving SOTA results on D&D, NCI1, NCI109, and Mutagenicity.
• Ablation studies confirm that normalized features (NF) improve performance on most datasets by providing better node importance scores, except on D&D and Mutagenicity.
• Edge-level structure learning (pE) further boosts performance by preserving high-difference edges, indicating redundancy in original graph edges.
• The full LookHops model (NF + pN + pE) achieves 78.2% accuracy on NCI1, 80.3% on Mutagenicity, and 65.0% on Far, with only 116.7k parameters and 196.3s training time over 50 epochs—significantly faster than SOTA methods.