[论文解读] Are Powerful Graph Neural Nets Necessary? A Dissection on Graph Classification

Ting Chen, Song Bian+1 more|arXiv (Cornell University)|May 11, 2019

Advanced Graph Neural Networks参考文献 25被引用 52

一句话总结

该论文提出 Graph Feature Network (GFN) 和 Graph Linear Network (GLN) 通过对 GNN 的图筛选和集合函数部分进行线性化。GFN 在成本更低的情况下达到或超过最先进的 GNN，而 GLN 表现较差，突显非线性集合函数的重要性。

ABSTRACT

Graph Neural Nets (GNNs) have received increasing attentions, partially due to their superior performance in many node and graph classification tasks. However, there is a lack of understanding on what they are learning and how sophisticated the learned graph functions are. In this work, we propose a dissection of GNNs on graph classification into two parts: 1) the graph filtering, where graph-based neighbor aggregations are performed, and 2) the set function, where a set of hidden node features are composed for prediction. To study the importance of both parts, we propose to linearize them separately. We first linearize the graph filtering function, resulting Graph Feature Network (GFN), which is a simple lightweight neural net defined on a extit{set} of graph augmented features. Further linearization of GFN's set function results in Graph Linear Network (GLN), which is a linear function. Empirically we perform evaluations on common graph classification benchmarks. To our surprise, we find that, despite the simplification, GFN could match or exceed the best accuracies produced by recently proposed GNNs (with a fraction of computation cost), while GLN underperforms significantly. Our results demonstrate the importance of non-linear set function, and suggest that linear graph filtering with non-linear set function is an efficient and powerful scheme for modeling existing graph classification benchmarks.

研究动机与目标

• Motivate understanding of what GNNs learn for graph classification by decomposing into graph filtering and set function stages.
• Introduce linearized variants (GFN and GLN) to isolate the impact of each part.
• Empirically evaluate on standard graph classification benchmarks to compare against state-of-the-art GNNs.
• Show that non-linear set functions are important while non-linear graph filtering may be unnecessary for the tested benchmarks.

提出的方法

• Define Graph Feature Network (GFN) as a neural set function operating on graph-augmented features X^G.
• Construct graph-augmented features X^G using node degrees and multi-scale propagated features: X^G = [d, X, A˜X, A˜²X, ..., A˜^K X].
• Describe GFN as a permutation-invariant function: GFN(G,X) = ρ( sum_{v in V} φ(X^G_v) ).
• Define Graph Linear Network (GLN) as a linear readout over augmented features: GLN(G,X) = σ( W sum_v X^G_v ).
• Linearize graph filtering to compare with GNNs: F_G(X) = Γ(G,X) θ, enabling equivalence GNN^lin(G,X) = GFN(G,X).
• Experimentally compare GFN, GLN, and GCN-like baselines on graph classification benchmarks, focusing on accuracy and efficiency.

实验结果

研究问题

• RQ1 Do we need a sophisticated graph filtering function for graph classification tasks/datasets?
• RQ2 If the set function is powerful, is a simple graph filtering function sufficient?
• RQ3 How do linearized variants (GFN/GLN) perform relative to standard GNNs on benchmark datasets?
• RQ4 What is the relative importance of non-linearity in graph filtering vs. the set function?
• RQ5 Do linear graph filtering and non-linear set functions provide a good trade-off between accuracy and computation?

主要发现

Algorithm	MUTAG	NCI1	PROTEINS	D&D	ENZYMES	Average
WL	82.05 ± 0.36	82.19 ± 0.18	74.68 ± 0.49	79.78 ± 0.36	52.22 ± 1.26	74.18
AWE	87.87 ± 9.76	-	-	71.51 ± 4.02	35.77 ± 5.93	-
DGK	87.44 ± 2.72	80.31 ± 0.46	75.68 ± 0.54	73.50 ± 1.01	53.43 ± 0.91	74.07
RetGK I	90.30 ± 1.10	84.50 ± 0.20	75.80 ± 0.60	81.60 ± 0.30	60.40 ± 0.80	78.52
RetGK II	90.10 ± 1.00	83.50 ± 0.20	75.20 ± 0.30	81.00 ± 0.50	59.10 ± 1.10	77.78
GNTK	90.00 ± 8.50	84.20 ± 1.50	75.60 ± 4.20	-	-	-
PSCN	88.95 ± 4.37	76.34 ± 1.68	75.00 ± 2.51	76.27 ± 2.64	-	-
DGCNN	85.83 ± 1.66	74.44 ± 0.47	75.54 ± 0.94	79.37 ± 0.94	51.00 ± 7.29	73.24
CapsGNN	86.67 ± 6.88	78.35 ± 1.55	76.28 ± 3.63	75.38 ± 4.17	54.67 ± 5.67	74.27
GIN	89.40 ± 5.60	82.70 ± 1.70	76.20 ± 2.80	-	-	-
GCN	87.20 ± 5.11	83.65 ± 1.69	75.65 ± 3.24	79.12 ± 3.07	66.50 ± 6.91	78.42
GLN	82.85 ± 12.15	68.61 ± 2.31	75.65 ± 4.43	76.75 ± 5.00	43.83 ± 5.16	69.54
GFN	90.84 ± 7.22	82.77 ± 1.49	76.46 ± 4.06	78.78 ± 3.49	70.17 ± 5.58	79.80
GFN-light	89.89 ± 7.14	81.43 ± 1.65	77.44 ± 3.77	78.62 ± 5.43	69.50 ± 7.37	79.38

• GFN matches or exceeds the best accuracies of recently proposed GNNs on multiple benchmarks at a fraction of the computation cost.
• GLN underperforms compared to GFN and standard GNNs, highlighting the importance of a non-linear set function.
• Linear graph filtering has little impact on performance, suggesting that linearized filtering can be sufficient for current graph classification benchmarks.
• GFN achieves competitive or superior performance across biological and social graph datasets.
• GFN generalizes as well or better than GCN, indicating helpful inductive bias from linear filtering on these tasks.