[Paper Review] 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 NetworksComputer Science25 references52 citations

TL;DR

The paper proposes Graph Feature Network (GFN) and Graph Linear Network (GLN) by linearizing graph filtering and set-function parts of GNNs. GFN matches or exceeds state-of-the-art GNNs with lower cost, while GLN underperforms, highlighting the importance of non-linear set functions.

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.

Motivation & Objective

• 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.

Proposed method

• 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.

Experimental results

Research questions

• 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?

Key findings

• 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.