Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs

Martin Simonovsky, N. Komodakis

Abstract

A number of problems can be formulated as prediction on graph-structured data. In this work, we generalize the convolution operator from regular grids to arbitrary graphs while avoiding the spectral domain, which allows us to handle graphs of varying size and connectivity. To move beyond a simple diffusion, filter weights are conditioned on the specific edge labels in the neighborhood of a vertex. Together with the proper choice of graph coarsening, we explore constructing deep neural networks for graph classification. In particular, we demonstrate the generality of our formulation in point cloud classification, where we set the new state of the art, and on a graph classification dataset, where we outperform other deep learning approaches. The source code is available at.

Benchmark Results

Tested on 4 datasets 2 baseline values reported too low

Tables show presented results in global context (best 3 papers + GCN + MLP).

TU Dortmund

MUTAG

Global leaderboard →

#	Model	Accuracy ↑	Paper
1	MSH-GNN GNN global	0.9910 ±0.0030	Multi-Scale Harmonic Encoding for Feature-Wise Graph Message Passing
2	ID-GNN+BEC Hyb global	0.9830 ±0.0360	Depth-Adaptive Graph Neural Networks via Learnable Bakry-Émery Curvature
3	SupCosine Hyb global	0.9830 ±0.0250	Supervised Contrastive Learning with Structure Inference for Graph Classification
39	GIN GNN global	0.9330 ±0.0290	ProtGNN: Towards Self-Explaining Graph Neural Networks
51	PSCN GNN baseline	0.9263	This paper
159	WL Trad baseline actual #159 vs paper #498 339 places worse	0.9040 ±0.0570 best reported	actual #159 vs paper #498 339 places worse paper 0.8378 best at pub: On Valid Optimal Assignment Kernels and Applications to Graph Classification (NeurIPS 2016) best today: How Powerful are $K$-hop Message Passing Graph Neural Networks (NeurIPS 2022) paper 0.8378 Δ at pub 0.0222 Δ today 0.0662
236	ECC GNN baseline	0.8944	This paper
323	structure2vec GNN baseline	0.8828	This paper
366	deepwl GNN baseline	0.8744	This paper
403	MLP code ↗ Trad global	0.8660 ±0.0495	Breaking the Limits of Message Passing Graph Neural Networks code ↗
770	DCNN Trad baseline actual #770 vs paper #770	0.6700 best reported	actual #770 vs paper #770 paper 0.6698 best today: IGNN-Solver: A Graph Neural Solver for Implicit Graph Neural Networks (2024) paper 0.6698 Δ today 0.0002

NCI1

Global leaderboard →

#	Model	Accuracy ↑	Paper
1	WL-MLP GT global	0.9954	1-WL Expressiveness Is (Almost) All You Need
2	GIN GNN global	0.9934	1-WL Expressiveness Is (Almost) All You Need
3	GCN GNN global	0.9727	1-WL Expressiveness Is (Almost) All You Need
12	WL Trad baseline actual #12 vs paper #27 15 places worse	0.8590 ±0.0010 best reported	actual #12 vs paper #27 15 places worse paper 0.8455 best at pub: Propagation Kernels (2014) paper 0.8455 Δ at pub 0.0135
43	ECC GNN baseline	0.8380	This paper
45	structure2vec GNN baseline	0.8372	This paper
131	GraphSAGE code ↗ GNN global	0.8200 ±0.0100	Weisfeiler and Leman Go Infinite: Spectral and Combinatorial Pre-Colorings code ↗
211	deepwl GNN baseline	0.8031	This paper
291	PSCN GNN baseline	0.7859	This paper
540	DCNN Trad baseline	0.6261	This paper

ENZYMES

Global leaderboard →

#	Model	Accuracy ↑	Paper
1	GMN code ↗ Hyb global	0.7866	Memory-Based Graph Networks code ↗
2	MemGNN code ↗ Hyb global	0.7550	Memory-Based Graph Networks code ↗
3	TFGW SP Hyb global	0.7510 ±0.0500	Template based Graph Neural Network with Optimal Transport Distances
17	GatedGCN code ↗ GNN global	0.7000 ±0.0494	GNNBenchmark code ↗
18	WL Trad baseline actual #18 vs paper #107 89 places worse	0.5905	actual #18 vs paper #107 89 places worse paper 0.5905 prev best: The Multiscale Laplacian Graph Kernel (NeurIPS 2016) best today: Template based Graph Neural Network with Optimal Transport Distances (NeurIPS 2022) paper 0.5905 Δ at pub 0.0530 Δ today 0.1045
26	GraphSAGE code ↗ GNN global	0.6817 ±0.0545	GNNBenchmark code ↗
80	structure2vec GNN baseline	0.6110	This paper
124	MLP code ↗ Trad global	0.5583 ±0.0352	GNNBenchmark code ↗
143	ECC GNN ★ proposed	0.5350	This paper
144	deepwl GNN baseline actual #144 vs paper #144	0.5343	actual #144 vs paper #144 paper 0.5343 prev best: Diffusion-Convolutional Neural Networks (NeurIPS 2015) paper 0.5343 Δ at pub 0.3188
181	DCNN Trad baseline actual #181 vs paper #298 117 places worse	0.4244 ±0.0176 best reported	actual #181 vs paper #298 117 places worse paper 0.1810 best today: Graph Capsule Convolutional Neural Networks (ICML 2018) paper 0.1810 Δ today 0.2434

D&D

Global leaderboard →

#	Model	Accuracy ↑	Paper
1	GC-GNN (GCN) GNN global	0.9210 ±0.0810	Rethinking the Power of Graph Canonization in Graph Representation Learning with Stability
2	SUGAR code ↗ Hyb global	0.8403 ±0.0133	SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information … code ↗
3	Ortho-g-U-Nets global	0.8387	Orthogonal Graph Neural Networks
7	structure2vec GNN baseline	0.8222	This paper
15	SAGE GNN global	0.8088 ±0.0233	Semi-Supervised Hierarchical Graph Classification
25	WL Trad baseline actual #25 vs paper #25	0.7978	actual #25 vs paper #25 paper 0.7978 prev best: On Valid Optimal Assignment Kernels and Applications to Graph Classification (NeurIPS 2016) paper 0.7978 Δ at pub 0.0078
101	PSCN GNN baseline	0.7712	This paper

SOTA performance (not significantly different from the best) Proposed method (this paper) Baseline / comparison (this paper) Global context (other papers) Best at pub — reported result worse than the best known when published (best reported in green) Best at pub — reported value improved over the best known when published Improved at pub — later paper surpassed this result Best today — OK at publication; today's leaderboard best is elsewhere