Research map / Graph learning / GNN architectures
Implicit Graph Neural Networks: A Monotone Operator Viewpoint
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| monotone parameterization (MIGNN-Mon) instead of IGNN's parameterization | IGNN · Cora / Citeseer / Pubmed node classification | accuracy: Cora 85.80->87.02; Citeseer 75.24->76.15; Pubmed 87.66->89.18 | Helped |
| orthogonal (Cayley) parameterization with Neumann series K-hop approximation (MIGNN-NK) | IGNN · Cora / Citeseer / Pubmed node classification | accuracy: Cora 85.80->88.31; Citeseer 75.24->76.91; Pubmed 87.66->89.28 | Helped |
| monotone parameterization (MIGNN-Mon) | IGNN · MUTAG / PTC graph classification | accuracy: MUTAG 76.0->81.8 (improves); PTC 60.5->72.6 (improves) | Mixed |
| monotone parameterization (MIGNN-Mon) | IGNN · NCI1 graph classification | accuracy: 73.5 -> 73.6 | No clear effect |
| orthogonal parameterization with Neumann order 1 (MIGNN-N1) | IGNN · Amazon node classification (5%-9% train) | Micro-F1: 5%: 84.01->84.59; 9%: 87.26->87.09 | Mixed |
| orthogonal parameterization with Neumann order 3 (MIGNN-N3) | IGNN · Graph classification (5 benchmarks) | accuracy: MUTAG 76.0->91.4; COX2 79.7->88.2; PROTEINS 76.5->80.1; NCI1 73.5->80.8 | Helped |
| orthogonal parameterization with Neumann series (MIGNN-N1) vs IGNN | IGNN · Amazon training time and iterations | time per epoch and forward iterations: lower time and iterations than IGNN | Helped |
| orthogonal parameterization with Neumann order 3 or 5 (MIGNN-N3/N5) | IGNN · Directed chain classification (binary and three-class, lengths 50-300) | accuracy: classify chains almost perfectly for all lengths | Helped |
| monotone and orthogonal parameterizations vs IGNN on 3D pore-network physical diffusion | IGNN · Pore networks (200-500 pores) MSE | MSE: MIGNN with both parameterizations outperforms IGNN by a significant margin | Helped |
| monotone parameterization vs IGNN on MUTAG/PTC/COX2/PROTEINS/NCI1 | IGNN · Five graph classification benchmarks | accuracy: MUTAG 76.0->81.8, PTC 60.5->72.6, COX2 79.7->85.0, PROTEINS 76.5->77.9, NCI1 73.5->73.6 | Mixed |
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