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Published at November 28

Scale Invariance of Graph Neural Networks

cs.LG

Released Date: November 28, 2024

Authors: Qin Jiang¹, Chengjia Wang¹, Michael Lones¹, Wei Pang¹

Aff.: ¹School of Mathematical and Computer Sciences Heriot-Watt University, Edinburgh, UK

Arxiv: http://arxiv.org/pdf/2411.19392v1

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Type	Method	Telegram	Cora-ML	CiteSeer	WikiCS	Chameleon	Squirrel
Base models	MLP	32.8±5.4	67.3±2.3	54.5±2.3	73.4±0.6	40.3±5.8	28.7±4.0
	GCN	86.0±4.5	81.2±1.4	65.8±2.3	78.8±0.4	64.8±2.2	46.3±1.9
	APPNP	67.3±3.0	81.8±1.3	65.9±1.6	77.6±0.6	38.7±2.4	27.0±1.5
	ChebNet	83.0±3.8	80.5±1.6	66.5±1.8	76.9±0.9	58.3±2.4	38.5±1.4
	SAGE	74.0±7.0	81.7±1.2	66.7±1.7	79.3±0.4	63.4±3.0	44.6±1.3
Hermitian	MagNet	87.6±2.9	79.7±2.3	66.5±2.0	74.7±0.6	58.2±2.9	39.0±1.9
	SigMaNet	86.9±6.2	71.7±3.3	44.9±3.1	71.4±0.7	64.1±1.6	OOM
	QuaNet	85.6±6.0	26.3±3.5	30.2±3.0	55.2±1.9	38.8±2.9	OOM
Symmetric	Sym	87.2±3.7	81.9±1.6	65.8±2.3	OOM	57.8±3.0	38.1±1.4
	DiG	82.0±3.1	78.4±0.9	63.8±2.0	77.1±1.0	50.4±2.1	39.2±1.8
	DiGib	64.1±7.0	77.5±1.9	60.3±1.5	78.3±0.7	52.2±3.7	37.7±1.5
Symmetric (Ours)	1ym	84.0±3.9	80.8±1.6	64.9±2.5	75.4±0.4	54.9±2.7	35.5±1.1
	1iG	95.8±3.5	82.0±1.3	65.5±2.4	77.4±0.6	70.2±1.6	50.7±5.8
	1iGi2	93.0±5.1	81.7±1.3	67.9±2.2	78.9±0.6	58.4±2.5	42.7±2.5
	1iGu2	92.6±4.9	82.1±1.2	67.6±1.8	75.6±0.9	60.4±2.4	40.4±1.8
BiDirection	Dir-GNN	90.2±4.8	79.2±2.1	61.6±2.6	77.2±0.8	79.4±1.4	75.2±1.7
Ours	ScaleNet	96.8±2.1	82.3±1.1	68.3±1.5	79.3±0.6	79.6±1.2	75.3±2.0
Ours	$\text{loop\_}\alpha,\beta,\gamma$	1_0.5,-1,-1	1_2,-1,-1	1_0.5,2,-1	1_0.5,2,-1	0_1,1,1	0_1,1,1