notesum.ai

Published at November 26

GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers

cs.LG

cs.AI

Released Date: November 26, 2024

Authors: Guoguo Ai¹, Guansong Pang², Hezhe Qiao², Yuan Gao¹, Hui Yan¹

Aff.: ¹School of Computer Science and Engineering Nanjing University of Science and Technology, Nanjing, China; ²School of Computing and Information Systems, Singapore Management University, Singapore

Arxiv: http://arxiv.org/abs/2411.17296v1

	Homophilic					Heterophilic
	Cora	Citeseer	Pubmed	Photo	Physics	Penn94	Chameleon	Squirrel	Actor	Texas
	Spatial-based GNNs
GCN	87.14 $\pm$ 1.01	79.86 $\pm$ 0.67	86.74 $\pm$ 0.27	88.26 $\pm$ 0.73	97.74 $\pm$ 0.35	82.47 $\pm$ 0.27	59.61 $\pm$ 2.21	46.78 $\pm$ 0.87	33.23 $\pm$ 1.16	77.38 $\pm$ 3.28
GAT	88.03 $\pm$ 0.79	80.52 $\pm$ 0.71	87.04 $\pm$ 0.24	92.94 $\pm$ 0.44	97.82 $\pm$ 0.28	81.53 $\pm$ 0.55	63.13 $\pm$ 1.93	44.49 $\pm$ 0.88	33.93 $\pm$ 2.47	80.82 $\pm$ 2.13
H2GCN	87.96 $\pm$ 0.37	80.90 $\pm$ 1.21	89.18 $\pm$ 0.28	95.45 $\pm$ 0.67	97.19 $\pm$ 0.13	81.31 $\pm$ 0.60	61.20 $\pm$ 4.28	39.53 $\pm$ 0.88	36.31 $\pm$ 2.58	91.89 $\pm$ 3.93
HopGNN	88.68 $\pm$ 1.06	80.38 $\pm$ 0.68	89.15 $\pm$ 0.35	94.49 $\pm$ 0.33	97.86 $\pm$ 0.16	OOM	65.25 $\pm$ 3.49	57.83 $\pm$ 2.11	39.33 $\pm$ 2.79	89.15 $\pm$ 4.04
	Spectral-based GNNs
ChebyNet	86.67 $\pm$ 0.82	79.11 $\pm$ 0.75	87.95 $\pm$ 0.28	93.77 $\pm$ 0.32	97.25 $\pm$ 0.78	81.55 $\pm$ 0.26	59.28 $\pm$ 1.25	40.55 $\pm$ 0.42	37.61 $\pm$ 0.89	86.22 $\pm$ 2.45
GPR-GNN	88.57 $\pm$ 0.69	80.12 $\pm$ 0.83	88.46 $\pm$ 0.33	93.85 $\pm$ 0.28	97.25 $\pm$ 0.13	81.38 $\pm$ 0.16	67.28 $\pm$ 1.09	50.15 $\pm$ 1.92	39.92 $\pm$ 0.67	92.95 $\pm$ 1.31
BernNet	88.52 $\pm$ 0.95	80.09 $\pm$ 0.79	88.48 $\pm$ 0.41	93.63 $\pm$ 0.35	97.36 $\pm$ 0.30	82.47 $\pm$ 0.21	68.29 $\pm$ 1.58	51.35 $\pm$ 0.73	41.79 $\pm$ 1.01	93.12 $\pm$ 0.65
JacobiConv	88.98 $\pm$ 0.46	80.78 $\pm$ 0.79	89.62 $\pm$ 0.41	95.43 $\pm$ 0.23	97.56 $\pm$ 0.28	83.35 $\pm$ 0.11	74.20 $\pm$ 1.03	57.38 $\pm$ 1.25	41.17 $\pm$ 0.64	93.44 $\pm$ 2.13
HiGCN	89.23 $\pm$ 0.23	81.12 $\pm$ 0.28	89.95 $\pm$ 0.13	95.33 $\pm$ 0.37	97.65 $\pm$ 0.35	OOM	68.47 $\pm$ 0.45	51.86 $\pm$ 0.42	41.81 $\pm$ 0.52	92.15 $\pm$ 0.73
	Graph Transformers
Transformer	76.29 $\pm$ 1.95	76.68 $\pm$ 1.21	86.66 $\pm$ 0.50	89.58 $\pm$ 1.05	OOM	OOM	45.21 $\pm$ 2.01	33.17 $\pm$ 1.32	39.95 $\pm$ .64	88.75 $\pm$ 6.30
NodeFormer	87.32 $\pm$ 0.92	79.56 $\pm$ 1.10	89.24 $\pm$ 0.23	95.27 $\pm$ 0.22	96.45 $\pm$ 0.28	69.66 $\pm$ 0.83	56.34 $\pm$ 1.11	43.42 $\pm$ 1.62	34.62 $\pm$ 1.82	84.63 $\pm$ 3.47
SGFormer	87.87 $\pm$ 2.67	79.62 $\pm$ 1.63	89.07 $\pm$ 0.14	94.34 $\pm$ 0.23	97.96 $\pm$ 0.81	76.65 $\pm$ 0.49	61.44 $\pm$ 1.37	45.82 $\pm$ 2.17	41.69 $\pm$ 0.63	92.46 $\pm$ 1.48
NAGphormer	88.15 $\pm$ 1.35	80.12 $\pm$ 1.24	89.70 $\pm$ 0.19	95.49 $\pm$ 0.11	97.85 $\pm$ 0.26	73.98 $\pm$ 0.53	54.92 $\pm$ 1.11	48.55 $\pm$ 2.56	40.08 $\pm$ 1.50	91.80 $\pm$ 1.85
Specformer	88.57 $\pm$ 1.01	81.49 $\pm$ 0.94	90.61 $\pm$ 0.23	95.48 $\pm$ 0.32	97.75 $\pm$ 0.53	84.32 $\pm$ 0.32	74.72 $\pm$ 1.29	64.64 $\pm$ 0.81	41.93 $\pm$ 1.04	88.23 $\pm$ 0.38
PolyFormer(Cheb)	87.67 $\pm$ 1.28	81.80 $\pm$ 0.76	90.68 $\pm$ 0.31	94.08 $\pm$ 1.37	98.08 $\pm$ 0.27	79.27 $\pm$ 0.26	60.17 $\pm$ 1.39	44.98 $\pm$ 3.03	41.51 $\pm$ 0.71	89.02 $\pm$ 5.44
GrokFormer	89.57 $\pm$ 1.43	81.92 $\pm$ 1.25	91.39 $\pm$ 0.51	95.52 $\pm$ 0.52	98.31 $\pm$ 0.18	83.59 $\pm$ 0.26	75.58 $\pm$ 1.73	65.12 $\pm$ 1.59	42.98 $\pm$ 1.48	94.59 $\pm$ 2.08