SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table 26: Graph Theory Benchmark results on Pseudotree graphs, all results are obtained using our codebase.
Category	Model	\(SP_{sssd}\)	MCC	Diameter	\(SP_{ss}\)	ECC
Baselines (h=1)	n=1	1.93 ±0.239	1.71 ±0.281	2.78 ±0.098	6.27 ±0.004	4.23 ±0.034
n=5	0.061 ±0.024	0.942 ±0.094	1.74 ±0.299	1.54 ±0.006	4.15 ±0.086
n=10	0.037 ±0.022	0.775 ±0.094	1.84 ±0.260	0.126 ±0.038	4.06 ±0.037
MeGraph(h=5)	n=1	0.404 ±0.096	1.75 ±0.133	1.50 ±0.494	2.25 ±0.280	3.97 ±0.270
EdgePool(\(τ_c\)=2)	n=5	0.141 ±0.022	0.999 ±0.054	1.16 ±0.069	0.148 ±0.034	3.12 ±0.202
\(\tau_c\)=3	0.130 ±0.069	0.912 ±0.073	0.669 ±0.080	0.115 ±0.015	0.797 ±0.079
MeGraph	\(\eta_v\)=0.3	0.048 ±0.030	0.839 ±0.077	0.758 ±0.134	0.246 ±0.021	0.838 ±0.023
S-EdgePool	\(\eta_v\)=0.3,\(τ_c\)=4	0.106 ±0.054	0.814 ±0.092	0.663 ±0.076	0.133 ±0.028	0.845 ±0.101
Variants (h=5, n=5)	\(\eta_v\)=0.5,\(τ_c\)=4	0.071 ±0.048	1.03 ±0.186	0.583 ±0.065	0.171 ±0.038	0.868 ±0.034
\(\eta_v\)=0.3,\(τ_c\)=4 (X-Pool)	0.564 ±0.155	0.966 ±0.172	0.977 ±0.054	0.611 ±0.065	1.10 ±0.036
\(\eta_v\)=0.3,\(τ_c\)=4 (w/o pw)	0.080 ±0.033	0.971 ±0.072	0.956 ±0.230	0.276 ±0.017	1.13 ±0.321
Graph-UNets	h=5,n=9,\(\eta_v\)=0.3,\(τ_c\)=4	0.467 ±0.065	1.09 ±0.072	1.71 ±0.295	0.721 ±0.092	2.25 ±0.327
Table 27: Graph Theory Benchmark results on Geo graphs, all results are obtained using our codebase.
Category	Model	\(SP_{sssd}\)	MCC	Diameter	\(SP_{ss}\)	ECC
Baselines (h=1)	n=1	5.79 ±0.630	0.424 ±0.023	11.85 ±0.391	12.49 ±0.035	14.82 ±0.056
n=5	1.02 ±0.772	0.407 ±0.040	8.37 ±0.468	5.10 ±0.435	14.33 ±0.079
n=10	0.304 ±0.125	0.404 ±0.061	9.41 ±0.759	0.803 ±0.162	14.33 ±0.136
MeGraph(h=5)	n=1	1.60 ±0.880	0.347 ±0.033	10.17 ±2.04	4.87 ±0.777	11.91 ±0.451
EdgePool(\(τ_c\)=2)	n=5	0.232 ±0.061	0.273 ±0.018	2.70 ±0.288	0.575 ±0.127	6.92 ±2.36
MeGraph S-EdgePool Variants (h=5, n=5)	\(\tau_c\)=3	0.188 ±0.100	0.288 ±0.020	2.04 ±0.225	0.562 ±0.186	2.42 ±0.333
\(\eta_v\)=0.3	1.38 ±0.617	0.330 ±0.025	4.40 ±1.15	1.37 ±0.083	5.45 ±0.465
\(\eta_v\)=0.3, \(\tau_c\)=4	0.230 ±0.070	0.231 ±0.034	1.99 ±0.549	0.454 ±0.057	2.69 ±0.369
\(\eta_v\)=0.5, \(\tau_c\)=4	0.374 ±0.148	0.368 ±0.043	3.95 ±0.319	0.777 ±0.122	4.61 ±0.717
\(\eta_v\)=0.3, \(\tau_c\)=4 (X-Pool)	1.04 ±0.502	0.362 ±0.031	2.32 ±0.440	2.37 ±0.260	5.08 ±0.737
\(\eta_v\)=0.3, \(\tau_c\)=4 (w/o pw)	0.233 ±0.046	0.261 ±0.035	2.58 ±0.617	1.09 ±0.226	4.85 ±0.805
Graph-UNets	h=5,n=9,\(\eta_v\)=0.3,\(\tau_c\)=4	1.49 ±0.451	0.400 ±0.020	4.63 ±0.647	2.42 ±0.458	7.36 ±1.62
Table 28: Graph Theory Benchmark results on SBM graphs, all results are obtained using our codebase.
Category	Model	\(SP_{sssd}\)	MCC	Diameter	\(SP_{ss}\)	ECC
Baselines (h=1)	n=1	1.14 ±0.084	3.28 ±0.135	3.05 ±0.171	1.43 ±0.020	3.47 ±0.026
n=5	0.420 ±0.018	3.14 ±0.131	2.77 ±0.383	0.100 ±0.050	3.18 ±0.093
n=10	0.704 ±0.264	3.29 ±0.063	2.70 ±0.235	0.012 ±0.005	2.97 ±0.051
MeGraph(h=5)	n=1	0.786 ±0.145	2.79 ±0.226	2.49 ±0.692	0.547 ±0.059	3.35 ±0.195
EdgePool(\(τ_c\)=2)	n=5	0.525 ±0.136	2.88 ±0.300	2.37 ±0.336	0.058 ±0.031	3.01 ±1.07
MeGraph S-EdgePool Variants (h=5, n=5)	\(\tau_c\)=3	0.783 ±0.149	2.80 ±0.172	2.16 ±0.449	0.076 ±0.044	1.98 ±0.497
\(\eta_v\)=0.3	1.16 ±0.131	3.51 ±0.312	2.03 ±0.429	0.058 ±0.027	1.86 ±0.098
\(\eta_v\)=0.3,\(τ_c\)=4	0.926 ±0.087	2.62 ±0.179	1.99 ±0.290	0.062 ±0.027	1.57 ±0.205
\(\eta_v\)=0.5,\(τ_c\)=4	0.798 ±0.255	3.14 ±0.234	2.05 ±0.375	0.063 ±0.013	1.70 ±0.049
\(\eta_v\)=0.3,\(τ_c\)=4 (X-Pool)	0.935 ±0.106	2.60 ±0.374	2.16 ±0.204	0.056 ±0.014	1.87 ±0.111
\(\eta_v\)=0.3,\(τ_c\)=4 (w/o pw)	0.788 ±0.063	2.52 ±0.100	1.38 ±0.131	0.484 ±0.063	2.21 ±0.169
Graph-UNets	h=5,n=9,\(\eta_v\)=0.3,\(τ_c\)=4	1.51 ±0.138	3.57 ±0.569	1.96 ±0.240	1.71 ±0.115	2.77 ±0.160
Table 29: Graph Theory Benchmark results on BA graphs, all results are obtained using our codebase.
Category	Model	\(SP_{sssd}\)	MCC	Diameter	\(SP_{ss}\)	ECC
Baselines (h=1)	n=1	0.004 ± 0.001	2.81 ± 0.142	0.092 ± 0.021	-	0.128 ± 0.006
n=5	0.007 ± 0.002	3.65 ± 0.660	0.098 ± 0.014	-	0.091 ± 0.011
n=10	0.011 ± 0.006	3.72 ± 0.376	0.122 ± 0.038	-	0.080 ± 0.004
MeGraph(h=5)	n=1	0.006 ± 0.004	2.00 ± 0.380	0.101 ± 0.020	-	0.084 ± 0.017
EdgePool(\(τ_c\)=2)	n=5	0.003 ± 0.001	2.00 ± 0.240	0.104 ± 0.011	-	0.052 ± 0.010
MeGraph S-EdgePool Variants (h=5, n=5)	\(\tau_c\)=3	0.007 ± 0.003	1.77 ± 0.403	0.089 ± 0.008	-	0.126 ± 0.027
\(\eta_v\)=0.3	0.013 ± 0.004	1.67 ± 0.333	0.084 ± 0.008	-	0.086 ± 0.005
\(\eta_v\)=0.3,\(τ_c\)=4	0.011 ± 0.005	1.42 ± 0.252	0.073 ± 0.015	-	0.163 ± 0.007
\(\eta_v\)=0.5,\(τ_c\)=4	0.008 ± 0.004	1.71 ± 0.403	0.074 ± 0.009	-	0.156 ± 0.021
\(\eta_v\)=0.3,\(τ_c\)=4 (X-Pool)	0.009 ± 0.003	1.22 ± 0.242	0.088 ± 0.021	-	0.076 ± 0.006
\(\eta_v\)=0.3,\(τ_c\)=4 (w/o pw)	0.009 ± 0.003	1.42 ± 0.209	0.068 ± 0.017	-	0.068 ± 0.017
Graph-UNets	h=5,n=9,\(\eta_v\)=0.3,\(τ_c\)=4	0.024 ± 0.009	2.84 ± 0.777	0.091 ± 0.01	-	0.179 ± 0.0227
Table 30: Graph Theory Benchmark results on mixed, ER, Caveman and Star graphs, all results are obtained using our codebase.
Category	Model	MCC	ECC
mix	ER	Caveman	Star	mix	ER
Baselines (h=1)	n=1	3.46 ±0.211	2.91 ±0.206	0.015 ±0.004	0.144 ±0.031	0.316 ±0.003	0.346 ±0.006
n=5	3.29 ±0.261	3.35 ±0.205	0.014 ±0.003	0.078 ±0.021	0.228 ±0.008	0.289 ±0.008
n=10	3.51 ±0.323	3.53 ±0.375	0.018 ±0.006	0.065 ±0.005	0.212 ±0.008	0.414 ±0.102
MeGraph(h=5)	n=1	1.25 ±0.167	0.749 ±0.058	0.018 ±0.005	0.135 ±0.055	0.150 ±0.011	0.320 ±0.071
EdgePool(τc=2)	n=5	1.11 ±0.143	0.723 ±0.073	0.017 ±0.005	0.052 ±0.017	0.125 ±0.010	0.345 ±0.064
τc=3	1.07 ±0.034	0.714 ±0.039	0.017 ±0.002	0.072 ±0.016	0.137 ±0.013	0.232 ±0.035
MeGraph	ηv=0.3	0.908 ±0.153	0.627 ±0.090	0.026 ±0.007	0.125 ±0.026	0.128 ±0.014	0.248 ±0.012
S-EdgePool	ηv=0.3, τc=4	1.10 ±0.085	0.709 ±0.092	0.019 ±0.004	0.073 ±0.012	0.129 ±0.009	0.224 ±0.053
Variants (h=5, n=5)	ηv=0.5, τc=4	1.12 ±0.219	0.722 ±0.128	0.026 ±0.008	0.058 ±0.010	0.147 ±0.017	0.219 ±0.042
ηv=0.3, τc=4 (X-Pool)	1.01 ±0.166	0.838 ±0.078	0.029 ±0.007	0.107 ±0.021	0.119 ±0.008	0.213 ±0.027
ηv=0.3, τc=4 (w/o pw)	1.13 ±0.059	0.622 ±0.073	0.019 ±0.003	0.075 ±0.015	0.126 ±0.016	0.307 ±0.062
Graph-UNets	h=5,n=9,ηv=0.3,τc=4	1.06 ±0.171	0.859 ±0.092	0.041 ±0.007	0.057 ±0.010	0.153 ±0.012	0.34 5±0.133