SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table 8: The integration time and number of trainable parameters corresponding to the best networks trained on CORA. Note that integration time can be considered as a surrogate for depth, since the temporal step-size of each network is fixed to 1.
Depth study (acc)	1 layer	2 layers	4 layers	8 layers	16 layers	32 layers	64 layers
Hamiltonian	75.0 ± 1.4	77.9 ± 1.0	62.0 ± 0.6	38.8 ± 1.0	32.0 ± 0.8	25.4 ± 0.5	17.1 ± 1.3
Gradient	69.6 ± 1.1	72.7 ± 1.0	74.5 ± 1.1	77.7 ± 1.0	80.2 ± 1.2	81.4 ± 1.0	82.0 ± 1.2
Double Bracket	77.8 ± 1.1	81.2 ± 0.8	83.9 ± 1.1	83.8 ± 1.0	80.1 ± 1.3	58.9 ± 1.0	19.3 ± 1.4
Metriplectic	61.0 ± 1.6	62.4 ± 1.9	62.0 ± 0.8	61.9 ± 1.3	61.6 ± 1.0	60.6 ± 1.3	61.2 ± 1.0
Hamiltonian	77.2 ± 0.8	77.5 ± 1.2	77.4 ± 1.2	77.0 ± 0.6	78.0 ± 0.7	77.8 ± 1.2	77.4 ± 0.7
Gradient	79.9 ± 1.4	79.9 ± 0.6	79.6 ± 0.6	79.6 ± 1.1	80.4 ± 1.1	80.5 ± 0.9	79.8 ± 1.1
Double Bracket	84.2 ± 0.9	84.5 ± 1.3	84.1 ± 0.5	84.2 ± 1.3	84.1 ± 0.8	83.8 ± 0.9	84.2 ± 1.0
Metriplectic	61.7 ± 1.4	61.0 ± 0.9	61.0 ± 1.0	61.4 ± 1.3	61.6 ± 1.4	61.7 ± 1.2	61.9 ± 1.1
Table 9: Accuracy results of a depth study on CORA. Test accuracies reported as mean±stdev over 10 runs with random train-valid/test splits. Top/bottom groups correspond to tasks 1 and 2 of the study, respectively, where Task 1 uses a fixed step-size while Task 2 uses a fixed integration domain.
Depth study (time)	1 layer	2 layers	4 layers	8 layers	16 layers	32 layers	64 layers
Hamiltonian	0.038 ± 0.003	0.060 ± 0.006	0.106 ± 0.011	0.191 ± 0.035	0.308 ± 0.035	0.497 ± 0.045	0.874 ± 0.035
Gradient	0.053 ± 0.005	0.091 ± 0.011	0.159 ± 0.015	0.273 ± 0.023	0.470 ± 0.031	0.809 ± 0.037	1.44 ± 0.038
Double Bracket	0.068 ± 0.007	0.125 ± 0.010	0.232 ± 0.023	0.434 ± 0.039	0.770 ± 0.068	1.36 ± 0.098	2.52 ± 0.103
Metriplectic	0.161 ± 0.010	0.305 ± 0.011	0.574 ± 0.014	1.10 ± 0.012	2.13 ± 0.040	4.11 ± 0.075	7.86 ± 0.129
Hamiltonian	0.052 ± 0.009	0.067 ± 0.013	0.114 ± 0.021	0.200 ± 0.040	0.350 ± 0.054	0.613 ± 0.056	1.17 ± 0.084
Gradient	0.365 ± 0.020	0.680 ± 0.012	1.26 ± 0.022	2.26 ± 0.058	4.22 ± 0.069	8.38 ± 0.451	19.4 ± 0.152
Double Bracket	0.241 ± 0.036	0.394 ± 0.046	0.731 ± 0.057	1.44 ± 0.132	2.98 ± 0.286	5.42 ± 0.609	9.44 ± 0.487
Metriplectic	1.05 ± 0.051	2.05 ± 0.097	3.87 ± 0.100	7.35 ± 0.149	14.1 ± 0.332	27.2 ± 0.378	53.8 ± 0.370
Table 10: Runtime results of a depth study on CORA. Wall clock times reported as mean±stdev over 10 runs with random train-valid/test splits. Top/bottom groups correspond to tasks 1 and 2 of the study, respectively, where Task 1 uses a fixed step-size while Task 2 uses a fixed integration domain.