Gumbel-softmax-based optimization: a simple general framework for optimization problems on graphs

Computational Social Networks

Table 4 The results on optimization of ground state energy of SK model

N	I	GSO (\(N_{{\text{bs}}}=1\))^a	GSO (\(N_{{\text{bs}}}=128\))^a	EvoGSO (\(N_{{\text{bs}}}=128\))^b
256	5000	\(-\,\)0.7267(2)/0.99 s	\(-\,\)0.7369(1)/0.96 s	\(-\,\)0.7364(1)/0.89 s
512	2500	\(-\,\)0.7405(2)/2.16 s	\(-\,\)0.7464(1)/2.14 s	\(-\,\)0.7462(1)/2.01 s
1024	1250	\(-\,\)0.7480(2)/4.49 s	\(-\,\)0.7521(1)/4.66 s	\(-\,\)0.7516(4)/4.41 s
2048	400	\(-\,\)0.7524(2)/7.23 s	\(-\,\)0.7555(2)/8.07 s	\(-\,\)0.7557(1)/7.51 s
4096	200	\(-\,\)0.7551(2)/10.46 s	\(-\,\)0.7566(5)/12.78 s	\(-\,\)0.7569(3)/12.80 s
8192	100	\(-\,\)0.7562(1)/25.15 s	\(-\,\)0.7568(8)/49.13 s	\(-\,\)0.7578(5)/49.04 s

We show that the parallel version of our proposed methods and EvoGSO can greatly improve the performance
The best results are denoted in italic. The corresponding standard error of the mean is given in brackets.
^aConfiguration: initial \(\tau\) = 20, final \(\tau\) = 1, and learning rate = 1
^bConfiguration: initial \(\tau\) = 20, final \(\tau\) = 1, learning rate = 1, cycle \(T_1\) = 100, and substitution ratio 1/u = 1/8