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

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

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