Research map / Learning theory and algorithms / Combinatorial and search optimization
Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| train the same GNN with the probabilistic loss instead of smooth relaxation losses (ablation) | Local graph partitioning GNN · SF-295, FACEBOOK, and TWITTER | conductance: SF-295: 0.188 $\pm$ 0.045 vs 0.124 $\pm$ 0.001; FACEBOOK: 0.571 $\pm$ 0.191 vs 0.156 $\pm$ 0.026; TWITTER: 0.388 $\pm$ 0 | Helped |
| use smooth relaxation losses instead of the probabilistic penalty loss (ablation) | Maximum clique GNN · TWITTER | clique constraint violation rate: 0\% vs 78.1\% (Bomze GNN); 84.7\% (MS GNN) | Hurt |
| train probabilities with the GNN rather than use uniform random probabilities (ablation) | Sequential clique decoding · TWITTER maximum clique, 1 sample | approximation ratio: 0.513 $\pm$ 0.266 -> 0.821 $\pm$ 0.222 | Helped |
| train probabilities with the GNN rather than use uniform random probabilities (ablation) | Sequential clique decoding · TWITTER maximum clique, 3 samples | approximation ratio: 0.694 $\pm$ 0.210 -> 0.875 $\pm$ 0.170 | Helped |
| train probabilities with the GNN rather than use uniform random probabilities (ablation) | Sequential clique decoding · TWITTER maximum clique, 5 samples | approximation ratio: 0.760 $\pm$ 0.172 -> 0.905 $\pm$ 0.139 | Helped |
| replace conditional-expectation decoding with smooth-relaxation thresholding (ablation) | Maximum clique GNN · TWITTER | clique constraint violation rate: 0\% vs 78.1\% (Bomze GNN); 84.7\% (MS GNN) | Hurt |
| use the probabilistic-loss model rather than smooth-relaxation models (ablation) | Maximum clique GNN · TWITTER | approximation ratio: 0.924 $\pm$ 0.133 (fast); 0.942 $\pm$ 0.111 (accurate); RUN-CSP (accurate): 0.987 $\pm$ 0.063 | Mixed |
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