Research map / Probabilistic and scientific modeling / Variational and generative sampling
Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| lift the Lovász SFE from scalar inputs to a neural high-dimensional representation (ablation) | GNN combinatorial solver · MaxClique and MIS across ENZYMES, PROTEINS, IMDB-Binary, MUTAG, and COLLAB | approximation ratio: improves in 8 out of 10 cases | Mixed |
| lift the Lovász SFE from scalar to neural on PROTEINS MaxClique (ablation) | GNN combinatorial solver · PROTEINS MaxClique | approximation ratio: 0.778 -> 0.926 | Helped |
| lift the Lovász SFE from scalar to neural on ENZYMES MIS (ablation) | GNN combinatorial solver · ENZYMES MIS | approximation ratio: 0.311 -> 0.775 | Helped |
| use the top k eigenvectors instead of only one (ablation) | Lovász neural SFE · MaxClique on ENZYMES and PROTEINS | approximation ratio | Helped |
| retain eigenvectors beyond the top 4 (ablation) | Lovász neural SFE · MaxClique on ENZYMES and PROTEINS | approximation ratio | No clear effect |
| replace the neural SFE with a column-wise sum of scalar SFEs (ablation) | high-dimensional GNN solver · MaxClique | performance | Hurt |
| use a k-bounded cardinality Lovász extension instead of the Lovász extension (ablation) | SFE solver · k-clique constraint satisfaction on ENZYMES and PROTEINS | F1 score | Helped |
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