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graph_id int64 0 449 | n int64 20 1.97k | density_p float64 0.05 0.5 | er_seed int64 1.72M 2.14B | edge_src listlengths 19 751k | edge_dst listlengths 19 751k | soft_label listlengths 20 1.97k | hard_label listlengths 20 1.97k | best_size int64 5 106 |
|---|---|---|---|---|---|---|---|---|
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1 | 598 | 0.151688 | 448,641,293 | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0(...TRUNCATED) | [6,10,11,19,20,27,32,41,42,63,65,70,73,81,83,87,99,106,110,120,121,122,132,135,137,138,139,161,170,1(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.3333333432674408,0.0,0.6666666865348816,0.0,0.0,0.0,0.333(...TRUNCATED) | [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0(...TRUNCATED) | 39 |
2 | 1,740 | 0.366161 | 2,115,348,104 | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0(...TRUNCATED) | [7,8,10,18,21,22,24,25,27,28,31,32,35,39,41,52,55,59,60,64,65,68,69,70,76,77,78,80,81,82,85,86,95,96(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0(...TRUNCATED) | 19 |
3 | 40 | 0.269538 | 364,328,595 | [0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5(...TRUNCATED) | [2,8,10,12,14,18,20,32,37,39,9,17,27,33,39,7,15,16,18,19,21,22,23,29,31,32,35,37,13,18,21,22,27,32,3(...TRUNCATED) | [0.0,1.0,0.4000000059604645,1.0,0.0,0.0,0.0,0.6000000238418579,0.5,0.0,0.550000011920929,1.0,0.5,0.0(...TRUNCATED) | [
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4 | 229 | 0.465563 | 1,134,433,139 | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0(...TRUNCATED) | [1,3,5,7,9,10,11,12,14,15,16,18,21,22,23,26,29,30,31,32,35,36,37,39,44,46,47,49,52,59,63,64,65,68,70(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0(...TRUNCATED) | 10 |
5 | 58 | 0.221694 | 1,408,587,445 | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3(...TRUNCATED) | [10,14,19,21,22,27,30,36,37,39,40,41,49,50,51,53,54,4,13,14,19,26,27,29,32,36,37,39,40,51,54,4,14,15(...TRUNCATED) | [0.47058823704719543,0.0,0.47058823704719543,0.5882353186607361,0.23529411852359772,0.0,0.0,0.882352(...TRUNCATED) | [0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0(...TRUNCATED) | 15 |
6 | 1,083 | 0.203959 | 1,621,350,668 | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0(...TRUNCATED) | [4,13,14,18,20,31,32,33,35,36,39,40,42,63,64,66,75,82,83,84,93,95,97,102,103,107,110,114,118,131,146(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.75,0.75,0.0,0.0,0.0,0.0,0.0,0(...TRUNCATED) | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0(...TRUNCATED) | 35 |
7 | 309 | 0.33188 | 1,002,936,838 | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0(...TRUNCATED) | [5,7,8,10,11,12,15,21,22,23,27,30,31,37,38,42,46,56,59,63,64,65,66,92,93,94,97,112,120,122,125,126,1(...TRUNCATED) | [0.949999988079071,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0(...TRUNCATED) | [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0(...TRUNCATED) | 16 |
8 | 75 | 0.072049 | 802,822,762 | [0,0,1,1,1,1,1,1,2,2,2,3,3,3,3,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,9,9,10,10(...TRUNCATED) | [49,59,6,18,19,50,64,73,12,16,69,28,44,45,62,22,23,50,24,27,34,61,68,10,35,38,48,49,67,10,19,24,27,3(...TRUNCATED) | [0.949999988079071,0.800000011920929,0.0,0.05000000074505806,0.949999988079071,0.25,0.0,0.6000000238(...TRUNCATED) | [1,1,0,0,1,0,0,0,0,0,1,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0,1,0(...TRUNCATED) | 31 |
9 | 167 | 0.187774 | 1,980,329,847 | [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) | [1,2,5,11,13,14,15,24,27,40,47,48,53,59,68,70,71,73,76,80,81,87,88,95,109,111,112,115,119,128,133,14(...TRUNCATED) | [0.0,0.6000000238418579,0.0,0.0,1.0,0.0,0.0,0.0,0.75,0.0,0.0,0.0,0.0,0.5,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | [0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0(...TRUNCATED) | 22 |
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Synthetic Maximum Independent Set training graphs
500 synthetic Erdos-Renyi graphs (20-1,972 nodes, density 0.05-0.5), each labelled by 20 restarts of randomized-greedy construction plus (1,2)-exchange local search. Built to train Bauxitiego/neural-mis, a GCN evaluated against QOBLIB's Maximum Independent Set benchmark — code, evaluation, and honest results (including a documented failure) at github.com/Bauxitiego/neural-mis.
Generated, not collected: free, unlimited, exactly-labelled by construction. Never overlaps QOBLIB's 50 evaluation instances — this dataset is training data only, the model's real evaluation happens entirely against QOBLIB's own ground truth.
Splits
train (450 graphs) and validation (50 graphs), a simple index split by generation
order, not a reconstruction of the exact random subset used during actual training (that
split came from a seeded PyTorch shuffle at training time; this one is simpler and
explicit, documented as such rather than implying false precision).
Schema
| Column | Type | Description |
|---|---|---|
graph_id |
int | Generation index, [seed, graph_id] was the RNG seed |
n |
int | Number of nodes |
density_p |
float | Erdos-Renyi edge probability used to generate the graph |
er_seed |
int | The specific seed passed to networkx.erdos_renyi_graph |
edge_src, edge_dst |
list<int32> | Edge list, one direction per edge, parallel arrays |
soft_label |
list<float32> | Per-node: fraction of near-best local-search restarts (within 1 of the best found) that included this node |
hard_label |
list<int8> | Per-node: 1 if in the single best independent set found across restarts, else 0 |
best_size |
int | Size of the best independent set found for this graph |
soft_label is the actual training target used (see the repo's src/dataset.py), not
hard_label — MIS has many symmetric optima, and supervising on one arbitrary tie-break
would teach a model to be confidently wrong about the others. hard_label is included
for anyone who wants a single-solution view instead.
Reproduce from scratch
python scripts/generate_training_data.py --n-graphs 500 --restarts 20 \
--out-dir data/synthetic_train
python scripts/build_hf_dataset.py
License
Apache 2.0. Fully synthetic, no third-party data involved.
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