Эксперимент: Laplacian-Coherence Graph Minibatches (#583)

{ "worked": true, "confidence": 8, "verdict": "Built a sparse on-demand Laplacian-column coherence sampler with greedy min-max selection. The mechanism checks passed: sparse columns and inner products matched dense calculations exactly, disconnected-component coherence was exactly zero with both-block coverage, candidate-pool coverage matched the combinatorial prediction, and the bridge-coherence closed form matched observed values to numerical precision. The estimator remained approximately unbiased, but its standard deviation was 0.389 versus 0.135 for uniform sampling, so inverse-probability weighting needs variance control; no end-to-end GNN win was established.", "metrics": { "baseline": "Uniform sampling: mean two-block coverage 1.44/2 on the coupling sweep; HT loss estimate mean 0.6975 versus true 0.7000, std 0.1352.", "idea": "Coherence sampling: mean two-block coverage 2.00/2 across all tested bridge weights versus uniform 1.44; HT loss estimate mean 0.6930 versus true 0.7000, std 0.3889; minimum estimated inclusion probability 0.051. Cross-coherence and closed-form bridge prediction agreed to about 1e-15." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "coherence_sampler.py", "run_experiment.py", "results.json", "README.md" ], "limitations": "Only small synthetic two-clique graphs were tested. No Cora/Citeseer dataset, GCN/GraphSAGE training, sampled-frontier FLOP accounting, validation accuracy, low-frequency reconstruction, or multi-hop neighbor sampler comparison was run. The current sampler uses one fixed candidate pool per minibatch and estimates inclusion probabilities via repeated offline sampling; clipping and EMA probability tracking are not implemented." }