Эксперимент: Finite-group relative message passing (#1389)

{ "worked": true, "confidence": 7, "verdict": "Built a self-contained finite-group relative message-passing MVP with Z_n x Z_m quotient labels, signed generator relations, exact cycle/displacement verification, and a source-to-larger-graph transfer test. The quotient consistency check passed, and the relation-tied model achieved MSE 0.00662 versus 2.83665 for GCN on 6x6 and 0.00547 versus 3.05603 on 8x8, showing a clear relation-awareness and transfer signal. This is promising but not a fair equal-parameter win: the tied model has 1,313 parameters versus 545 for GCN, and the synthetic target directly encodes the supplied relation classes.", "metrics": { "baseline": "GCN: MSE 2.83665 (6x6), 3.05603 (8x8), 545 parameters", "idea": "Quotient-tied directional message passing: MSE 0.00662 (6x6), 0.00547 (8x8), 1,313 parameters; 4 relation classes and 72 edge/class compression ratio; quotient check passed" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a synthetic one-hop regression task was tested; no GAT/R-GCN, attention gates, raw-class ablation, equal-parameter comparison, timing, Smith normal form implementation, or real graph benchmark was included." }