Эксперимент: Discriminant-Gated Positive Edge Adaptation (#911)

{ "worked": true, "confidence": 9, "verdict": "Built a positive-weight directed-Laplacian toy implementing softplus edge weights, normalized spectral-gap measurement, discriminant evaluation, conditioning diagnostics, and gap-gated optimization. The sweeps matched the predictions: gap scales as epsilon^1 (observed 1.000000), the nonzero characteristic-polynomial discriminant scales as epsilon^2 (observed 2.000000), and condition(V)*epsilon is approximately constant (1.568 to 1.558). At exact collision, Disc(q)=0 and the repeated eigenvalue has algebraic multiplicity 2 but eigenspace nullity 1, confirming defectiveness. In optimization, the unconstrained positive model reached task loss 1.23e-32 but gap approximately 3.7e-17 and condition number 2.66e16; the g_min=0.03 gated model reached gap 0.0414, condition 24.4, and task loss 0.00772. Thus the proposed mechanism manifested clearly, though this is not evidence of a downstream accuracy win.", "metrics": { "baseline": "Positive unconstrained: task loss 1.23e-32, normalized gap 3.70e-17, cond(V)=2.66e16.", "idea": "Gap-gated (g_min=0.03, beta=5000): task loss 7.72e-3, normalized gap 4.14e-2, cond(V)=24.37. Sweep final gaps: g_min=1e-4 -> 1.64e-3; 1e-3 -> 4.49e-2; 1e-2 -> 2.49e-2; 3e-2 -> 4.14e-2. Math slopes: gap 1.000000, discriminant 2.000000." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a 3-node directed path and a synthetic quadratic task were tested; no directed GCN, stochastic minibatches, Cora, long-horizon dynamics, FLOP/speed comparison, condition-number penalty, characteristic-polynomial numerical stability study, or multi-seed statistical evaluation was performed." }