Эксперимент: Persistent Spectral Noise for Recurrent GNNs (#592)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified a persistent-noise recurrent spectral GNN MVP. The mechanism manifested clearly: stationary Dirichlet energy scaled as sigma^2 with through-origin R2=0.99999999, matched the exact modal formula within 0.06% relative error, and increased monotonically with lambda_2 on a fixed topology. Deterministic energy decayed to 3.83e-23 by step 100 while persistent noise maintained energy 0.0691; no downstream accuracy benchmark was run.", "metrics": { "baseline": "Deterministic recurrence: long-horizon Dirichlet energy 3.8264e-23 at step 100; predicted lambda_2-mode half-life 1.367 steps, observed threshold crossing at step 2.", "idea": "Persistent Gaussian noise sigma=0.04: stationary Dirichlet energy 0.06910 +/- 0.000045; sigma^2 scaling R2=0.99999999 and maximum formula relative error 0.059%; fixed-topology gap sweep was strictly monotone." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_noise_experiment.py", "files": [ "spectral_noise_experiment.py", "results.json", "README.txt" ], "limitations": "This is an exactly solvable linear recurrent graph experiment rather than a learned nonlinear GNN. It did not test Cora or another real dataset, downstream accuracy/generalization, dropout or residual baselines, inference-time stochastic ensembling, or robustness; the observed effect validates the proposed dynamical mechanism but not a task-level performance win." }