# Эксперимент: Spanning-Tree Connectivity Loss (#1201)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a differentiable spanning-tree connectivity loss using the rank-one-shifted Laplacian, with exact spectral and autograd checks plus a fixed-seed edge-learning mini-experiment. The identities matched to numerical precision, with relative errors around 1e-14 and derivative error 8.5e-9. Alpha=1e-3 increased mean Fiedler connectivity from 1.043 to 1.235 and pseudo-determinant from 1.42e8 to 2.15e8 while remaining connected, but task-fit MSE worsened from 2.4e-5 to 2.6e-4; alpha=1e-2 caused severe task degradation.",
  "metrics": {
    "baseline": "fit MSE 2.39e-05; Fiedler 1.043; components 1.0; pseudo-det 1.424e8; runtime 1.477 s",
    "idea": "alpha=1e-3: fit MSE 2.60e-04; Fiedler 1.235; components 1.0; pseudo-det 2.153e8; runtime 1.401 s; alpha=1e-2: fit MSE 1.14e-02; Fiedler 2.494; components 0.667 by numerical eigenthreshold; runtime 1.335 s"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "run_output.txt"
  ],
  "limitations": "This is a tiny unconstrained dense edge-weight learner, not the proposed six-layer GCN, top-k sparse routing, ZINC, or degree-penalty baseline. No large-graph stochastic logdet, wall-clock scaling study, validation accuracy, or gluing-theorem experiment was performed."
}