# Эксперимент: Coarse-to-fine active-support transport attention (#867)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a readable NumPy/SciPy MVP for balanced transport, coarse-support lifting, active-edge expansion, Schur conditioning diagnostics, and a fixed-top-k comparison. Global slack scaling preserved kappa to 1.35e-13 and the identity kappa=(1+sigma)/(1-sigma) had zero measured error, but the hypothesized coarse-support transition at separation >0.2 was falsified: the lifted support was already exact at separation 0.1. The idea matched dense transport exactly on the representative case, but used 50% of all edges and did not improve the top-k objective, so there is no demonstrated practical win.",
  "metrics": {
    "baseline": "Dense LP objective 0.036666666666666674; fixed top-k (48/144 edges) objective 0.036666666666666674 and feasible.",
    "idea": "Coarse-to-fine active support objective 0.03666666666666667; 72/144 edges (50%), 0 expansion rounds at separation 0.4, runtime 0.0143 s. Scale-sweep kappa range 1.35e-13; Schur formula max absolute error 0."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 transport_active_support.py",
  "files": [
    "transport_active_support.py",
    "results.json"
  ],
  "limitations": "Only a small synthetic balanced-transport experiment was tested; no Transformer, CIFAR/WikiText task, GPU implementation, Newton primal-dual solver, wall-clock attention benchmark, memory measurement, nonuniform marginals, masking, or accuracy/perplexity evaluation was included. The active-set expansion uses a simple cheapest-edge proposal rather than full reduced-cost and residual-based Newton updates."
}