# Эксперимент: Boundary-Safe Log-Barrier Mirror Optimizer (#703)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built and ran a safeguarded simplex log-barrier mirror optimizer with Bregman, positivity, root-condition, boundary-scaling, and toy routing tests. The mechanism manifested clearly: simplex residuals were at most 3.3e-16, all coordinates stayed positive, reciprocal boundary growth matched the predicted slope alpha within 0.15% at alpha=0.5 and below 0.004% for alpha>=1, and the one-step boundary approximation had under 1% relative error. However, on the imbalanced convex routing toy, the barrier method ended with higher loss than exponentiated gradient or Adam, so it is mechanism-validated but not an optimization win.",
  "metrics": {
    "baseline": "Exponentiated gradient: final cross-entropy 0.855829, step-20 loss 0.915598, minimum probability 0.001000; Adam-logits: final cross-entropy 0.857150, step-20 loss 0.906594, minimum probability 0.003582.",
    "idea": "Barrier mirror with alpha=0.08: final cross-entropy 0.924108, step-20 loss 1.236211, minimum probability 0.049750; all 13 alpha values retained positive coordinates and root residual <=1.11e-16; reciprocal boundary slope/alpha ratios ranged 0.9985-0.999999."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 barrier_experiment.py",
  "files": [
    "barrier_experiment.py",
    "results.json"
  ],
  "limitations": "This is a NumPy toy experiment, not a neural MoE or stochastic minibatch training test. Alpha tuning, loss-increase backtracking, GPU execution, FLOP accounting, multiple random seeds, and the claimed O(log k/k) convergence rate were not tested."
}