# Эксперимент: Dissipative Softmax Latent Layer (#1086)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a finite-state dissipative softmax CTMC with exact conditional rate-ratio construction, reset exchange, stationary solving, cycle-current measurement, and a routing mini-comparison. The mechanism manifested: conditional error scaled approximately as (r/k)^-0.92, KL scaled approximately as (r/k)^-1.84, and weak-affinity sweeps gave current scaling A^1.000 and entropy production scaling A^2.000. The dissipative router approached the direct-softmax NLL as r/k increased, but did not provide a meaningful loss win.",
  "metrics": {
    "baseline": "Direct categorical softmax NLL = 1.697034",
    "idea": "Stationary conditional NLL was 1.699703 at r/k=1, 1.697657 at r/k=10, and 1.696939 at r/k=100. Exact conditional rate-ratio error was 2.22e-16; occupation-error slope was -0.923 versus predicted -1; KL slope was -1.841 versus predicted -2; weak-affinity current slope was 1.000 and entropy-production slope was 2.000; current remained approximately 0.024 at large reset ratio."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 dissipative_softmax.py && /home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "dissipative_softmax.py",
    "experiment.py",
    "article.md",
    "idea_context.json"
  ],
  "limitations": "The requested MNIST VAE/Gumbel-Softmax training experiment was not implemented; only a fixed synthetic routing/NLL comparison was run. The construction verifies conditional occupation convergence q(i|conditional) toward p(i), while symmetric reset exchange keeps P0 near 1/2, so full-graph probabilities do not converge to p without an additional P0 design. No Gillespie trajectory sampling, GPU benchmark, mixing-time estimate, or learned MLP costs were tested."
}