# Эксперимент: Sharp JL Hidden-State Bottleneck (#893)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built and verified a frozen Gaussian JL hidden-state bottleneck with the sharp finite-set width rule. The core predictions were observed: mean squared norm ratio 0.986 versus 1, fixed-pair ratio SD 0.1235 versus the predicted 0.125 at r=32, and finite-set distortion decreased approximately with the predicted r^{-1/2} trend; the schedule also saturated at n−1 and d as expected. In the toy downstream task, projected representations preserved 100% validation accuracy at r=16–23 versus full width d=96, giving 4.2–6x lower activation width, but no realistic Transformer or speed benchmark was tested.",
  "metrics": {
    "baseline": "Full-width d=96: validation accuracy 1.000, validation loss 0.000807, activation width 96.",
    "idea": "Best narrow settings retained accuracy 1.000: epsilon=0.3,C=1,r=16 (width ratio 0.167, p95 absolute pair distortion 0.358, loss 0.000849) and epsilon=0.1,C=1,r=23 (width ratio 0.240, p95 distortion 0.278, loss 0.001945). At epsilon=0.2,C=4,r=92, p95 distortion was 0.161 and loss 0.000678."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py",
  "files": [
    "run_experiment.py",
    "results.json",
    "article.md",
    "idea_context.json"
  ],
  "limitations": "The downstream task is synthetic and linearly separable, so accuracy is not a stringent test of representation quality. No CIFAR-10/LM Transformer, wall-clock throughput, actual attention/MLP memory, learned or orthogonal projections, repeated seeds, or rigorous high-probability distortion certification was evaluated; the finite-set maximum-error scaling comparison is a heuristic concentration-scale check rather than a theorem-tight constant test."
}