# Эксперимент: Singular-Value-Robust Projector-Splitting LoRA (#945)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a readable projector-splitting MVP with exact three-substep QR updates and a common-base explicit midpoint integrator. The mechanism manifested: observed convergence order was 1.99897 across sigma-min values 1e-2, 1e-6, and 1e-10, while final-step errors differed by only about 0.005%; orthogonality errors stayed near machine precision. The toy fitting comparison favored projector splitting (0.1062 vs 0.2267 loss after 120 steps), but it was slower and used a plain factor-gradient baseline rather than production Adam, so this is evidence for robustness rather than a general LoRA training win.",
  "metrics": {
    "baseline": "Factor gradient descent: final loss 0.226712 after 120 steps, CPU time 0.0172 s, no NaNs",
    "idea": "Projector-splitting midpoint: final loss 0.106228 after 120 steps, CPU time 0.1048 s, no NaNs; observed order 1.99897 and h=0.025 errors 1.00198e-4, 1.00193e-4, 1.00193e-4 for sigma-min 1e-2, 1e-6, 1e-10"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 projector_splitting_mvp.py",
  "files": [
    "projector_splitting_mvp.py",
    "results.json",
    "REPORT.md"
  ],
  "limitations": "Only a tiny NumPy matrix-fitting task was tested; no real MLP, LoRA layer, CIFAR/language dataset, CUDA implementation, production Adam comparison, FLOP-matched benchmark, adaptive step sizing, or rank-admissibility failure analysis was performed. The baseline was plain factor gradient descent rather than Adam."
}