# Эксперимент: Positive-Measure Span Regularizer (#1309)

{
  "worked": true,
  "confidence": 7,
  "verdict": "Built a differentiable local effective-rank regularizer with Frobenius normalization and label-defined local groups, plus a numerical sanity check. The toy check confirmed that collapsed features have low rank, optimization increases their rank, and uniform feature rescaling leaves the proxy unchanged. In the digits experiment, the regularizer improved worst-group rank from 2.6055 to 2.7393 and mean rank from 3.1458 to 3.2542, but accuracy slightly fell from 95.78% to 95.33%; thus the rank effect is real, while an accuracy win was not demonstrated.",
  "metrics": {
    "baseline": "accuracy=0.9578, test 10th-percentile rank=2.6055, mean rank=3.1458",
    "idea": "accuracy=0.9533, test 10th-percentile rank=2.7393, mean rank=3.2542; toy collapsed rank 0.9780 -> 6.7793 after optimization; scale invariance 6.2335 vs 6.2335"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py",
  "files": [
    "run_experiment.py",
    "results.json"
  ],
  "limitations": "Only one small digits dataset and one random seed were tested; no CIFAR-10, ResNet, scattering classifier, augmentation robustness, FLOP-matched analysis, or hyperparameter sweep was performed. Local groups use class labels rather than geometric neighborhoods, and the initial soft-min sign error was corrected before the reported run."
}