{
  "id": "r05_learned_null",
  "order": 15,
  "tag": "null",
  "eyebrow": "05 \u00b7 Learned null",
  "title": "A classifier finds no information in the depth profiles beyond surface brightness",
  "question": "Could a trained model extract something from these tomograms that a human reader misses?",
  "finding": "No. Separating Khafre pixels from open-desert pixels is an easy task and surface brightness alone reaches an area under the curve of 0.64. The depth profiles reach 0.51, and once the comparison is restricted to pixels of matched brightness they fall to 0.51, which is chance. Training on labelled voids would face the same problem with far fewer labels: Giza offers on the order of ten surveyed chambers, all of them under monuments, so a model would learn where the monuments are.",
  "limitations": "A linear model on binned profiles; a larger network could fit more, but with spatially blocked folds and a matched-brightness control there is little left for it to fit. The test shows an absence of separable information in these features, not a proof that no representation could ever separate them.",
  "method": "Logistic regression on 32-bin normalised depth profiles and on log amplitude, scored by area under the ROC curve with five folds blocked into contiguous azimuth strips. The matched control keeps only pixels between the fortieth and sixtieth percentile of brightness.",
  "figures": [
    {
      "file": "/Users/eugene/prj/sar/results/r05_learned_null/figs/r05_auc.png",
      "caption": "<b>The depth axis adds nothing a brightness map does not already have.</b> A logistic classifier is trained to separate pixels on Khafre from pixels on open plateau, with folds blocked in space so that neighbouring speckle cannot leak between training and test. Surface brightness separates them easily, which it should: a pyramid is not sand. The depth profiles the method produces do not, and inside an amplitude-matched band they fall to chance. This is the machine-learning form of the null control: a learner is a good instrument for measuring whether information is present, and here it measures that it is not."
    }
  ],
  "metrics": {
    "auc": {
      "amplitude only": {
        "mean": 0.6381699257851715,
        "std": 0.011485950830088526
      },
      "depth profile only": {
        "mean": 0.5128378796348951,
        "std": 0.011368035921737431
      },
      "depth profile + amplitude": {
        "mean": 0.6357887782218011,
        "std": 0.014055474838970971
      },
      "depth profile, amplitude-matched": {
        "mean": 0.5135435663478273,
        "std": 0.016128074966702533
      },
      "amplitude, amplitude-matched": {
        "mean": 0.5381286171527727,
        "std": 0.009385123715078509
      }
    },
    "pixels_khafre": 47880,
    "pixels_desert": 47880,
    "profile_bins": 32,
    "blocks": 16,
    "runtime_s": 0.978388786315918
  },
  "date": "2026-09-23"
}