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<title>faeval.git/experiments/perturbation_correlation_calibration.py, branch master</title>
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<entry>
<title>Add perturbation correlation metric calibration</title>
<updated>2026-04-08T07:22:08+00:00</updated>
<author>
<name>YurenHao0426</name>
<email>Blackhao0426@gmail.com</email>
</author>
<published>2026-04-08T07:22:08+00:00</published>
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Anchors the rho +0.08 finding with positive and negative controls:

  positive control (BP grad as a_l):     +0.9965  (perfect, expected ~1)
  negative control (random vector):      +0.0056  (noise floor, expected ~0)
  vanilla DFA s42 (||g|| at floor):      +0.0020  (within noise floor)
  penalized DFA s42 (||g|| healthy):     +0.0937  (~48x above noise, ~9% of perfect)

The metric is well-calibrated. BP gradient as a_l gives rho ~1 (Taylor),
random vector gives rho ~0 (noise floor), random feedback in degenerate
regime is indistinguishable from noise floor, random feedback in
penalized regime is small-but-well-above-noise (~48x noise, ~9% perfect).

Defensible paper claim: 'rho +0.08 is small in absolute terms but
clearly above the calibrated noise floor and on the order of 10% of
the perfect-signal ceiling — consistent with the 60% of BP accuracy
the penalized network achieves.'

Closes round 19's 'is rho +0.08 a meaningful number on this metric?'
question with explicit calibration.
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<pre>
Anchors the rho +0.08 finding with positive and negative controls:

  positive control (BP grad as a_l):     +0.9965  (perfect, expected ~1)
  negative control (random vector):      +0.0056  (noise floor, expected ~0)
  vanilla DFA s42 (||g|| at floor):      +0.0020  (within noise floor)
  penalized DFA s42 (||g|| healthy):     +0.0937  (~48x above noise, ~9% of perfect)

The metric is well-calibrated. BP gradient as a_l gives rho ~1 (Taylor),
random vector gives rho ~0 (noise floor), random feedback in degenerate
regime is indistinguishable from noise floor, random feedback in
penalized regime is small-but-well-above-noise (~48x noise, ~9% perfect).

Defensible paper claim: 'rho +0.08 is small in absolute terms but
clearly above the calibrated noise floor and on the order of 10% of
the perfect-signal ceiling — consistent with the 60% of BP accuracy
the penalized network achieves.'

Closes round 19's 'is rho +0.08 a meaningful number on this metric?'
question with explicit calibration.
</pre>
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