For Gaussian data with homoscedastic class-conditional distributions, IID mass-mean probing coincides with logistic regression (Theorem F.1)

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• Why were interventions with mass-mean probe directions extracted from the likely dataset so effective, despite these probes not being accurate at classifying true/false statements?question0.754
  Open question raised in §7.1 about an unexplained anomalous result
• Mass-mean probe directions outperform LR and CCS in causal intervention experiments (NIE) in 7/8 experimental conditionsfinding0.752
  Core result showing MM is superior to LR for causal implication despite similar classification accuracy
• Simple difference-in-mean probes generalize as well as other probing techniques while identifying directions which are more causally implicated in model outputsclaim0.740
  Key methodological claim: MM probes are both competitive in accuracy and superior in causal influence
• Mass-mean probes generalize about as well as LR and CCS for LLaMA-2-13B and 70Bfinding0.739
  Despite being simpler and optimization-free, MM probes match accuracy of other techniques at scale
• The logistic fit for threshold behavior is a phenomenological surrogate for interpretability, not a mechanistic derivationclaim0.736
  Authors' explicit epistemic limitation on the threshold model
• Logistic regression fails to identify the true feature direction when a confounding feature is non-orthogonal to the truth direction, converging instead to the maximum margin separatorclaim0.735
  Motivates the introduction of mass-mean probing as an alternative to LR
• The model converges to a more stable truth direction in middle-to-late layers, as evidenced by increasing cosine similarity between layer-wise probes.claim0.732
  Supported by the geometric transition visible in cosine similarity heatmaps for F0-F3.
• Do pattern density ρd and prior-target distance dr serve as predictive correlates of few-shot thresholds?question0.731
  First E2 research question directly testing UCCT's core predictive claims