Drop a plumb line into the frozen hidden state and see how deep the answer is likely to be right. P(I Know) is a linear probe we train to read correctness off the model's own activations — decodability, not an inner oracle. Fit it live, then watch a shuffled-label control collapse it back to a coin.
LIT the probe, AUROC & every number, fit live by gradient descent FIG a toy hidden-state field, labelled AMBER WALL a real model bake
running self-check…
Fit — BCE by gradient descent
■ training loss (BCE) the probe P(IK)=σ(w·h+b) is fit on the 16-dim hidden vectors; the softmax-confidence baseline reads one feature alone. If the probe's AUROC beats the baseline's, the state carries correctness signal beyond raw confidence.
Reliability & the confidently-wrong corner
Top: reliability — each bar is the empirical fraction correct among held-out examples in that predicted-P(IK) bin; the ○ marks the bin at (mean predicted P(IK), fraction correct). A well-calibrated probe puts the ○ on the dashed diagonal. Bottom: every example by its P(IK); the red band past τ is confidently wrong — high P(IK), actually wrong. That corner is why P(IK) is a reader, not a guarantee.