When Do Internal Probes Beat Reading the Answer? Miscalibrated Readouts and Behavior-Concealed Knowledge in Language Models

Abstract: A 0.6B LLM, asked to verify 1,200 logical conclusions (half valid, half corrupted by a single semantic edit), answers YES every time. Judged by behavior it discriminates nothing; linear probes on its hidden states read the correct verdict at 0.96 AUC, transferring to unseen logical structures and separating foils built from exactly the words of the true conclusion (0.90). We ask where the verdict is lost, and find the dominant failure is a single scalar. The verdict survives to the model's own output logits (margin AUC 0.89) along a well-aligned readout direction; a saturated decision threshold, offset by +4.6 sigma, erases it. The diagnosis generalizes: across 90 semantic-label configurations of a five-model, three-family factorial, behavioral accuracy collapses onto a single function of threshold offset (Spearman -0.93) while margin ranking moves far less. Across a 13x scale range, internal knowledge saturates while free-form behavior is non-monotone: an 8B model underperforms its 4B sibling through an answer-channel failure rather than the threshold; forced-choice accuracy is monotone. The diagnosis is actionable: a one-parameter correction, never fit on evaluated structures, repairs behavior from 50% to 81% (0.6B); calibrated margin decoding recovers 94% at 8B; few-shot prompting works the same way, recentering the threshold (+4.6 sigma to 0.0 sigma) while preserving ranking. Comparing probe to margin separates three regimes: concealed, miscalibrated, and undetected. On a maze task built so foils carry no surface cues, the audit correctly reports the third. In the standard generation setting, answer-surface features and heuristic labels reproduce published probing results without any internal access.