The Expression Gap: Probing What Language Models Know but Don't Say

Instruction-tuned language models represent their own epistemic state—whether a claim is uncertain, self-contradictory, or unsupported by a provided document—more reliably inside the network than they reveal in generation. We call the difference between this internal representation and the model's output the expression gap, define it at a deployed threshold as probe fire-rate minus generation hedge-rate, and measure it across four open-weights families (Qwen2.5-7B, Mistral-7B-v0.3, OLMo-2-7B, Llama-3.1-8B). One recipe—a linear probe on the layer-17 last-input-token hidden state, fit per model and task—reads this state at AUC 0.97–1.00 on paired uncertainty and retrieval faithfulness across all four families, beats every input-only baseline (decisively on sycophancy prompts whose wording is identical across conditions), and transfers zero-shot across tasks within a model (off-diagonal mean AUC 0.96 on Qwen, 0.89 on Mistral). The gap it exposes is large and model-ordered (regex-scored 0.14–0.49; OLMo largest, Llama near zero under semantic judging) and instruction-gated: under a permissive prompt, retrieval unfaithfulness spans a 0.00–0.78 gap across families. Gating a sparse flag-token logit bias on the probe recovers expression with zero added false positives on the evaluation set (held-out gate exposure 1.7–6.3%); a blinded semantic audit of every stored generation (κ=0.94) confirms the lift on two families, exposes a third as surface-form conversion, and finds a null on the fourth. The obvious alternative—a one-line hedging instruction—lifts expression on every family but always at commensurate false-positive cost (+12 to +33pp), because a prompt cannot condition on what the model internally knows. A gated-actuator factorial locates the mechanism: the zero-FP property belongs to the probe gate, which every actuator behind it (logit bias, ITI, CAA) inherits. We release datasets, code, and the full judging record.