Can models recognize question difficulty before they reason?

S1-Bench's probing analysis demonstrates that difficulty is already there in LRM representations. A single-layer MLP trained on the final-layer hidden state of the last token in an encoded question predicts difficulty with monotonically increasing accuracy across difficulty levels. The structure is implicit but linear — no extra training, no specialized probes, no auxiliary signal is required. The model knows.

The behavioral result then forms a contradiction with this internal knowledge. On simple questions that the linear probe correctly classifies as easy, LRMs still produce redundant solution rounds, repeatedly reverify already-correct answers, and emit higher average token entropy than necessary. The hidden-state signal that says "this is easy" is overridden during generation by exploratory behavior that says "let me check again."

The authors' interpretation — and the most plausible mechanism — is that models exhibit self-doubt about their own early difficulty judgments. The model perceives the question is simple, then second-guesses that perception, then engages in exploratory generation to compensate for the imagined possibility that its initial assessment was wrong. This is a structural failure mode: the architecture lacks a mechanism to commit to an early difficulty assessment and act on it.

The deeper insight is that LRM overthinking is not a perception failure (the model fails to recognize a simple question) but an action failure (the model recognizes the question is simple but cannot translate that recognition into terminating behavior). This distinction matters for fixes: prompt-engineering for "shorter answers on easy questions" treats it as a perception problem and produces brittle results. Mechanistic fixes that route generation through the difficulty representation — for example, conditioning continued-thinking decisions on the probe output — treat it as the action problem it appears to be.

The methodology generalizes. A linear probe on a hidden state is a cheap diagnostic for any property the model is suspected to track implicitly. If the probe succeeds and the behavior contradicts it, the gap localizes the failure to the perception-to-action interface — not to representation, not to capacity.