Does thinking time need to scale with problem difficulty?

The same overthinking study makes a second, structural claim: the token budget that maximizes accuracy is not a constant — it varies across problem difficulty. This means any uniform allocation policy is dominated. A fixed budget large enough for hard problems over-thinks easy ones (buying flip risk, per the flip-event finding) while a budget tuned to easy ones under-thinks hard ones. There is no single length that is right everywhere, so the field's habit of one decoding budget for all queries leaves accuracy and compute on the table.

This grounds the adaptive-compute program from the demand side. Can we allocate inference compute based on prompt difficulty? proposes allocating budget by difficulty; this note supplies the empirical justification — a measured difficulty-dependence of the optimum, not just of the return. It also complements When should AI systems do their thinking?: both reject the "more is better" default, one by moving compute in time, the other by sizing it to the problem.

The measurement contribution is what makes this actionable: a cost-aware evaluation framework that reports efficiency frontiers, so a system can pick the knee of the curve per difficulty band. The upshot for anyone deploying reasoning models is that a difficulty estimator plus early stopping is a cheaper accuracy lever than a bigger uniform budget — you are not trying to think more, you are trying to think the right amount, which is a moving target.