When Does Adaptive Halting Win? Selection Rules Matter in Looped Language Models

Looped language models can stop iterating early, and recent work shows that post-hoc readouts of the loop trajectory often rival the learned exit gate of the looped model Ouro. Such comparisons reduce each method to one operating point chosen by a selection rule. We ask whether that rule decides the outcome. On a frozen Ouro-1.4B with four loops, we compared a trained stability probe ($π_1$-x) with Ouro's native gate, adapted to a per-question stopping decision, in pre-registered studies; the confirmatory study was designed after an exploratory finding on development data and evaluated once on a sealed test set of 8,517 questions. In the pre-registered confirmatory comparison, which selected operating points with a bootstrap-screened 1 pp accuracy-loss rule, the probe saved more of the four-loop budget than the native gate (+0.053 gross macro saving over three benchmarks, 95% CI [+0.049, +0.057]), mostly from CommonsenseQA, where the probe's test upper bound on accuracy loss exceeded 1 pp. Under a point-only rule, a pre-specified secondary analysis on the same test set reversed the preference (-0.022 [-0.026, -0.018]), with operating points that exceeded the budget. In pre-specified secondary comparisons, the probe showed no demonstrated advantage over an untrained KL divergence between successive loops (+0.00125 [-0.0041, +0.0065]); we emphasise this result post hoc and claim no equivalence. The probe also broke its budget on one of two out-of-distribution benchmarks (3.26 pp loss on Social IQa). Savings are estimated from stored full-depth traces, not measured inference time, and our screen carries no formal risk-control guarantee. We conclude that halting methods should be compared as signals together with selection procedures, with strong untrained baselines and out-of-distribution checks.