Input-Blind Controls Produce Substantial Oracle Headroom for Layer Programs in Multiple-Choice Evaluation

Abstract

Adaptive computation aims to improve language-model inference by tailoring execution to each input. For layer programs, oracle evaluations use known answers to estimate the potential gain from this flexibility, before a practical selector is available. However, a gain from selection does not by itself explain why the chosen programs help. This study examines this distinction using 32 layer-skipping and repetition programs on two models and 4,413 multiple-choice items. The analysis compares their gains over a fixed action selected without the evaluation prompt with those of input-blind perturbations at the same sites, re-evaluating selections on another prompt. With shared option order, the controls give 10.2-11.8 and 15.6-19.4 percentage points of headroom on Qwen3-4B-Base and Llama-3.1-8B, exceeding the real programs'9.0 and 10.1 in all three random-direction draws per model. They match answer-change rate only, and the ordering depends on the menu: in post hoc comparisons, real programs lead on Llama's repeat-only menu in every draw. A smaller KL-calibrated comparison, including an input-dependent control, favours real programs in point estimate, with inconclusive corrected tests. Fixed letter offsets produce headroom of similar scale. Rotating options sharply reduces both families'headroom, while leaving positive real-minus-control differences of 1.4-2.3 and 3.7-4.5 points; their magnitudes and statistical support depend on further adjustments and the reference. A supplementary generated-answer test finds that search-selected programs keep a 26.0-point advantage over programs selected for other problems after rewording, without a placebo comparison. These results show that substantial headroom can persist across prompts with shared option order without establishing a benefit specific to the selected layer computation; neither ordering against these controls identifies that benefit.