Value-Conditioned Proposal Acquisition for Test-Time Reasoning

Abstract

Sampling and selection spend test-time compute inside a candidate pool, but they cannot recover a correct answer that never enters it. We introduce ValueFormation, a test-time policy that decides after each primary-model draw whether to stop, continue sampling, or acquire one proposal from a heterogeneous reasoning specialist. The three actions are compared on one cost-regularized value scale learned from vote-state features; the calibration is frozen across tasks and primary models, and acquired proposals are accepted only through a frozen posterior comparison. On held-out MATH-500, one Llama-fitted calibration improves over the strongest of eight identically evaluated baselines by more than fifteen points for each of three 8B primaries and transfers unchanged to Qwen3-14B. Removing acquisition lowers Llama MATH accuracy by 20.43 points, while same-trace and same-access replays attribute the gain to state-conditioned acquisition rather than specialist access alone. Where primary coverage is high, as on GSM8K, acquisition is rare and gains mainly come from cheaper allocation; on MBPP, a fixed code route attains the top accuracy at the lowest interaction cost. Varying the token price monotonically reduces calls without retraining.