Adaptive Test-Time Compute Allocation via Learned Heuristics over Categorical Structure

TL;DR

This paper introduces a learned heuristics-based framework for adaptive test-time compute allocation in large language models, significantly reducing verification costs while improving reasoning accuracy.

Contribution

It proposes a novel state-level selective verification method combining gating, ranking, and adaptive verifier allocation to optimize reasoning efficiency.

Findings

Achieves higher accuracy than existing methods on the MATH benchmark.

Uses 44% fewer verifier calls compared to baseline approaches.

Effectively distributes verification effort to most informative intermediate states.

Abstract

Test-time computation has become a primary driver of progress in large language model (LLM) reasoning, but it is increasingly bottlenecked by expensive verification. In many reasoning systems, a large fraction of verifier calls are spent on redundant or unpromising intermediate hypotheses. We study reasoning under a \emph{verification-cost-limited} setting and ask how verification effort should be allocated across intermediate states. We propose a state-level selective verification framework that combines (i) deterministic feasibility gating over a structured move interface, (ii) pre-verification ranking using a hybrid of learned state-distance and residual scoring, and (iii) adaptive allocation of verifier calls based on local uncertainty. Unlike solution-level best-of-$N$ or uniform intermediate verification, our method distributes verification where it is most informative. On the \textsc{MATH} benchmark, our approach achieves higher accuracy than best-of-$N$, majority voting, and beam search while using 44\% fewer verifier calls.