A Single Revision Step Improves Token-Efficient LLM Reasoning
Yingchuan Zhang, Terry Ma, Wenxuan Zhong, Ping Ma
TL;DR
The paper tackles the inefficiency and brittleness of large-language-model reasoning ensembles by introducing PACER, a training-free coordination layer that enables a single consensus-conditioned revision of reasoning traces. PACER constructs a compact consensus packet containing top candidate answers, their support, and representative rationales, and then prompts each trace to perform a brief self-review conditioned on this packet, followed by confidence-weighted voting over revised traces. The authors provide a theoretical framework showing repair-vs-damage dynamics and margin-based conditions under which revision improves accuracy, and demonstrate empirically that PACER matches or exceeds the performance of large majority ensembles (e.g., MV@256) on challenging math benchmarks like AIME, HMMT, and BRUMO while using substantially fewer tokens. This training-free, token-efficient approach offers a practical path to robustly scaling reasoning quality in real-world deployments with constrained compute budgets.
Abstract
Large language models (LLMs) achieve higher accuracy on challenging reasoning tasks by scaling test-time compute through multiple trajectory sampling. However, standard aggregation methods like majority voting or individual confidence-based filtering face a fundamental "blind spot": they evaluate each trace in isolation. As problems scale in difficulty, models often generate hallucinated paths that exhibit misleadingly high confidence, causing the true solution to be suppressed by a narrow margin in traditional voting. We ask: can we enable traces to "peer-review" each other to resolve these near-miss errors? We introduce Packet-Conditioned Revision (PACER), a training-free, inference-only framework that enables reasoning traces to revise their conclusions through a structured coordination step. After a preliminary screening of generated traces, PACER constructs a compact consensus packet containing (i) unique candidate answers, (ii) their aggregated confidence scores, and (iii) representative reasoning summaries for each candidate answer. Individual traces then perform a targeted self-review conditioned on this packet, allowing them to identify specific logical junctions where they diverged from the broader consensus and pivot if their original reasoning is found to be flawed. Final predictions are obtained via confidence-weighted voting over these revised trajectories. On challenging competitive math benchmarks such as AIME and BRUMO, PACER matches or exceeds the accuracy of 256-sample majority voting, significantly outperforming raw ensemble baselines by transforming simple consensus into a collaborative logical refinement process.