SHAPE: Stage-aware Hierarchical Advantage via Potential Estimation for LLM Reasoning

TL;DR

SHAPE is a novel framework that improves LLM reasoning by distinguishing meaningful progress from verbosity, using hierarchical advantage estimation to enhance accuracy and efficiency.

Contribution

It introduces a stage-aware hierarchical advantage framework with a new credit assignment mechanism for better reasoning in LLMs.

Findings

Achieves an average 3% accuracy improvement across benchmarks.

Reduces token consumption by 30%.

Effective in math reasoning tasks across multiple models.

Abstract

Process supervision has emerged as a promising approach for enhancing LLM reasoning, yet existing methods fail to distinguish meaningful progress from mere verbosity, leading to limited reasoning capabilities and unresolved token inefficiency. To address this, we propose Stage-aware Hierarchical Advantage via Potential Estimation (SHAPE), a framework that formalizes reasoning as a trajectory through a state space of empirical solvability. SHAPE introduces a hierarchical credit assignment mechanism: at the segment level, it employs a stage-aware advantage function to prioritize efficient breakthroughs in low-potential states; at the token level, it utilizes entropy-driven redistribution to sharpen execution signals. Extensive experiments in math reasoning across three base models and five benchmarks demonstrate that SHAPE achieves an average accuracy gain of 3% with 30% reduced token consumption.