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

2026-04-07

AI Summary

This work addresses the inefficiency of large language models in reasoning tasks, where existing process supervision methods struggle to distinguish valid reasoning from redundant outputs, leading to excessive token consumption. The authors model reasoning as trajectories within an empirically solvable state space and introduce a stage-aware hierarchical advantage mechanism. At the paragraph level, state potential estimation guides efficient exploration by prioritizing low-potential regions; at the token level, entropy-driven reallocation sharpens execution signals. This approach uniquely integrates multi-granularity credit assignment with state potential evaluation, achieving an average 3% accuracy gain across three base models and five mathematical reasoning benchmarks while reducing token usage by 30%.

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.

Problem

• process supervision
• LLM reasoning
• token inefficiency
• reasoning progress
• credit assignment

Innovation

• process supervision
• hierarchical credit assignment
• stage-aware advantage
• potential estimation
• token efficiency