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The paper introduces SHAPE, a novel process supervision framework that enhances LLM reasoning by formalizing it as a trajectory through a state space of empirical solvability. SHAPE employs a hierarchical credit assignment mechanism, using a stage-aware advantage function at the segment level and entropy-driven redistribution at the token level, to prioritize efficient breakthroughs. Experiments on math reasoning tasks show that SHAPE improves accuracy by 3% while reducing token consumption by 30% across multiple models and benchmarks.
LLMs can achieve 3% higher accuracy in math reasoning while using 30% fewer tokens by explicitly rewarding efficient progress toward solutions, not just verbosity.
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.
