Strategy Executability in Mathematical Reasoning: Leveraging Human-Model Differences for Effective Guidance

TL;DR

This paper investigates the gap between strategy usage and executability in mathematical reasoning, proposing a framework that improves model guidance by selectively retrieving strategies, leading to more reliable reasoning performance.

Contribution

It introduces Selective Strategy Retrieval (SSR), a novel framework that models executability to enhance guidance effectiveness in mathematical reasoning tasks.

Findings

SSR improves accuracy by up to 13 points on AIME25.

SSR achieves consistent performance gains across multiple benchmarks.

The study reveals a systematic dissociation between human and model strategies.

Abstract

Example-based guidance is widely used to improve mathematical reasoning at inference time, yet its effectiveness is highly unstable across problems and models-even when the guidance is correct and problem-relevant. We show that this instability arises from a previously underexplored gap between strategy usage-whether a reasoning strategy appears in successful solutions-and strategy executability-whether the strategy remains effective when instantiated as guidance for a target model. Through a controlled analysis of paired human-written and model-generated solutions, we identify a systematic dissociation between usage and executability: human- and model-derived strategies differ in structured, domain-dependent ways, leading to complementary strengths and consistent source-dependent reversals under guidance. Building on this diagnosis, we propose Selective Strategy Retrieval (SSR), a test-time framework that explicitly models executability by selectively retrieving and combining strategies using empirical, multi-route, source-aware signals. Across multiple mathematical reasoning benchmarks, SSR yields reliable and consistent improvements over direct solving, in-context learning, and single-source guidance, improving accuracy by up to $+13$ points on AIME25 and $+5$ points on Apex for compact reasoning models. Code and benchmark are publicly available at: https://github.com/lwd17/strategy-execute-pipeline.