Strategy Executability in Mathematical Reasoning: Leveraging Human-Model Differences for Effective Guidance
arXiv:2602.22583v1 Announce Type: new 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
arXiv:2602.22583v1 Announce Type: new 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.
Executive Summary
This study investigates the gap between strategy usage and executability in mathematical reasoning, proposing Selective Strategy Retrieval (SSR) as a novel framework to improve guidance. By analyzing paired human-written and model-generated solutions, the authors identify a systematic dissociation between usage and executability, leading to complementary strengths and source-dependent reversals. SSR explicitly models executability, selectively retrieving and combining strategies using empirical signals, resulting in consistent improvements over existing methods across multiple mathematical reasoning benchmarks. The study's findings and proposed framework contribute to a deeper understanding of strategy executability and offer practical implications for improving guidance in mathematical reasoning.
Key Points
- ▸ The study identifies a systematic dissociation between strategy usage and executability in mathematical reasoning.
- ▸ Selective Strategy Retrieval (SSR) is proposed as a novel framework to improve guidance.
- ▸ SSR yields consistent improvements over existing methods across multiple mathematical reasoning benchmarks.
Merits
Strength in Addressing a Critical Gap
The study effectively addresses a previously underexplored gap in mathematical reasoning, shedding light on the relationship between strategy usage and executability.
Practical and Effective Framework
Selective Strategy Retrieval (SSR) offers a practical and effective framework for improving guidance in mathematical reasoning, demonstrating consistent improvements over existing methods.
Demerits
Limited Generalizability
The study's findings and proposed framework may not generalize to other domains or tasks beyond mathematical reasoning, limiting their broader applicability.
Dependence on Empirical Signals
The effectiveness of SSR relies on the availability and quality of empirical signals, which may not be universally applicable or feasible to obtain.
Expert Commentary
The study's contribution lies in its systematic investigation of the gap between strategy usage and executability in mathematical reasoning, shedding light on a critical aspect of AI development. The proposed framework, SSR, is a significant advancement in addressing this gap, offering a practical and effective solution for improving guidance. However, the study's findings and proposed framework are limited by their dependence on empirical signals and the potential for limited generalizability. To fully realize the implications of this study, further research is needed to explore the broader applicability of SSR and its potential applications in other domains and tasks.
Recommendations
- ✓ The study's findings and proposed framework should be further explored and validated in other domains and tasks to assess their broader applicability and potential impact.
- ✓ Future research should focus on developing more robust and generalizable methods for obtaining empirical signals, ensuring the effectiveness of SSR in various contexts.
