Go to ACL ARR 2026 January homepageSTAR: Strategy-Aware Routing for Mathematical Reasoning
Keywords: Mathematical Reasoning, Large Language Model Reasoning
Abstract: Existing methods usually leverage a fixed strategy, such as natural language reasoning, code-augmented reasoning, tool-integrated reasoning, or ensemble-based reasoning, to guide Large Language Models (LLMs) to perform mathematical reasoning. However, a single strategy cannot adequately handle diverse problems and thus neglects the trade-off between effectiveness and efficiency. To address these issues, we propose STAR (STrategy-Aware Routing for mathematical reasoning), a novel framework that decouples mathematical reasoning into two stages: strategy evaluation and targeted execution. Specifically, we first construct a multi-strategy preference dataset, which we call \texttt{MathStrat}, capturing correctness, process quality, and computational efficiency for each problem–strategy pair. We then train a lightweight strategy adapter on the dataset to obtain a confidence distribution over the four reasoning strategies. Based on this distribution, an adaptive routing mechanism is leveraged to select the most appropriate reasoning strategy dynamically. This mechanism directs LLMs to use single-strategy execution for high-confidence predictions, dual-strategy verification for competitive scenarios, and comprehensive multi-strategy exploration for uncertain cases, respectively. Extensive experiments across five mathematical reasoning benchmarks demonstrate that PRISM consistently outperforms individual and ensemble reasoning strategies, achieving improvements ranging from 0.9\% to 7.6\% across different LLMs. In addition, the adaptive routing mechanism shows particularly strong benefits for mathematical reasoning tasks across various LLMs with different sizes. Our code is released at https://anonymous.4open.science/r/STAR-2C61.
Paper Type: Long
Research Area: Mathematical, Symbolic, Neurosymbolic, and Logical Reasoning
Research Area Keywords: Mathematical, Question Answering, Language Modeling
Contribution Types: Approaches low compute settings-efficiency, Data resources
Languages Studied: English
Submission Number: 9561
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