Teaching LLMs According to Their Aptitude: Adaptive Reasoning for Mathematical Problem Solving

TL;DR

This paper introduces TATA, an adaptive framework that enables large language models to autonomously select and apply the most suitable reasoning strategy based on their inherent capabilities, improving mathematical problem-solving performance.

Contribution

TATA is the first approach to allow LLMs to spontaneously adapt their reasoning strategies according to their aptitude during inference.

Findings

TATA improves performance on six mathematical benchmarks.

It combines strengths of Chain-of-Thought and Tool-Integrated Reasoning.

Aptitude-aware data selection is crucial for effective adaptation.

Abstract

Existing approaches to mathematical reasoning with large language models (LLMs) rely on Chain-of-Thought (CoT) for generalizability or Tool-Integrated Reasoning (TIR) for precise computation. While efforts have been made to combine these methods, they primarily rely on post-selection or predefined strategies, leaving an open question: whether LLMs can autonomously adapt their reasoning strategy based on their inherent capabilities. In this work, we propose TATA (Teaching LLMs According to Their Aptitude), an adaptive framework that enables LLMs to personalize their reasoning strategy spontaneously, aligning it with their intrinsic aptitude. TATA incorporates base-LLM-aware data selection during supervised fine-tuning (SFT) to tailor training data to the model's unique abilities. This approach equips LLMs to autonomously determine and apply the appropriate reasoning strategy at test time. We evaluate TATA through extensive experiments on six mathematical reasoning benchmarks, using both general-purpose and math-specialized LLMs. Empirical results demonstrate that TATA effectively combines the complementary strengths of CoT and TIR, achieving superior or comparable performance with improved inference efficiency compared to TIR alone. Further analysis underscores the critical role of aptitude-aware data selection in enabling LLMs to make effective and adaptive reasoning decisions and align reasoning strategies with model capabilities.