HintMR: Eliciting Stronger Mathematical Reasoning in Small Language Models

TL;DR

HintMR introduces a cooperative two-model framework where a hint-generating small language model guides a reasoning model through multi-step mathematical problems, significantly improving accuracy.

Contribution

This work presents a novel hint-assisted reasoning framework that decomposes solutions into steps with context-aware hints generated by a separate model, enhancing small language models' mathematical reasoning.

Findings

Hint assistance improves reasoning accuracy across benchmarks.

The cooperative system reduces error propagation in multi-step reasoning.

Structured hint generation enhances small language models' problem-solving capabilities.

Abstract

Small language models (SLMs) often struggle with complex mathematical reasoning due to limited capacity to maintain long chains of intermediate steps and to recover from early errors. We address this challenge by introducing a hint-assisted reasoning framework that incrementally guides SLMs through multi-step mathematical problem solving. Our approach decomposes solutions into sequential reasoning steps and provides context-aware hints, where hints are generated by a separate SLM trained via distillation from a strong large language model. While the hint-generating SLM alone is not capable of solving the problems, its collaboration with a reasoning SLM enables effective guidance, forming a cooperative two-model system for reasoning. Each hint is generated conditionally on the problem statement and the accumulated reasoning history, providing stepwise, localized guidance without revealing full solutions. This reduces error propagation and allows the reasoning model to focus on manageable subproblems. Experiments across diverse mathematical benchmarks and models demonstrate that hint assistance consistently improves reasoning accuracy for SLMs, yielding substantial gains over standard prompting while preserving model efficiency. These results highlight that structured collaboration between SLMs-via hint generation and reasoning-offers an effective and lightweight mechanism for enhancing mathematical reasoning.