HintMR: Eliciting Stronger Mathematical Reasoning in Small Language Models

2026-04-13

AI Summary

This work addresses the challenge that small language models struggle to maintain long reasoning chains and are highly susceptible to early errors in complex mathematical reasoning. To mitigate this, the authors propose a dual-model collaborative prompting framework: a distilled prompt-generation model dynamically produces context-aware, history-conditioned step-by-step prompts that guide a separate reasoning model through the solution process, deliberately withholding the final answer until the last step. This lightweight cooperative mechanism significantly enhances the reasoning accuracy of small models across multiple mathematical benchmarks, outperforming existing prompting strategies while preserving computational efficiency.

Technology Category

• Natural Language Processing: Prompt Engineering / Prompting
• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• mathematical reasoning
• small language models
• error propagation
• reasoning chains
• multi-step problem solving

Innovation

• hint-assisted reasoning
• small language models
• mathematical reasoning
• model collaboration
• distillation