# Tool-Augmented Hybrid Ensemble Reasoning with Distillation for Bilingual Mathematical Problem Solving

arXiv: https://arxiv.org/abs/2512.19093 · HTML: https://mlsanity.com/paper/2512.19093/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 5 of 5)

- [Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning](https://mlsanity.com/paper/2306.02408/) (2023)
- [Advancing Tool-Augmented Large Language Models via Meta-Verification and Reflection Learning](https://mlsanity.com/paper/2506.04625/) (2025)
- [Reasoning Beyond Limits: Advances and Open Problems for LLMs](https://mlsanity.com/paper/2503.22732/) (2025)
- [Multilingual Mathematical Reasoning: Advancing Open-Source LLMs in Hindi and English](https://mlsanity.com/paper/2412.18415/) (2024)
- [Improving Math Problem Solving in Large Language Models Through Categorization and Strategy Tailoring](https://mlsanity.com/paper/2411.00042/) (2024)

## Abstract (arXiv)

Bilingual mathematical problem solving needs a clear link between language reasoning and symbolic calculation. Large language models often handle language well but are weak in accurate computation. This paper presents HERALD (Hybrid Ensemble Reasoning with Adaptive Learning and Distillation), a framework that joins reasoning and calculation using NuminaMath-7B-TIR, GPT-4o, and Mistral-7B. HERALD uses adaptive routing, tool-based reinforcement learning, and knowledge distillation to connect different reasoning paths. Confidence calibration keeps weighting stable, and dual-path checking keeps results correct. Reinforcement learning controls tool use to cut redundancy, and distillation lowers delay without hurting accuracy. The system shows that combining symbolic checking, adaptive ensembles, and bilingual fine-tuning helps achieve both fluent reasoning and precise calculation. HERALD offers a practical solution for multilingual mathematical reasoning with better accuracy, stability, and clarity.