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

TL;DR

HERALD is a novel framework that combines language reasoning, symbolic calculation, and adaptive ensemble techniques to improve bilingual mathematical problem solving accuracy and stability.

Contribution

The paper introduces HERALD, a tool-augmented hybrid ensemble framework with adaptive routing and knowledge distillation for bilingual math reasoning.

Findings

HERALD improves reasoning accuracy and calculation precision in bilingual math problems.

Adaptive routing and reinforcement learning reduce redundancy and enhance stability.

Knowledge distillation accelerates inference without sacrificing accuracy.

Abstract

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.