Tool-Augmented Hybrid Ensemble Reasoning with Distillation for Bilingual Mathematical Problem Solving
This work addresses the challenge of accurate computation in bilingual mathematical reasoning for users needing both fluent reasoning and precise calculation, representing an incremental improvement through hybrid methods.
The paper tackled the problem of bilingual mathematical problem solving by linking language reasoning with symbolic calculation, resulting in a framework that achieves better accuracy, stability, and clarity in multilingual mathematical reasoning.
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.