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

Bilingual mathematical problem solving needs aclear link between language reasoning and symbolic calculation.Large language models often handle language well but areweak in accurate computation. This paper presents HERALD(Hybrid Ensemble Reasoning with Adaptive Learning and Distillation),a framework that joins reasoning and calculationusing NuminaMath-7B-TIR, GPT-4o, and Mistral-7B. HERALDuses adaptive routing, tool-based reinforcement learning, andknowledge distillation to connect different reasoning paths. Confidencecalibration keeps weighting stable, and dual-path checkingkeeps results correct. Reinforcement learning controls tool use tocut redundancy, and distillation lowers delay without hurtingaccuracy. The system shows that combining symbolic checking,adaptive ensembles, and bilingual fine-tuning helps achieve bothfluent reasoning and precise calculation. HERALD offers apractical solution for multilingual mathematical reasoning withbetter accuracy, stability, and clarity.