Numerical reasoning is an essential ability for NLP systems to handle numeric information. Recent research indicates that fine-tuning a small-scale model to learn generating reasoning processes alongside answers can significantly enhance performance. However, current methods have the limitation that most methods generate reasoning processes with large language models (LLMs), which are "unreliable" since such processes could contain information unrelated to the answer. To address this limitation, we introduce Enhancing NumeriCal reasOning with Reliable procEsses (Encore), which derives the reliable reasoning process by decomposing the answer formula, ensuring which fully supports the answer. Nevertheless, models could lack enough data to learn the reasoning process generation adequately, since our method generates only one single reasoning process for one formula. To overcome this difficulty, we present a series of pre-training tasks to help models learn the reasoning process generation with synthesized data. The experiments show that Encore yields improvement on all five experimental datasets with an average of 1.8%, proving the effectiveness of our method.

翻译：数值推理是自然语言处理系统处理数值信息的关键能力。近期研究表明，微调小规模模型以学习生成推理过程及对应答案可显著提升性能。然而，现有方法普遍存在局限性——多数方法依赖大语言模型（LLM）生成推理过程，这类过程可能包含与答案无关的干扰信息，因而具有"不可靠性"。针对这一局限，我们提出Encore（Enhancing NumeriCal reasOning with Reliable procEsses）方法，通过解构答案公式推导出可靠推理过程，确保其完整支撑最终答案。但该方法存在数据稀缺问题：每个公式仅能生成单一推理过程，导致模型难以充分学习推理过程生成范式。为突破这一瓶颈，我们设计系列预训练任务，利用合成数据帮助模型掌握推理过程生成能力。实验表明，Encore在所有五个实验数据集上均实现性能提升（平均提升1.8%），充分验证了方法的有效性。