Large language models (LLMs) often struggle with complex mathematical tasks, prone to "hallucinating" incorrect answers due to their reliance on statistical patterns. This limitation is further amplified in average Small LangSLMs with limited context and training data. To address this challenge, we propose an "Inductive Learning" approach utilizing a distributed network of SLMs. This network leverages error-based learning and hint incorporation to refine the reasoning capabilities of SLMs. Our goal is to provide a framework that empowers SLMs to approach the level of logic-based applications achieved by high-parameter models, potentially benefiting any language model. Ultimately, this novel concept paves the way for bridging the logical gap between humans and LLMs across various fields.

翻译：大型语言模型（LLM）在处理复杂数学任务时常常表现不佳，由于依赖统计模式而容易"幻觉"出错误答案。这一局限在上下文有限、训练数据较少的普通小型语言模型（SLM）中尤为突出。为应对这一挑战，我们提出了一种基于分布式SLM网络的"归纳学习"方法。该网络利用基于错误的学习与提示整合机制，来提升SLM的推理能力。我们的目标是构建一个框架，使SLM能够达到高参数模型在逻辑应用中的表现水平，从而有望惠及各类语言模型。最终，这一创新概念为弥合人类与LLM在各领域之间的逻辑鸿沟铺平了道路。