Foundation models like chatGPT have demonstrated remarkable performance on various tasks. However, for many questions, they may produce false answers that look accurate. How do we train the model to precisely understand the concepts? In this paper, we introduce succinct representations of concepts based on category theory. Such representation yields concept-wise invariance properties under various tasks, resulting a new learning algorithm that can provably and accurately learn complex concepts or fix misconceptions. Moreover, by recursively expanding the succinct representations, one can generate a hierarchical decomposition, and manually verify the concept by individually examining each part inside the decomposition.

翻译：象聊天GPT这样的基础模型在各种任务上表现出了非凡的成绩。 但是,对于许多问题,它们可能产生看起来准确的假答案。 我们如何训练模型来准确理解概念? 在本文中,我们介绍基于分类理论的概念的简明表述。这种表述在各种任务下产生概念上顺理成章的变异特性,从而产生一种新的学习算法,可以准确和准确地学习复杂的概念或纠正错误观念。 此外,通过反复扩展简明的表述,人们可以产生等级分解,并通过对分解内部的每个部分进行单独检查来人工核实概念。</s>