Leveraging ``chain-of-thought (CoT)'' reasoning to elicit rapid and precise responses from large language models (LLMs) is rapidly attracting research interest. A notable challenge here is how to design or select optimal prompts. The process of prompt selection relies on trial and error, involving continuous adjustments and combinations of input prompts by users based on the corresponding new responses generated from LLMs. Furthermore, minimal research has been conducted to explore how LLMs employ the mathematical problem-solving capabilities learned from user interactions to address issues in narrative writing. To improve interpretability and explore the balance principle between generality and personalization under a multi-domain CoT prompt selection scenario, we propose the Federated Logic rule learning approach (FedLogic). We introduce a theoretical formalization and interactive emulation of the multi-domain CoT prompt selection dilemma in the context of federated LLMs. We cast the problem of joint probability modeling as a bilevel program, where the CoT prompt selection intricacy can be likened to a fuzzy score-based rule selection with the LLMs function as rule generators. FedLogic solves this problem through variational expectation maximization (V-EM). In addition, we incorporate two KL-divergence constraints within this probabilistic modeling framework to surmount the intricacies of managing extensive search spaces and accomplishing cross-domain personalization of CoTs. To the best of our knowledge, FedLogic is the first interpretable and principled federated multi-domain CoT prompt selection approach for LLMs.

翻译：摘要：利用“链式思维（CoT）”推理机制激发大型语言模型（LLMs）的快速精准响应能力正迅速成为研究热点。其中一个显著挑战在于如何设计或选择最优提示。当前提示选择过程依赖试错法，即用户根据LLMs生成的新响应不断调整和组合输入提示。此外，目前鲜有研究探讨LLMs如何将用户交互中习得的数学问题求解能力迁移至叙事性写作任务。为提升可解释性并探索多领域CoT提示选择场景下通用性与个性化之间的平衡原理，我们提出联邦逻辑规则学习方法（FedLogic）。我们建立了联邦LLMs背景下多领域CoT提示选择困境的理论形式化模型与交互仿真框架。将联合概率建模问题转化为双层规划问题，其中CoT提示选择的复杂性可类比为基于模糊得分的规则选择过程，而LLMs作为规则生成器。FedLogic通过变分期望最大化（V-EM）算法求解该问题。此外，我们在该概率建模框架中引入双重KL散度约束，以克服大规模搜索空间管理及跨领域CoT个性化实现的复杂性。据我们所知，FedLogic是首个面向LLMs的可解释且具备理论原则性的联邦多领域CoT提示选择方法。