思維格：自思維樹演進之結構化推理方法

Abstract

近年來，大型語言模型（LLMs）在各種任務上展現出優異的表現。然而，其推理能力仍受到傳統提示方法的限制，例如直接的輸入輸出（I/O）映射或是線性的思維鏈（Chain-of-Thought, CoT）提示。雖然「思維樹」（Tree of Thought, ToT）框架透過探索多條推理路徑來提升模型的推理表現，但因為存在大量重複節點與高昂的 token 使用量，使其在效率上仍有不足。 本論文提出一個改良的框架──「思維格」（Lattice of Thought, LoT），以解決 ToT 中的效率問題。該方法透過辨識並合併語意相同的推理狀態，將原本的樹狀結構壓縮為格狀結構，從而減少重複探索與不必要的 token 消耗。在 Game of 24 任務上的實驗結果顯示，LoT 在維持與 ToT 相當甚至更高的成功率下，平均 token 使用量降低了 29.04%。此外，本研究也對多種提示策略進行了成本、效率與成功率的分析與比較。 結果證明，LoT 提供了一種更有效率且可擴展的推理方式，為大型語言模型在多步驟問題解決上的應用帶來新的可能性。

In recent years, large language models (LLMs) have shown impressive performance across a wide range of tasks. However, their reasoning ability is often limited by traditional prompting methods such as direct input-output (I/O) mapping or sequential Chain-of-Thought (CoT) prompting. While the Tree of Thought (ToT) framework improves reasoning by exploring multiple reasoning paths in a tree structure, it suffers from inefficiency due to redundant node expansion and high token usage. This thesis proposes a new framework called Lattice of Thought (LoT), which enhances ToT by identifying and merging semantically equivalent reasoning states into a lattice structure. By eliminating repeated paths and overlapping subtrees, LoT reduces unnecessary token consumption and computational cost during exploration. Our experiments on the Game of 24 task show that LoT achieves a 29.04% reduction in token usage while maintaining a comparable or higher success rate than ToT. We also provide a detailed analysis of cost, efficiency, and success rate across various prompting strategies. The results demonstrate that LoT offers a more efficient and scalable approach to structured reasoning in LLMs and opens up opportunities for further improvements in multi-step problem-solving tasks.