Everything of Thoughts: Defying the Law of Penrose Triangle for Thought Generation

Everything of Thoughts: Defying the Law of Penrose Triangle for Thought Generation
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Original Paper
Recent advancements in Large Language Models (LLMs) have revolutionized decision-making by breaking down complex problems into more manageable language sequences referred to as "thoughts". An effective thought design should consider three key perspectives: performance, efficiency, and flexibility. However, existing thought can at most exhibit two of these attributes. To address these limitations, we introduce a novel thought prompting approach called "Everything of Thoughts" (XoT) to defy the law of "Penrose triangle of existing thought paradigms. XoT leverages pretrained reinforcement learning and Monte Carlo Tree Search (MCTS) to incorporate external domain knowledge into thoughts, thereby enhancing LLMs' capabilities and enabling them to generalize to unseen problems efficiently. Through the utilization of the MCTS-LLM collaborative thought revision framework, this approach autonomously produces high-quality comprehensive cognitive mappings with minimal LLM interactions. Additionally, XoT empowers LLMs to engage in unconstrained thinking, allowing for flexible cognitive mappings for problems with multiple solutions. We evaluate XoT on several challenging multi-solution problem-solving tasks, including Game of 24, 8-Puzzle, and Pocket Cube. Our results demonstrate that XoT significantly outperforms existing approaches. Notably, XoT can yield multiple solutions with just one LLM call, showcasing its remarkable proficiency in addressing complex problems across diverse domains.

Summary Notes

Breaking New Ground with AI: The XoT Framework

The field of AI and machine learning is constantly evolving, with Large Language Models (LLMs) playing a crucial role in mimicking human thought processes to solve complex issues.
Yet, finding the sweet spot between high performance, efficiency, and flexibility in thought generation has been a longstanding challenge.
This blog post introduces the pioneering "Everything of Thoughts" (XoT) framework, a groundbreaking approach designed to push beyond the limitations of existing models, offering a fresh perspective for AI Engineers in large corporations.


Traditional models like Chain-of-Thought, Tree-of-Thought, and Graph-of-Thought have advanced the capability of LLMs in dissecting and addressing complex problems.
However, they often struggle to optimize performance, efficiency, and flexibility all at once. This dilemma is reminiscent of the Penrose triangle in thought generation – aiming to excel in these three aspects simultaneously seems unachievable. Enter the XoT framework, poised to challenge this notion.

XoT Framework

The essence of XoT lies in its innovative combination of Monte Carlo Tree Search (MCTS) with LLMs. This blend leverages MCTS's strategic prowess, seen in games like Go, with LLMs' nuanced understanding, creating a new way of generating thoughts.
XoT uses this combination to incorporate external knowledge and planning, significantly boosting performance, efficiency, and flexibility.


XoT employs a detailed process to ensure effective problem-solving:
  • Selection: Choosing the most promising paths to explore based on existing knowledge.
  • Expansion & Evaluation: Venturing into new paths and evaluating their viability using policy and value networks.
  • Backpropagation: Strengthening successful paths to refine the approach.
This method, powered by the synergy between MCTS and LLMs, enables XoT to efficiently navigate through complex thought processes.


Experiments with tasks like the Game of 24, 8-Puzzle, and Pocket Cube have proven XoT's capabilities. It outperformed existing methods in both accuracy and computational efficiency, while also demonstrating an ability to handle multiple solutions and generate intricate thought structures. This marks a significant advancement in AI problem-solving.


The XoT framework redefines what's possible in thought generation, overcoming the challenges posed by the Penrose triangle. By combining MCTS's exploration skills with LLMs' depth of understanding, XoT pushes the boundaries of AI problem-solving.
It offers a new level of performance, efficiency, and flexibility, opening up new possibilities for AI applications in large corporations.

Future Work

XoT's journey is just beginning. Future projects may expand its application to more complex problems and further enhance the integration of external knowledge, boosting the autonomy and effectiveness of LLMs. The potential for XoT to transform problem-solving across various fields is vast, signaling a new wave of AI innovation.
In summary, the XoT framework not only challenges existing limitations in thought generation but also establishes a new standard for AI and machine learning capabilities.
For AI Engineers in large companies, XoT presents a valuable tool for tackling complex challenges with an unmatched level of efficiency, flexibility, and performance, representing a significant leap in the development of LLM-based solutions.

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