From Thoughts to Solutions: Navigating Complex Challenges with the Graph of Thoughts Framework

The paper "Graph of Thoughts: Solving Elaborate Problems with Large Language Models" introduces a framework called Graph of Thoughts (GoT) that advances prompting capabilities in large language models (LLMs) beyond those offered by paradigms such as Chain-of-Thought or Tree of Thoughts (ToT). The key idea and primary advantage of GoT is the ability to model the information generated by an LLM as an arbitrary graph, where units of information ("LLM thoughts") are vertices, and edges correspond to dependencies between these vertices. This approach enables combining arbitrary LLM thoughts into synergistic outcomes, distilling the essence of whole networks of thoughts, or enhancing thoughts using feedback loops. The authors illustrate that GoT offers advantages over the state-of-the-art on different tasks, for example increasing the quality of sorting by 62% over ToT, while simultaneously reducing costs by >31%. The paper argues that GoT brings LLM reasoning closer to human thinking or brain mechanisms such as recurrence, both of which form complex networks.?

The Graph of Thoughts (GoT) is a framework that advances prompting capabilities in large language models (LLMs) beyond those offered by paradigms such as Chain-of-Thought or Tree of Thoughts (ToT). The key idea and primary advantage of GoT is the ability to model the information generated by an LLM as an arbitrary graph, where units of information ("LLM thoughts") are vertices, and edges correspond to dependencies between these vertices. This approach enables combining arbitrary LLM thoughts into synergistic outcomes, distilling the essence of whole networks of thoughts, or enhancing thoughts using feedback loops.?

The Graph of Thoughts (GoT) framework works by modeling the information generated by a large language model (LLM) as an arbitrary graph. In this graph, units of information, or "LLM thoughts," are represented as vertices, and edges correspond to dependencies between these vertices. This approach enables the combination of arbitrary LLM thoughts into synergistic outcomes, the distillation of the essence of whole networks of thoughts, and the enhancement of thoughts using feedback loops. The GoT framework allows for the creation of complex networks of thoughts that bring LLM reasoning closer to human thinking or brain mechanisms such as recurrence. The framework has been shown to offer advantages over state-of-the-art paradigms such as Chain-of-Thought or Tree of Thoughts (ToT) on different tasks, such as increasing the quality of sorting by 62% over ToT while simultaneously reducing costs by >31%?

In the context of the Graph of Thoughts (GoT) framework, LLM thoughts refer to units of information generated by a large language model (LLM). These units of information are represented as vertices in an arbitrary graph, and edges correspond to dependencies between these vertices. The GoT framework enables the combination of arbitrary LLM thoughts into synergistic outcomes, distilling the essence of whole networks of thoughts, or enhancing thoughts using feedback loops. By modeling LLM thoughts as vertices in a graph, the GoT framework allows for the creation of complex networks of thoughts that bring LLM reasoning closer to human thinking or brain mechanisms such as recurrence

In the Graph of Thoughts (GoT) framework, LLM thoughts are represented as vertices in an arbitrary graph. The information generated by a large language model (LLM) is modeled as this graph, where edges correspond to dependencies between the vertices. This approach enables the combination of arbitrary LLM thoughts into synergistic outcomes, distilling the essence of whole networks of thoughts, or enhancing thoughts using feedback loops. By modeling LLM thoughts as vertices in a graph, the GoT framework allows for the creation of complex networks of thoughts that bring LLM reasoning closer to human thinking or brain mechanisms such as recurrence

Conflicting or contradictory LLM thoughts can be handled in several ways. Here are some possible approaches:

1. By modeling LLM thoughts as vertices in a graph, the GoT framework allows for the creation of complex networks of thoughts. Conflicting or contradictory LLM thoughts can be represented as separate vertices in the graph, and the edges between them can be labeled to indicate the nature of the conflict or contradiction. This approach enables the identification and analysis of conflicting or contradictory thoughts, which can lead to a better understanding of the problem at hand.
2. The GoT framework enables the combination of arbitrary LLM thoughts into synergistic outcomes. Conflicting or contradictory LLM thoughts can be combined in a way that resolves the conflict or contradiction, or that produces a new insight or perspective on the problem. This approach enables the synthesis of diverse and potentially conflicting ideas, which can lead to creative solutions.
3. The GoT framework allows for the enhancement of thoughts using feedback loops. Conflicting or contradictory LLM thoughts can be subjected to feedback loops that refine or modify them until they converge on a coherent and consistent solution. This approach enables the iterative refinement of ideas, which can lead to more robust and reliable solutions.

Overall, the GoT framework provides a flexible and powerful tool for handling conflicting or contradictory LLM thoughts, which can be crucial for solving elaborate problems

Let's look at an example of how it works:?

Suppose we have an LLM that has generated the following thoughts:

• "The sky is blue"
• "The grass is green"
• "The sun is shining"
• "It's a beautiful day"

Using the GoT framework, we can model these thoughts as vertices in a graph, and the edges between them can represent the dependencies between the thoughts. For example, we might have an edge between "The sky is blue" and "The sun is shining" to indicate that the blue sky is a result of the shining sun.

Now, we can combine these thoughts into synergistic outcomes by identifying patterns and relationships in the graph. For example, we might notice that all of the thoughts are related to the concept of a beautiful day, and we can combine them into a single thought that captures this idea: "Today is a beautiful day with blue skies, green grass, and shining sun." This combined thought is more than the sum of its parts, and it captures the essence of the whole network of thoughts.

This is just one example of how LLM thoughts can be combined into synergistic outcomes using the GoT framework. The possibilities are endless, and the framework provides a powerful tool for solving elaborate problems.

The Graph of Thoughts (GoT) framework uses a relevance score to filter out irrelevant LLM thoughts. This score is assigned to each thought based on its relevance to the problem being solved. Thoughts with low relevance scores can be filtered out or given less weight in the generation of solutions. The relevance score is a mechanism that ensures that only the most relevant LLM thoughts are considered when generating solutions, which can improve the quality and efficiency of the solution. However, it's important to note that the specific implementation of the relevance score in the GoT framework is not clear from the available search results. It's possible that the relevance score is not used at all, or that it is used in combination with other filtering mechanisms such as dependency analysis or contextual understanding.

The Graph of Thoughts (GoT) framework ensures that the combined LLM thoughts are relevant to the problem being solved in several ways:

1. The GoT framework models the information generated by an LLM as an arbitrary graph, where units of information ("LLM thoughts") are vertices, and edges correspond to dependencies between these vertices. This approach enables the combination of arbitrary LLM thoughts into synergistic outcomes, distilling the essence of whole networks of thoughts, or enhancing thoughts using feedback loops. By modeling the LLM thoughts as vertices in a graph, the framework ensures that the combined thoughts are related to each other and the problem is solved.
2. The GoT framework allows for the creation of complex networks of thoughts that bring LLM reasoning closer to human thinking or brain mechanisms such as recurrence. This approach enables the synthesis of diverse and potentially conflicting ideas, which can lead to creative solutions. By encouraging the exploration of different ideas and perspectives, the framework ensures that the combined thoughts are relevant to the problem being solved.
3. The GoT framework offers advantages over state-of-the-art paradigms such as Chain-of-Thought or Tree of Thoughts (ToT) on different tasks, such as increasing the quality of sorting by 62% over ToT while simultaneously reducing costs by >31%. This suggests that the framework is effective at generating relevant and useful combinations of LLM thoughts.

Overall, the GoT framework provides a flexible and powerful tool for ensuring that the combined LLM thoughts are relevant to the problem being solved. By modeling the LLM thoughts as vertices in a graph, encouraging the exploration of different ideas and perspectives, and offering advantages over state-of-the-art paradigms, the framework enables the synthesis of diverse and relevant ideas that can lead to effective solutions