Last week, I came across an intriguing paper on Large Language Models (LLMs). It appears to further develop the "Tree of Thoughts" (ToT) reasoning method I mentioned before, introducing a new technique called the "Graph of Thoughts" (GoT). Let's take a closer look.

Features of GoT

First, let's compare various methods using the chart provided in the paper.

The far right shows the newly introduced GoT. Key differences from ToT may be that GoT allows for the merging of thoughts, and that users can define the shape of the GoT themselves. Incidentally, this merging is referred to as "aggregation" within the paper. While it may seem similar to ToT, the differences might be significant. Let's explore this in more detail.

2. Four Key Modules

GoT (Graph of Thoughts) has the following four crucial modules. Understanding these will clarify the differences between it and ToT (Tree of Thoughts).

Prompter
Parser
Scoring & Validation
Controller

Let's look at each one in detail. The Prompter, as the name suggests, is the module responsible for creating prompts. The Parser extracts the required information, or "thoughts," from the LLM (Large Language Model). You might think of the Prompter as handling input and the Parser as managing output. Scoring & Validation is the module that evaluates the gathered thoughts. This evaluation allows us to select the thoughts worth keeping. Finally, let's elaborate on the Controller. It is responsible for adding new thoughts or merging multiple thoughts, a process referred to as "transform." The Controller decides which transformations should be applied to which thoughts and passes this information to the Prompter. It is a critical module for executing problem-solving strategies. It has two functions: Graph of Operations (GoO), which is an execution plan for operations defined by the user, and Graph Reasoning State (GRS), which maintains the ongoing LLM reasoning process based on the thought state.

3. Considering the Number Sorting Problem

Since merely talking abstractly may not advance understanding, let's consider an actual task. This time we will consider sorting a list of 64 numbers in ascending order. Here, we'll see how the Graph of Operations (GoO) comes into play. In the chart below, each thought is tagged with operations like G (Generate), S (Sort), K (Keep the best), and A (Merge). Initially, we take a list of 64 numbers and divide it into four lists, each containing 16 numbers. Each of these lists is then sorted and evaluated. Only the list with the highest accuracy is kept. These are then further merged to form a new list containing 32 numbers. You'll see various operations functioning as the process progresses.

For those who want to delve deeper, detailed explanations are available here, particularly in the green part of the chart above.

It might feel complex at a glance, but it's user-controllable, allowing you to incorporate your domain knowledge. I am excited to conduct various experiments in the future.

Thank you for your attention! I will keep you updated on the progress of GoT and hope to share more with you soon. Stay tuned!

1) "Graph of Thoughts: Solving Elaborate Problems with Large Language Models", Maciej Besta, Nils Blach, Ales Kubicek, Robert Gerstenberger, Lukas Gianinazzi, Joanna Gajda, Tomasz Lehmann, Michal Podstawski, Hubert Niewiadomski, Piotr Nyczyk, Torsten Hoefler, 21 Aug 2023, https://arxiv.org/abs/2308.09687v2

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