Planning: Chain-of-Thought, Tree-of-Thoughts & Graph-of-Thoughts
How LLMs deliberate: Chain-of-Thought writes one reasoning line, Tree-of-Thoughts explores branches and backtracks, Graph-of-Thoughts merges many partial answers. This topic covers how each works, what each costs, and what reasoning models changed in 2024–2025.
01.The Problem: The Model's First Thought Can Be Wrong
Give a model a puzzle:
"Make 24 using the cards 4, 9, 10, 13 — you may use +, −, ×, ÷ and parentheses."
Ask it directly and it blurts one answer in a single pass. If its first internal step is wrong, there is no way to take that step back. It can't even see that it was wrong — it just keeps generating, rationalizing its own mistake.
That is the structural weakness of plain generation:
- One shot. The answer is decoded greedily from the question.
- No undo. Wrong early steps get rationalized, not reverted.
- No alternatives. The model never asks "what if I tried a different approach first?"
So the question becomes
Can we make the model deliberate — write out steps, consider alternatives, check itself — before committing?
The last three years of prompting research is one long answer to that question, organized by the shape of the deliberation:
- a line (Chain-of-Thought),
- a tree you search (Tree-of-Thoughts),
- a graph you merge (Graph-of-Thoughts).
This topic walks up that ladder — and ends with the 2024–2025 twist: reasoning models moved all of this inside the model.
Reasoning Topologies
Reasoning Topologies
CoT samples one path; ToT searches a tree with BFS/DFS and value functions; GoT merges and refines parallel thoughts like a DAG operation.
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