| # Chain-of-Thought as Sequential Conditional Probability Constriction | |
| ## Author | |
| **Kevin T.N** | |
| Email: jkdkr2439@gmail.com | |
| --- | |
| ## What is this? | |
| This repository contains a **theoretical / mathematical interpretation of Chain-of-Thought (CoT) prompting** for large language models. | |
| Instead of treating CoT as: | |
| - "reasoning" | |
| - "thinking step by step" | |
| - or a cognitive mechanism | |
| this work formalizes CoT as: | |
| > **A sequential conditional probability constriction process**, | |
| > where each intermediate token re-conditions the model distribution, | |
| > progressively narrowing entropy and steering probability mass. | |
| In short: | |
| - CoT does **not** add intelligence | |
| - It reshapes **how probability is conditioned and sampled** | |
| --- | |
| ## Who is this for? | |
| This work may be useful if you are: | |
| - A researcher working on **LLM interpretability** | |
| - Interested in **reasoning vs. probability steering** | |
| - Designing **prompting, inference, or sampling strategies** | |
| - Thinking about CoT, ToT, ReAct from a **theoretical / information-theoretic** angle | |
| This is **not**: | |
| - a benchmark paper | |
| - a performance hack | |
| - a production recipe | |
| It is a **conceptual tool**. | |
| --- | |
| ## How to use this work | |
| You are encouraged to: | |
| - Reuse the mathematical framing | |
| - Adapt the notation to your own context | |
| - Extend it with: | |
| - Bayesian inference | |
| - filtering / particle methods | |
| - causal or SCM analysis | |
| - empirical validation | |
| If you find it useful: | |
| - **Please credit or shout out the author** (Kevin T.N) | |
| - You do **not** need permission | |
| - You **should** adapt and update it to your own framing | |
| This work is intentionally open and unfinished. | |
| --- | |
| ## Citation / Attribution (informal) | |
| If you reference this idea in writing or discussion, a simple attribution is enough: | |
| > “Based on a probabilistic interpretation of Chain-of-Thought as sequential conditional distribution constriction by Kevin T.N.” | |
| Formal citation is optional. | |
| --- | |
| ## License | |
| This project is released under the **MIT License**. | |
| You are free to: | |
| - use | |
| - copy | |
| - modify | |
| - merge | |
| - publish | |
| - distribute | |
| - sublicense | |
| with **no warranty**, as long as the license notice is included. | |
| --- | |
| ## MIT License | |
| MIT License | |
| Copyright (c) 2026 Kevin T.N | |
| Permission is hereby granted, free of charge, to any person obtaining a copy | |
| of this software and associated documentation files (the "Software"), to deal | |
| in the Software without restriction, including without limitation the rights | |
| to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | |
| copies of the Software, and to permit persons to whom the Software is | |
| furnished to do so, subject to the following conditions: | |
| The above copyright notice and this permission notice shall be included in all | |
| copies or substantial portions of the Software. | |
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | |
| IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | |
| FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | |
| AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | |
| LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | |
| OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | |
| SOFTWARE. | |