# Chain-of-Thought Tokens are Computer Program Variables

arXiv: https://arxiv.org/abs/2505.04955 · HTML: https://mlsanity.com/paper/2505.04955/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 8 May 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 10 of 10)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinking](https://mlsanity.com/paper/2501.04519/) (2025)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [Text and Patterns: For Effective Chain of Thought, It Takes Two to Tango](https://mlsanity.com/paper/2209.07686/) (2022)
- [LLaMA-Berry: Pairwise Optimization for O1-like Olympiad-Level Mathematical Reasoning](https://mlsanity.com/paper/2410.02884/) (2024)
- [Theoretical limitations of multi-layer Transformer](https://mlsanity.com/paper/2412.02975/) (2024)

## Built on by (most cited first, 6 of 6)

- [KG-Hopper: Empowering Compact Open LLMs with Knowledge Graph Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2603.21440/) (2026)
- [Reading Between the Dots: Decoding Hidden Computation across Filler Tokens](https://mlsanity.com/paper/2607.03502/) (2026)
- [CoLT: Reasoning with Chain of Latent Tool Calls](https://mlsanity.com/paper/2602.04246/) (2026)
- [Internalized Reasoning for Long-Context Visual Document Understanding](https://mlsanity.com/paper/2604.02371/) (2026)
- [KG-Reasoner: A Reinforced Model for End-to-End Multi-Hop Knowledge Graph Reasoning](https://mlsanity.com/paper/2604.12487/) (2026)
- [From Candidate Tokens to Final Outcomes: Decoding Relative Long-Horizon Candidate Value from Reasoning Model Representations](https://mlsanity.com/paper/2610.15412/) (2026)

## Abstract (arXiv)

Chain-of-thoughts (CoT) requires large language models (LLMs) to generate intermediate steps before reaching the final answer, and has been proven effective to help LLMs solve complex reasoning tasks. However, the inner mechanism of CoT still remains largely unclear. In this paper, we empirically study the role of CoT tokens in LLMs on two compositional tasks: multi-digit multiplication and dynamic programming. While CoT is essential for solving these problems, we find that preserving only tokens that store intermediate results would achieve comparable performance. Furthermore, we observe that storing intermediate results in an alternative latent form will not affect model performance. We also randomly intervene some values in CoT, and notice that subsequent CoT tokens and the final answer would change correspondingly. These findings suggest that CoT tokens may function like variables in computer programs but with potential drawbacks like unintended shortcuts and computational complexity limits between tokens. The code and data are available at https://github.com/solitaryzero/CoTs_are_Variables.