# CIRF: Tokenizing Chain-of-Thoughts into Reusable Functional Units for Efficient Latent Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2605.28292 · HTML: https://mlsanity.com/paper/2605.28292/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 31 references that are in the map.
- First posted on arXiv 27 May 2026.

## 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, 15 of 15)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Chain of Draft: Thinking Faster by Writing Less](https://mlsanity.com/paper/2502.18600/) (2025)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [Let's Think Dot by Dot: Hidden Computation in Transformer Language Models](https://mlsanity.com/paper/2404.15758/) (2024)
- [Don't Overthink it. Preferring Shorter Thinking Chains for Improved LLM Reasoning](https://mlsanity.com/paper/2505.17813/) (2025)
- [SIM-CoT: Supervised Implicit Chain-of-Thought](https://mlsanity.com/paper/2509.20317/) (2025)
- [SemCoT: Accelerating Chain-of-Thought Reasoning through Semantically-Aligned Implicit Tokens](https://mlsanity.com/paper/2510.24940/) (2025)

## Abstract (arXiv)

Implicit Chain-of-Thought (CoT) reduces the inference cost of large language models by internalizing the explicit rationales. However, existing approaches typically lack alignment with explicit rationales and adaptivity to example complexity. In this work, we propose CIRF (textitunderlineChain-of-thoughts underlineInto underlineReusable underlineFunctional units), an implicit CoT framework that performs reasoning as a dynamic sequence of discrete functional tokens. CIRF assigns a functional token to each semantically coherent reasoning unit in explicit CoT traces. The model is then fine-tuned to autoregressively generate functional tokens and their optional results, followed by the final answer. This design aligns latent reasoning with a sequence of functional units, facilitating parallel training, explicit rationale alignment, and adaptive reasoning. Extensive experiments on mathematical, symbolic, and commonsense reasoning benchmarks show that CIRF provides a favorable accuracy-latency trade-off compared with state-of-the-art implicit CoT methods. Further analyses demonstrate that CIRF constructs distinct, interpretable functional tokens, leading to consistent performance improvements.