# To CoT or To Loop? A Formal Comparison Between Chain-of-Thought and Looped Transformers

arXiv: https://arxiv.org/abs/2505.19245 · HTML: https://mlsanity.com/paper/2505.19245/

## Key facts

- Cited by 11 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 18 of its 30 references that are in the map.
- First posted on arXiv 25 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, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [Looped Transformers as Programmable Computers](https://mlsanity.com/paper/2301.13196/) (2023)
- [The Parallelism Tradeoff: Limitations of Log-Precision Transformers](https://mlsanity.com/paper/2207.00729/) (2022)
- [From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models](https://mlsanity.com/paper/2406.16838/) (2024)
- [Why think step by step? Reasoning emerges from the locality of experience](https://mlsanity.com/paper/2304.03843/) (2023)
- [Transformers, parallel computation, and logarithmic depth](https://mlsanity.com/paper/2402.09268/) (2024)
- [MoEUT: Mixture-of-Experts Universal Transformers](https://mlsanity.com/paper/2405.16039/) (2024)
- [A Little Depth Goes a Long Way: The Expressive Power of Log-Depth Transformers](https://mlsanity.com/paper/2503.03961/) (2025)
- [On Expressive Power of Looped Transformers: Theoretical Analysis and Enhancement via Timestep Encoding](https://mlsanity.com/paper/2410.01405/) (2024)
- [On the Representational Capacity of Neural Language Models with Chain-of-Thought Reasoning](https://mlsanity.com/paper/2406.14197/) (2024)

## Built on by (most cited first, 11 of 11)

- [SIM-CoT: Supervised Implicit Chain-of-Thought](https://mlsanity.com/paper/2509.20317/) (2025)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [Implicit Reasoning in Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2509.02350/) (2025)
- [Training-Free Looped Transformers](https://mlsanity.com/paper/2605.23872/) (2026)
- [Bridging the Gap Between Latent and Explicit Reasoning with Looped Transformers](https://mlsanity.com/paper/2606.31779/) (2026)
- [MeSH: Memory-as-State-Highways for Recursive Transformers](https://mlsanity.com/paper/2510.07739/) (2025)
- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)
- [On the Reasoning Abilities of Masked Diffusion Language Models](https://mlsanity.com/paper/2510.13117/) (2025)
- [DAG-Math: Graph-of-Thought Guided Mathematical Reasoning in LLMs](https://mlsanity.com/paper/2510.19842/) (2025)
- [CoLT: Reasoning with Chain of Latent Tool Calls](https://mlsanity.com/paper/2602.04246/) (2026)
- [Running Fewer Loops Removes Refusal Behaviour in Recurrent-Depth Language Models](https://mlsanity.com/paper/2610.15218/) (2026)

## Abstract (arXiv)

Chain-of-Thought (CoT) and Looped Transformers have been shown to empirically improve performance on reasoning tasks and to theoretically enhance expressivity by recursively increasing the number of computational steps. However, their comparative capabilities are still not well understood. In this paper, we provide a formal analysis of their respective strengths and limitations. We show that Looped Transformers can efficiently simulate parallel computations for deterministic tasks, which we formalize as evaluation over directed acyclic graphs. In contrast, CoT with stochastic decoding excels at approximate inference for compositional structures, namely self-reducible problems. These separations suggest the tasks for which depth-driven recursion is more suitable, thereby offering practical cues for choosing between reasoning paradigms.