# Circular Reasoning: Understanding Self-Reinforcing Loops in Large Reasoning Models

arXiv: https://arxiv.org/abs/2601.05693 · HTML: https://mlsanity.com/paper/2601.05693/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 9 Jan 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 18 of 18)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://mlsanity.com/paper/1909.05858/) (2019)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [SemDeDup: Data-efficient learning at web-scale through semantic deduplication](https://mlsanity.com/paper/2303.09540/) (2023)
- [Scaling Laws and Interpretability of Learning from Repeated Data](https://mlsanity.com/paper/2205.10487/) (2022)
- [SuperGPQA: Scaling LLM Evaluation across 285 Graduate Disciplines](https://mlsanity.com/paper/2502.14739/) (2025)
- [Knowledge Circuits in Pretrained Transformers](https://mlsanity.com/paper/2405.17969/) (2024)
- [Missing Premise exacerbates Overthinking: Are Reasoning Models losing Critical Thinking Skill?](https://mlsanity.com/paper/2504.06514/) (2025)
- [LLM Latent Reasoning as Chain of Superposition](https://mlsanity.com/paper/2510.15522/) (2025)
- [Innate Reasoning is Not Enough: In-Context Learning Enhances Reasoning Large Language Models with Less Overthinking](https://mlsanity.com/paper/2503.19602/) (2025)
- [Everything is Editable: Extend Knowledge Editing to Unstructured Data in Large Language Models](https://mlsanity.com/paper/2405.15349/) (2024)
- [The Evolution of Thought: Tracking LLM Overthinking via Reasoning Dynamics Analysis](https://mlsanity.com/paper/2508.17627/) (2025)
- [Related Knowledge Perturbation Matters: Rethinking Multiple Pieces of Knowledge Editing in Same-Subject](https://mlsanity.com/paper/2502.06868/) (2025)
- [Focusing by Contrastive Attention: Enhancing VLMs' Visual Reasoning](https://mlsanity.com/paper/2509.06461/) (2025)
- [Large Language Model Sourcing: A Survey](https://mlsanity.com/paper/2510.10161/) (2025)
- [GloSS over Toxicity: Understanding and Mitigating Toxicity in LLMs via Global Toxic Subspace](https://mlsanity.com/paper/2505.17078/) (2025)
- [Word Salad Chopper: Reasoning Models Waste A Ton Of Decoding Budget On Useless Repetitions, Self-Knowingly](https://mlsanity.com/paper/2511.00536/) (2025)

## Built on by (most cited first, 5 of 5)

- [Latent-GRPO: Group Relative Policy Optimization for Latent Reasoning](https://mlsanity.com/paper/2604.27998/) (2026)
- [ShortOPD: Recovering Pruned LLMs with Short-to-Long On-Policy Distillation](https://mlsanity.com/paper/2607.13124/) (2026)
- [Sanity Checks for Long-Form Hallucination Detection](https://mlsanity.com/paper/2605.08346/) (2026)
- [CUSUM-Shaped Inference-Time Monitoring and Targeted Re-Decoding for Quantized Small Language Model Reasoning](https://mlsanity.com/paper/2607.20129/) (2026)
- [Calibrated e-CUSUM Decoding for Quantized Reasoning Models: Why Token Log-Probability Is the Wrong Observable for Decoding Monitors](https://mlsanity.com/paper/2607.11317/) (2026)

## Abstract (arXiv)

Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular Reasoning. Unlike traditional model degeneration, this phenomenon manifests as a self-reinforcing trap where generated content acts as a logical premise for its own recurrence, compelling the reiteration of preceding text. To systematically analyze this phenomenon, we introduce LoopBench, a dataset designed to capture two distinct loop typologies: numerical loops and statement loops. Mechanistically, we characterize circular reasoning as a state collapse exhibiting distinct boundaries, where semantic repetition precedes textual repetition. We reveal that reasoning impasses trigger the loop onset, which subsequently persists as an inescapable cycle driven by a self-reinforcing V-shaped attention mechanism. Guided by these findings, we employ the Cumulative Sum (CUSUM) algorithm to capture these precursors for early loop prediction. Experiments across diverse LRMs validate its accuracy and elucidate the stability of long-chain reasoning.