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

Zenghao Duan, Liang Pang, Zihao Wei, Wenbin Duan, Yuxin Tian, Shicheng Xu, Jingcheng Deng, Zhiyi Yin, Xueqi Cheng

TL;DR

The paper identifies Circular Reasoning as a self-reinforcing loop in Large Reasoning Models, observable as token-level and sentence-level repetitions that emerge at a phase-transition in internal dynamics. It introduces LoopBench, a two-pronged benchmark with 700 samples across high-precision arithmetic and complex recursive tasks, to systematically study loop triggers, persistence, and model robustness. A mechanistic analysis reveals a deterministic state collapse and a characteristic V-shaped attention pattern, with semantic circularity preceding explicit repetition. To counteract this pathology, the authors propose a Predict–Intervene framework using real-time CUSUM-based detection on hidden states and soft prompt interventions, achieving early warning and substantial reductions in loop incidence across diverse models. The work advances understanding of reasoning stability in LRMs and offers a practical approach to mitigating computational waste in long-horizon reasoning tasks.

Abstract

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.

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

TL;DR

The paper identifies Circular Reasoning as a self-reinforcing loop in Large Reasoning Models, observable as token-level and sentence-level repetitions that emerge at a phase-transition in internal dynamics. It introduces LoopBench, a two-pronged benchmark with 700 samples across high-precision arithmetic and complex recursive tasks, to systematically study loop triggers, persistence, and model robustness. A mechanistic analysis reveals a deterministic state collapse and a characteristic V-shaped attention pattern, with semantic circularity preceding explicit repetition. To counteract this pathology, the authors propose a Predict–Intervene framework using real-time CUSUM-based detection on hidden states and soft prompt interventions, achieving early warning and substantial reductions in loop incidence across diverse models. The work advances understanding of reasoning stability in LRMs and offers a practical approach to mitigating computational waste in long-horizon reasoning tasks.

Abstract

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.
Paper Structure (50 sections, 9 equations, 46 figures, 13 tables)

This paper contains 50 sections, 9 equations, 46 figures, 13 tables.

Table of Contents

  1. Introduction
  2. LoopBench: A Benchmark for Reasoning Loop in LRMs
  3. Benchmark Construction
  4. Key Observations on LoopBench
  5. LoopBench triggers significantly higher repetition than other benchmarks.
  6. Loop patterns exhibit distinct granular behaviors.
  7. Closed-source models exhibit superior yet imperfect robustness.
  8. Decoding strategies mitigate but do not eliminate repetition.
  9. Analysis of Circular Reasoning
  10. Loop Behavior Analysis
  11. Determinism Surge and State Collapse.
  12. High Separability of Internal States.
  13. Reasoning Graphs in Statement Loops.
  14. Loop Triggering Mechanisms
  15. Triggers of Statement Loops.
  16. ...and 35 more sections

Figures (46)

  • Figure 1: The Trap of Circular Reasoning. A logical deadlock that blocks step-by-step inference. Analogous to a software deadlock (a), this mode entraps the model in a self-reinforcing cycle (c),preventing the flexible backtracking seen in normal reasoning (b).
  • Figure 2: Taxonomy of LoopBench. The benchmark is organized into two primary categories: High-Precision Arithmetic and Complex Recursive Reasoning.
  • Figure 3: Abrupt shift in decoding dynamics in DS-Qwen-14B. The loop onset triggers an immediate entropy collapse (red) and probability surge (blue), marking a sudden entry into rigid determinism in both cases.
  • Figure 4: Collapse of Internal States. We report the layer-wise Cosine Similarity and $L_2$ Distance in DS-Qwen-14B. Curves labelled "Repeat $k$" denote the comparison between the representation in the "$k$"-th loop and "$k-1$"-th cycle. Trend: As loop deepens (darker red lines), the internal state becomes rigid.
  • Figure 5: Reasoning graph visualization of a statement loop in DS-Qwen-14B. (a) and (b) show internal states collapsing into cycles. Crucially, (c) plots cluster labels against sentence IDs, demonstrating that semantic circularity (shaded region) significantly precedes explicit textual repetition (dashed line), serving as an early warning.
  • ...and 41 more figures