# LoopCD: Loop-wise Contrastive Decoding for Improving Reasoning in Looped Language Models

arXiv: https://arxiv.org/abs/2609.24196 · HTML: https://mlsanity.com/paper/2609.24196/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 20 of its 45 references that are in the map.
- First posted on arXiv 21 Sep 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, 20 of 20)

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- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Large Language Model Guided Tree-of-Thought](https://mlsanity.com/paper/2305.08291/) (2023)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Contrastive Decoding Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2309.09117/) (2023)
- [Less is More: Recursive Reasoning with Tiny Networks](https://mlsanity.com/paper/2510.04871/) (2025)
- [Universal Reasoning Model](https://mlsanity.com/paper/2512.14693/) (2025)

## Abstract (arXiv)

Looped Language Models (LoopLMs) perform "latent reasoning" by recursively refining internal latent representations with shared weights, offering a more effective alternative to explicit verbal reasoning. Despite their effectiveness, we find that LoopLMs remain prone to loop instability: unstable refinement across iterations can produce localized uncertain "hard" tokens associated with reasoning errors. To address this, we propose LoopCD, loop-wise contrastive decoding that enhances the reasoning performance of LoopLMs by intervening on these tokens at inference time. Specifically, we exploit the internal dynamics of LoopLMs and contrast the logits from earlier iterations with logits from the last refined iteration to form the final sampling distribution. We find that this strategy is highly efficient, introducing only negligible inference overhead and requiring no additional training, while effectively improving reasoning performance by naturally refining reasoning-critical hard tokens. Extensive experiments show that our method improves the performance of recent representative LoopLMs across various reasoning tasks.