# Decoding Looped Transformers Better for (Almost) Free

arXiv: https://arxiv.org/abs/2610.02185 · HTML: https://mlsanity.com/paper/2610.02185/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 45 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 30 of 38)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [DoLa: Decoding by Contrasting Layers Improves Factuality in Large Language Models](https://mlsanity.com/paper/2309.03883/) (2023)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [Trusting Your Evidence: Hallucinate Less with Context-aware Decoding](https://mlsanity.com/paper/2305.14739/) (2023)
- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (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)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Looped Transformers are Better at Learning Learning Algorithms](https://mlsanity.com/paper/2311.12424/) (2023)
- [Looped Transformers for Length Generalization](https://mlsanity.com/paper/2409.15647/) (2024)
- [Stay on topic with Classifier-Free Guidance](https://mlsanity.com/paper/2306.17806/) (2023)
- [Reasoning Beyond Language: A Comprehensive Survey on Latent Chain-of-Thought Reasoning](https://mlsanity.com/paper/2505.16782/) (2025)
- [Contrastive Decoding Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2309.09117/) (2023)
- [Parcae: Scaling Laws For Stable Looped Language Models](https://mlsanity.com/paper/2604.12946/) (2026)
- [LaDiR: Latent Diffusion Enhances LLMs for Text Reasoning](https://mlsanity.com/paper/2510.04573/) (2025)

## Abstract (arXiv)

Looped Transformers achieve parameter efficiency by repeatedly executing a shared block across recurrent loops. Each loop yields an intermediate representation decodable for the same next token, yet standard decoding discards earlier states. Because earlier loops embody less computation, recurrence inherently supplies aligned weak-and-strong prediction pairs without auxiliary models or external training. We introduce LoopCD, a training-free contrastive decoding framework that guides token selection by contrasting the final prediction with an earlier recurrent pass, operating either in logit space with one extra output pass (LoopCD-Logits) or in hidden-state space with zero output overhead (LoopCD-Hidden). Across four looped Transformer families, LoopCD delivers substantial, consistent gains at full recurrent depth: LoopCD-Logits raises Ouro-2.6B-Thinking's AIME 2024 pass@1 from 61.88% to 73.33%, while LoopCD-Hidden lifts Huginn's HumanEval pass@1 from 22.56% to 31.71%. Crucially, these performance gains enable halving the number of recurrent loops while still matching or exceeding full-depth unguided baselines, reducing forward FLOPs by 22.5% to 48.2%. By transforming intermediate recurrent states into effective guidance signals, LoopCD achieves superior decoding quality while substantially reducing inference compute.