# LoopUS: Recasting Pretrained LLMs into Looped Latent Refinement Models

arXiv: https://arxiv.org/abs/2605.11011 · HTML: https://mlsanity.com/paper/2605.11011/

## Key facts

- Cited by 15 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 39 of its 58 references that are in the map.
- First posted on arXiv 10 May 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, 30 of 39)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [Training Very Deep Networks](https://mlsanity.com/paper/1507.06228/) (2015)
- [SOLAR 10.7B: Scaling Large Language Models with Simple yet Effective Depth Up-Scaling](https://mlsanity.com/paper/2312.15166/) (2023)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [The Bottom-up Evolution of Representations in the Transformer: A Study with Machine Translation and Language Modeling Objectives](https://mlsanity.com/paper/1909.01380/) (2019)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [Mamba-3: Improved Sequence Modeling using State Space Principles](https://mlsanity.com/paper/2603.15569/) (2026)

## Built on by (most cited first, 15 of 15)

- [Loop the Loopies!](https://mlsanity.com/paper/2607.16051/) (2026)
- [RecurTrace: Adaptive Latent Reasoning with Loop-Time Memory](https://mlsanity.com/paper/2609.03379/) (2026)
- [LoopCoder-v2: Only Loop Once for Efficient Test-Time Computation Scaling](https://mlsanity.com/paper/2606.18023/) (2026)
- [Hidden Decoding at Scale: Latent Computation Scaling for Large Language Models](https://mlsanity.com/paper/2607.08186/) (2026)
- [Forward-Free Diffusion Language Models with BPTT-Free Looped Refinement](https://mlsanity.com/paper/2606.08357/) (2026)
- [LoopSpec: Pipelined Self-Speculative Decoding for Looped Transformers](https://mlsanity.com/paper/2609.17184/) (2026)
- [Looped Transformers with Source-Centered State Evolution](https://mlsanity.com/paper/2607.27656/) (2026)
- [Right Direction, Wrong Step: Geometric Analysis of Finite-Step Failure in Looped Transformers](https://mlsanity.com/paper/2609.16665/) (2026)
- [Improving Test-Time Scaling with Adaptive Looped Transformers](https://mlsanity.com/paper/2609.35748/) (2026)
- [ReLoop-UME: Recurrent Depth with Learnable Retrieval Registers for Universal Multimodal Embedding](https://mlsanity.com/paper/2607.28751/) (2026)
- [WaveFront Decoding: Parallelized Self-Speculative Decoding for Looped Language Models](https://mlsanity.com/paper/2609.23033/) (2026)
- [Loop Dropout: Regularizing Shared Updates in Looped Language Models](https://mlsanity.com/paper/2609.34218/) (2026)
- [SanSi: A Looped Typed Decision Model for System 1.5 Thinking](https://mlsanity.com/paper/2610.07730/) (2026)
- [Enabling Dynamic Computation in Looped LMs](https://mlsanity.com/paper/2610.09013/) (2026)
- [Monitoring latent reasoning in looped language models](https://mlsanity.com/paper/2610.18127/) (2026)

## Abstract (arXiv)

Looped computation shows promise in improving the reasoning-oriented performance of LLMs by scaling test-time compute. However, existing approaches typically require either training recurrent models from scratch or applying disruptive retrofits, which involve substantial computational costs and may compromise pretrained capabilities. To address these limitations, we introduce Looped Depth Up-Scaling (LoopUS), a post-training framework that converts a standard pretrained LLM into a looped architecture. As a key technical contribution, LoopUS recasts the pretrained LLM into an encoder, a looped reasoning block, and a decoder. It operationalizes this latent-refinement architecture through four core components: (1) block decomposition, guided by staged representation dynamics; (2) an input-dependent selective gate to mitigate hidden-state drift; (3) random deep supervision for memory-efficient learning over long recursive horizons; and (4) a confidence head for adaptive early exiting. Collectively, these mechanisms transform a standard non-looped model into a looped form while stabilizing it against both computational bottlenecks and representation collapse. Through stable latent looping, LoopUS improves reasoning-oriented performance without extending the generated traces or requiring recurrent training from scratch. For more details, see https://thrillcrazyer.github.io/LoopUS