# Loopy: Low-Bit Quantization Framework for Looped Language Models

arXiv: https://arxiv.org/abs/2610.05265 · HTML: https://mlsanity.com/paper/2610.05265/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 23 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 20 of 20)

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Reasoning with Latent Thoughts: On the Power of Looped Transformers](https://mlsanity.com/paper/2502.17416/) (2025)
- [Non-stochastic Best Arm Identification and Hyperparameter Optimization](https://mlsanity.com/paper/1502.07943/) (2015)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [FlatQuant: Flatness Matters for LLM Quantization](https://mlsanity.com/paper/2410.09426/) (2024)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence](https://mlsanity.com/paper/2511.07384/) (2025)
- [Memory-Efficient Looped Transformer: Decoupling Compute from Memory in Looped Language Models](https://mlsanity.com/paper/2605.07721/) (2026)
- [LoopQ: Quantization for Looped Language Models](https://mlsanity.com/paper/2605.16343/) (2026)

## Abstract (arXiv)

Looped language models provide a parameter-efficient way to scale iterative test-time computation by repeatedly executing a shared recurrent core. Post-training quantization (PTQ) can reduce the memory footprint and inference cost of looped language models, but errors introduced by a quantized shared core affect subsequent cores. Among PTQ methods, channel scaling and orthogonal rotations preserve the floating-point computation while producing representations with different quantization quality. We find that quantization configuration candidate rankings can change with recurrent depth, motivating configuration selection at the target deployment depth. However, evaluating every candidate over the full calibration set at this depth is costly. We therefore propose Loopy, a PTQ framework that formulates shared-core quantization through a recurrent-depth-aware objective, selecting shared low-bit representations by their final prediction loss at the target deployment depth. Channel scaling and orthogonal rotations parameterize the candidate representations. To approximately solve this selection problem efficiently, Loopy progressively allocates calibration windows to promising candidates while preserving complete target-depth execution, using only forward evaluations. Across eight settings, Loopy achieves the state-of-the-art results among different baselines. On Ouro-1.4B under W4A4, Loopy reduces LAMBADA perplexity by 36.5% relative to SpinQuant. Our code is available at https://github.com/Shameless0817/Loopy-review.git.