# LoopQ: Quantization for Looped Language Models

arXiv: https://arxiv.org/abs/2605.16343 · HTML: https://mlsanity.com/paper/2605.16343/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 44 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 30 of 37)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [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)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [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)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [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 Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [FlatQuant: Flatness Matters for LLM Quantization](https://mlsanity.com/paper/2410.09426/) (2024)
- [Looped Transformers for Length Generalization](https://mlsanity.com/paper/2409.15647/) (2024)
- [OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting](https://mlsanity.com/paper/2501.13987/) (2025)
- [Exploiting LLM Quantization](https://mlsanity.com/paper/2405.18137/) (2024)
- [Robust Quantization: One Model to Rule Them All](https://mlsanity.com/paper/2002.07686/) (2020)
- [SliM-LLM: Salience-Driven Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2405.14917/) (2024)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [Parcae: Scaling Laws For Stable Looped Language Models](https://mlsanity.com/paper/2604.12946/) (2026)
- [Transformer Fusion with Optimal Transport](https://mlsanity.com/paper/2310.05719/) (2023)
- [ResQ: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals](https://mlsanity.com/paper/2412.14363/) (2024)
- [RobustMQ: Benchmarking Robustness of Quantized Models](https://mlsanity.com/paper/2308.02350/) (2023)
- [Pruning via Merging: Compressing LLMs via Manifold Alignment Based Layer Merging](https://mlsanity.com/paper/2406.16330/) (2024)
- [Hyperloop Transformers](https://mlsanity.com/paper/2604.21254/) (2026)

## Built on by (most cited first, 6 of 6)

- [When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation](https://mlsanity.com/paper/2607.23390/) (2026)
- [Quantizing Looped Transformers: Feedback Exposure and Calibration Blindness](https://mlsanity.com/paper/2609.30820/) (2026)
- [Q-DEQ: Discrete Solving and Quantization for Deep Equilibrium Models in Time Series Forecasting under Edge Deployment Coding Constraints](https://mlsanity.com/paper/2609.24042/) (2026)
- [A Tilted Bowl Is Not a Slippery Slope: Compressing Looped Models](https://mlsanity.com/paper/2609.39277/) (2026)
- [Loopy: Low-Bit Quantization Framework for Looped Language Models](https://mlsanity.com/paper/2610.05265/) (2026)
- [ResidualQuant: KV Cache Quantization for Looped Transformers with 2-Bit Residuals](https://mlsanity.com/paper/2610.10381/) (2026)

## Abstract (arXiv)

Looped language models (LoopLMs) increase effective computational depth by repeatedly applying shared Transformer blocks without increasing the parameter count. However, this reuse makes them particularly sensitive to post-training quantization (PTQ). We systematically study PTQ in LoopLMs and identify three sources of degradation: distribution shift across roles, state reuse across loop transitions, and recursive error accumulation. We propose LoopQ, a loop-aware PTQ framework that preserves a shared quantized backbone while introducing lightweight adaptations. LoopQ combines loop-aware activation scaling and selective transformations to accommodate changing hidden-state distributions, cross-loop state alignment to stabilize transitions, and trajectory-aware calibration to limit accumulated error. Under W4A4 quantization, LoopQ achieves a 67.8% average relative improvement in five-task mean accuracy across four backbones and a conservative estimate of 75.2% for the average relative perplexity reduction across eight backbone-dataset pairs, compared with the strongest static PTQ baseline for each comparison.