# LoopQuant: Accurate and Efficient Post-Training Quantization for Looped Transformers

arXiv: https://arxiv.org/abs/2610.16368 · HTML: https://mlsanity.com/paper/2610.16368/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 31 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 26 of 26)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [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)
- [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)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [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)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [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)
- [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)
- [Relaxed Recursive Transformers: Effective Parameter Sharing with Layer-wise LoRA](https://mlsanity.com/paper/2410.20672/) (2024)
- [ResQ: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals](https://mlsanity.com/paper/2412.14363/) (2024)
- [DartQuant: Efficient Rotational Distribution Calibration for LLM Quantization](https://mlsanity.com/paper/2511.04063/) (2025)
- [QUARK: Quantization-Enabled Circuit Sharing for Transformer Acceleration by Exploiting Common Patterns in Nonlinear Operations](https://mlsanity.com/paper/2511.06767/) (2025)
- [Nanbeige4.2-3B: Unlocking Agentic Capabilities in a Compact Model](https://mlsanity.com/paper/2607.22083/) (2026)
- [SpecQuant: Spectral Decomposition and Adaptive Truncation for Ultra-Low-Bit LLMs Quantization](https://mlsanity.com/paper/2511.11663/) (2025)
- [KBVQ-MoE: KLT-guided SVD with Bias-Corrected Vector Quantization for MoE Large Language Models](https://mlsanity.com/paper/2602.11184/) (2026)
- [TWLA: Achieving Ternary Weights and Low-Bit Activations for LLMs via Post-Training Quantization](https://mlsanity.com/paper/2606.13054/) (2026)
- [BWLA: Breaking the Barrier of W1AX Post-Training Quantization for LLMs](https://mlsanity.com/paper/2605.00422/) (2026)
- [All for 1-Bit: Towards Genuine 1-Bit Post-Training Quantization for LLMs](https://mlsanity.com/paper/2609.06161/) (2026)

## Abstract (arXiv)

Looped Language Models (LoopLMs) improve parameter efficiency by recursively reusing shared Transformer modules, yet their repeated computation over evolving recurrent states poses new challenges for low-bit deployment. Existing post-training quantization (PTQ) methods, largely designed for feed-forward Transformers, fail to account for cross-loop activation dynamics, heterogeneous loop sensitivity, and recursive error propagation, leading to substantial performance degradation at low precision. To address these challenges, we propose LoopQuant, a loop-aware PTQ framework for accurate and efficient low-bit quantization of LoopLMs. LoopQuant is built on three core components: 1) Cross-Loop Distribution Canonicalization (CLDC) learns a shared quantization-friendly representation across recurrent states while preserving parameter sharing; 2) Interaction-Aware Loop-wise Precision Allocation (ILPA) allocates activation precision under a fixed bit budget by modeling task-level loop sensitivity and cross-loop interactions; and 3) Loop-Conditioned Task Calibration (LCTC) further aligns quantized inference with the low-bit recursive trajectory through lightweight task-space calibration. Extensive experiments across LoopLM architectures demonstrate that LoopQuant consistently outperforms existing low-bit PTQ methods. On Ouro-2.6B, LoopQuant under W4A4 surpasses all W4A8 baselines in performance, while reducing model memory by 65.3% with only 3.4% additional storage overhead over naive INT4 and achieving a 1.7 times decoding speedup over BF16. These results demonstrate a strong balance among accuracy, compression, and inference efficiency, providing a practical and deployment-friendly solution for low-bit LoopLM inference. The code is available at [https://github.com/Kishon-zzx/LoopQuant].