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

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://anonymous.4open.science/r/LoopQuant-D211/.