# Breaking the Blocks: Continuous Low-Rank Decomposed Scaling for Unified LLM Quantization and Adaptation

arXiv: https://arxiv.org/abs/2601.22716 · HTML: https://mlsanity.com/paper/2601.22716/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 41 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [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)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT](https://mlsanity.com/paper/1909.05840/) (2019)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [Q8BERT: Quantized 8Bit BERT](https://mlsanity.com/paper/1910.06188/) (2019)
- [Parameter-Efficient Fine-Tuning Methods for Pretrained Language Models: A Critical Review and Assessment](https://mlsanity.com/paper/2312.12148/) (2023)
- [LoftQ: LoRA-Fine-Tuning-Aware Quantization for Large Language Models](https://mlsanity.com/paper/2310.08659/) (2023)
- [Low-bit Quantization of Neural Networks for Efficient Inference](https://mlsanity.com/paper/1902.06822/) (2019)
- [LSQ+: Improving low-bit quantization through learnable offsets and better initialization](https://mlsanity.com/paper/2004.09576/) (2020)
- [Memory-Efficient Fine-Tuning of Compressed Large Language Models via sub-4-bit Integer Quantization](https://mlsanity.com/paper/2305.14152/) (2023)
- [BitDistiller: Unleashing the Potential of Sub-4-Bit LLMs via Self-Distillation](https://mlsanity.com/paper/2402.10631/) (2024)
- [OneBit: Towards Extremely Low-bit Large Language Models](https://mlsanity.com/paper/2402.11295/) (2024)
- [Towards Efficient Post-training Quantization of Pre-trained Language Models](https://mlsanity.com/paper/2109.15082/) (2021)

## Built on by (most cited first, 1 of 1)

- [Scale-QLoRA: Code-Invariant Adapter Merging for Native 4-bit Microscaling LLMs](https://mlsanity.com/paper/2609.04526/) (2026)

## Abstract (arXiv)

Current quantization methods for LLMs predominantly rely on block-wise structures to maintain efficiency, often at the cost of representational flexibility. In this work, we demonstrate that element-wise quantization can be made as efficient as block-wise scaling while providing strictly superior expressive power by modeling the scaling manifold as continuous low-rank matrices (S = BA). We propose Low-Rank Decomposed Scaling (LoRDS), a unified framework that rethinks quantization granularity through this low-rank decomposition. By "breaking the blocks" of spatial constraints, LoRDS establishes a seamless efficiency lifecycle: it provides high-fidelity PTQ initialization refined via iterative optimization, enables joint QAT of weights and scaling factors, and facilitates high-rank multiplicative PEFT adaptation. Unlike additive PEFT approaches such as QLoRA, LoRDS enables high-rank weight updates within a low-rank budget while incurring no additional inference overhead. Supported by highly optimized Triton kernels, LoRDS consistently outperforms state-of-the-art baselines across various model families in both quantization and downstream fine-tuning tasks. Notably, on Llama3-8B, our method achieves up to a 27.0% accuracy improvement at 3 bits over NormalFloat quantization and delivers a 1.5x inference speedup on NVIDIA RTX 4090 while enhancing PEFT performance by 9.6% on downstream tasks over 4bit QLoRA, offering a robust and integrated solution for unified compression and adaptation of LLMs.