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

• URL: http://arxiv.org/abs/2601.22716v1
• Date: Fri, 30 Jan 2026 08:46:02 GMT
• Title: Breaking the Blocks: Continuous Low-Rank Decomposed Scaling for Unified LLM Quantization and Adaptation
• Authors: Pingzhi Tang, Ruijie Zhou, Fanxu Meng, Wenjie Pei, Muhan Zhang,
• Abstract summary: Low-Rank Decomposed Scaling (LoRDS) is a unified framework that rethinks quantization granularity through this low-rank decomposition.<n>By "breaking the blocks" of spatial constraints, LoRDS establishes a seamless efficiency lifecycle.<n>LoRDS consistently outperforms state-of-the-art baselines across various model families in both quantization and downstream fine-tuning tasks.
• Score: 46.34608916687127
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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