# FLRQ: Faster LLM Quantization with Flexible Low-Rank Matrix Sketching

arXiv: https://arxiv.org/abs/2601.05684 · HTML: https://mlsanity.com/paper/2601.05684/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 9 Jan 2026.

## Builds on (most cited first, 16 of 16)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Towards Accurate Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2303.14341/) (2023)
- [Compressing Large Language Models using Low Rank and Low Precision Decomposition](https://mlsanity.com/paper/2405.18886/) (2024)
- [A Systematic Classification of Knowledge, Reasoning, and Context within the ARC Dataset](https://mlsanity.com/paper/1806.00358/) (2018)
- [Pruning vs Quantization: Which is Better?](https://mlsanity.com/paper/2307.02973/) (2023)
- [LQER: Low-Rank Quantization Error Reconstruction for LLMs](https://mlsanity.com/paper/2402.02446/) (2024)
- [RILQ: Rank-Insensitive LoRA-based Quantization Error Compensation for Boosting 2-bit Large Language Model Accuracy](https://mlsanity.com/paper/2412.01129/) (2024)

## Built on by (most cited first, 2 of 2)

- [TWLA: Achieving Ternary Weights and Low-Bit Activations for LLMs via Post-Training Quantization](https://mlsanity.com/paper/2606.13054/) (2026)
- [TileQ: Efficient Low-Rank Quantization of Mixture-of-Experts with 2D Tiling](https://mlsanity.com/paper/2605.09281/) (2026)

## Abstract (arXiv)

Traditional post-training quantization (PTQ) is considered an effective approach to reduce model size and accelerate inference of large-scale language models (LLMs). However, existing low-rank PTQ methods require costly fine-tuning to determine a compromise rank for diverse data and layers in large models, failing to exploit their full potential. Additionally, the current SVD-based low-rank approximation compounds the computational overhead. In this work, we thoroughly analyze the varying effectiveness of low-rank approximation across different layers in representative models. Accordingly, we introduce underlineFlexible underlineLow-underlineRank underlineQuantization (FLRQ), a novel solution designed to quickly identify the accuracy-optimal ranks and aggregate them to achieve minimal storage combinations. FLRQ comprises two powerful components, Rank1-Sketch-based Flexible Rank Selection (R1-FLR) and Best Low-rank Approximation under Clipping (BLC). R1-FLR applies the R1-Sketch with Gaussian projection for the fast low-rank approximation, enabling outlier-aware rank extraction for each layer. Meanwhile, BLC aims at minimizing the low-rank quantization error under the scaling and clipping strategy through an iterative method. FLRQ demonstrates strong effectiveness and robustness in comprehensive experiments, achieving state-of-the-art performance in both quantization quality and algorithm efficiency.