# LC-QAT: Data-Efficient 2-Bit QAT for LLMs via Linear-Constrained Vector Quantization

arXiv: https://arxiv.org/abs/2606.10531 · HTML: https://mlsanity.com/paper/2606.10531/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 35 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 30 of 32)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [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)
- [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)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (2024)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [RedPajama: an Open Dataset for Training Large Language Models](https://mlsanity.com/paper/2411.12372/) (2024)
- [EfficientQAT: Efficient Quantization-Aware Training for Large Language Models](https://mlsanity.com/paper/2407.11062/) (2024)
- [OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting](https://mlsanity.com/paper/2501.13987/) (2025)
- [QTIP: Quantization with Trellises and Incoherence Processing](https://mlsanity.com/paper/2406.11235/) (2024)
- [GPTVQ: The Blessing of Dimensionality for LLM Quantization](https://mlsanity.com/paper/2402.15319/) (2024)
- [Optimizing Large Language Model Training Using FP4 Quantization](https://mlsanity.com/paper/2501.17116/) (2025)
- [ParetoQ: Improving Scaling Laws in Extremely Low-bit LLM Quantization](https://mlsanity.com/paper/2502.02631/) (2025)
- [BitNet b1.58 2B4T Technical Report](https://mlsanity.com/paper/2504.12285/) (2025)
- [NestQuant: Nested Lattice Quantization for Matrix Products and LLMs](https://mlsanity.com/paper/2502.09720/) (2025)
- [Model-Preserving Adaptive Rounding](https://mlsanity.com/paper/2505.22988/) (2025)
- [Unveiling the Basin-Like Loss Landscape in Large Language Models](https://mlsanity.com/paper/2505.17646/) (2025)

## Built on by (most cited first, 3 of 3)

- [BiSCo-LLM: Lookup-Free Binary Spherical Coding for Extreme Low-Bit Large Language Model Compression](https://mlsanity.com/paper/2607.08643/) (2026)
- [Few Bits, One Law: Toward W2A4KV2](https://mlsanity.com/paper/2610.09202/) (2026)
- [SAGE: Pushing 2-Bit Vector-Quantized LLMs toward Real-World Usability](https://mlsanity.com/paper/2610.14745/) (2026)

## Abstract (arXiv)

Quantization-aware training (QAT) is essential for extremely low-bit large language models (LLMs). Current QAT methods are mainly based on scalar quantization (SQ), which enables efficient optimization but suffers from severe performance degradation at 2-bit precision. On the other hand, vector quantization (VQ) provides substantially higher representational capacity, but its discrete codebook lookup prevents end-to-end training. We propose LC-QAT, a 2-bit weight-only VQ-QAT framework that represents quantized weights via a learned affine mapping over discrete vectors, which yields a high-quality PTQ initialization and enables fully differentiable end-to-end optimization without explicit codebook lookup in the training forward pass. This strong post-training initialization makes LC-QAT highly data-efficient. Experiments across diverse LLMs demonstrate that LC-QAT consistently outperforms state-of-the-art QAT methods while using only 0.1%--10% of the training data. Our results establish LC-QAT as a practical and scalable solution for extreme low-bit model deployment. Codes are publicly available at https://github.com/AI9Stars/UniSVQ.