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

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.

UniSVQ: 2-bit Unified Scalar-Vector Quantization

Post-training quantization at the 2-bit level enables low-cost deployment and inference acceleration for large language models (LLMs). Scalar quantization (SQ) and vector quantization (VQ) are two primary quantization methods, however, the former suffers from significant performance degradation, and the latter incurs computational and storage overhead. We propose UniSVQ, a unified 2-bit quantization framework that bridges scalar and vector quantization by parameterizing codewords as an affine transform of integer lattices. This structure preserves compatibility with optimized integer kernels while retaining much of VQ's flexibility. We further introduce a data-driven block-wise fine-tuning strategy to directly minimize quantization reconstruction error. Extensive experiments across multiple LLM families and zero-shot benchmarks demonstrate that UniSVQ consistently outperforms state-of-the-art SQ methods and achieves performance comparable to advanced VQ methods, while providing higher inference throughput.