GSQ: Highly-Accurate Low-Precision Scalar Quantization for LLMs via Gumbel-Softmax Sampling
Authors: Alireza Dadgarnia, Soroush Tabesh, Mahdi Nikdan, Michael Helcig, Eldar Kurtic, Maximilian Kleinegger, Dan Alistarh
Abstract
Quantization has become a standard tool for efficient LLM deployment, especially for local inference, where models are now routinely served at 2-3 bits per parameter. The state of the art is currently split into simple scalar quantization techniques, such as GPTQ or AWQ, which are widely deployed but plateau in accuracy at 3-4 bits per parameter (bpp), and "second-generation" vector- or trellis-quantized methods, such as QTIP, GPTVQ and AQLM, which push the accuracy frontier but are notoriously hard to implement and to scale. In this paper, we ask whether this gap is fundamental, or whether a carefully optimized scalar quantizer can recover most of it. We answer in the affirmative, by introducing GSQ (Gumbel-Softmax Quantization), a post-training scalar quantization method which jointly learns the per-coordinate grid assignments and the per-group scales using a Gumbel-Softmax relaxation of the discrete grid. GSQ matches the cardinality of the relaxation to the small number of levels available in the target bit-width regime (e.g., 3-8 levels for ternary and 3 bpp, respectively), making optimization tractable. Practically, on the standard Llama-3.1-8B/70B-Instruct models, GSQ closes most of the gap between scalar quantization and the QTIP frontier at 2 and 3 bits, while using a symmetric scalar grid with group-wise quantization, and thus remains compatible with existing scalar inference kernels. We further show that the same discrete-assignment optimization can be applied to practical GGUF K-Quant checkpoints: starting from publicly released GGUF models, GSQ improves accuracy while projecting the result back into the same deployment format. Finally, GSQ scales to trillion-scale Mixture-of-Experts models such as Kimi-K2.5, where vector-quantized methods are difficult to apply. The source code is publicly available at https://github.com/IST-DASLab/GSQ.
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. Codes are publicly available at https://github.com/AI9Stars/UniSVQ.
Compressing large language models (LLMs) for deployment on commodity GPUs remains challenging: conventional scalar quantization is limited to fixed bit-widths (e.g., 8/4/3-bit), offers only a few discrete compression points, and typically requires calibration data. We present FASQ (Flexible Accelerated Subspace Quantization), a calibration-free framework that applies product quantization to LLM weight matrices. By tuning two parameters, sub-vector size and codebook cardinality, FASQ exposes a continuous design space spanning 27-49% of the original FP16 model size, filling compression gaps that fixed-bit schemes cannot reach. On Meta-Llama-3-8B, FASQ surpasses 4-bit GPTQ and AWQ in accuracy (67.1-67.7 avg.) at 37-42% model size, with consistent results on Qwen3-8B and Qwen3.5-9B-Base. To make product quantization practical at inference time, we design custom CUDA kernels: a LUT-free direct-compute GEMV for decode and an output-stationary double-buffered LUT GEMM for prefill, both with split-K parallelism. On an RTX~3090, FASQ achieves 45.2 tok/s decode at effective 4-bit (2.56x memory reduction) and 51.8 tok/s at effective 3-bit (2.80x), both surpassing FP16 tensor-core performance (43.9 tok/s) and delivering 1.6 to 1.8x the throughput of AWQ, 2.5 to 2.5x of GPTQ, and 4.3 to 5x of RTN. FASQ is the only compressed method that accelerates decode beyond FP16, offering calibration-free compression, continuous size-quality trade-offs, and real-time inference on a single consumer GPU.
Post-training quantization (PTQ) is critical for the efficient deployment of large language models (LLMs). Recent ultra-low-bit PTQ methods rely on rigid weight-saliency assumptions or position heuristics, introducing substantial hidden scaling overhead. We propose SAGE-PTQ (Saliency-Aware Graph-guided Efficient PTQ), a novel ultra-low-bit quantization framework for LLMs that minimizes hidden scaling cost. SAGE-PTQ separates salient and unsalient weights using distributional statistics, then models subsampled unsalient weights as a sparse graph to estimate the optimal number of groups per layer. SAGE-PTQ applies dual-mode quantization, assigning multi-bit precision to salient weights and binarizing unsalient weights. To reduce scaling overhead, SAGE-PTQ uses one per-channel scale for salient weights and one scalar per unsalient group. Finally, SAGE-PTQ implements adaptive saliency thresholding to select the optimal saliency ratio per matrix. SAGE-PTQ achieves 1.03 weight bits and only 0.004 scaling bits per matrix on average, outperforming state-of-the-art methods such as BiLLM and PB-LLM. On LLaMA-3-8B, SAGE-PTQ achieves 6.74 WikiText2 perplexity, compared to 55.8 for BiLLM, while using less than 50% of BiLLM's GPU memory. On LLaMA-2-70B, SAGE-PTQ provides 1.5x faster decoding on one NVIDIA L40 GPU, demonstrating practical inference efficiency.