Statistically-Lossless Quantization of Large Language Models

• URL: http://arxiv.org/abs/2605.02404v1
• Date: Mon, 04 May 2026 09:46:47 GMT
• Title: Statistically-Lossless Quantization of Large Language Models
• Abstract summary: This paper explores the middle ground of statistically-lossless compression through three complementary notions of losslessness for quantized LLMs.<n>First, task-lossless compression preserves zero-shot benchmark accuracy within natural sampling variance and remains achievable at aggressive bitwidths.<n>Second, we formalize the stricter notion of distribution-lossless compression, requiring the quantized model's next-token distribution to be practically indistinguishable from the original.<n>Third, we prove a gamma-squared variance law showing that symmetric quantization inflates noise variance by gamma squared relative to asymmetric quantization.
• Score: 41.38595517076645
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Model quantization has become essential for efficient large language model deployment, yet existing approaches involve clear trade-offs: methods such as GPTQ and AWQ achieve practical compression but are lossy, while lossless techniques preserve fidelity but typically do not accelerate inference. This paper explores the middle ground of statistically-lossless compression through three complementary notions of losslessness for quantized LLMs. First, task-lossless compression preserves zero-shot benchmark accuracy within natural sampling variance and remains achievable at aggressive bitwidths. Second, we formalize the stricter notion of distribution-lossless compression, requiring the quantized model's next-token distribution to be practically indistinguishable from the original, and propose the Expected Acceptance Rate (EAR), the maximum token-agreement probability under optimal coupling, as a directly interpretable fidelity metric (for example, EAR >= 0.99 indicates 99% agreement). Third, we prove a gamma-squared variance law showing that symmetric quantization inflates noise variance by gamma squared relative to asymmetric quantization, making asymmetry necessary for distribution-lossless fidelity but not for task-level preservation. Using SLQ, a layer-wise non-uniform method with asymmetric quantization and wide bitwidth search, we achieve task-lossless compression at well below 4 bits per parameter (as low as 3.3 bits depending on the model), distribution-lossless compression at 5 to 6 bits per parameter on average, and inference speedups of 1.7 to 3.6x relative to FP16 with optimized kernels. Source code is available at https://github.com/IST-DASLab/SLQ.

Related papers

• Does Compression Preserve Uncertainty? A Unified Benchmark for Quantized and Sparse LLMs via Conformal Prediction [21.411353047208777]
  We benchmark 12 large language models (LLMs) under various compression configurations across five NLP tasks.<n>Our experiments reveal that: (I) compression frequently decouples accuracy from uncertainty; (II) larger models absorb compression-induced uncertainty far more effectively than smaller ones; and (III) uncertainty inflation is often threshold-like rather than gradual.
  arXiv  Detail & Related papers  (2026-06-01T08:00:17Z)
• BPDQ: Bit-Plane Decomposition Quantization on a Variable Grid for Large Language Models [56.504879072674015]
  We propose Bit-Plane Decomposition Quantization (BPDQ), which constructs a variable quantization grid via bit-planes and scalar coefficients.<n>BPDQ enables serving Qwen2.5-72B on a single GTX 3090 with 83.85% GSM8K accuracy (vs. 90.83% at 16-bit)
  arXiv  Detail & Related papers  (2026-02-04T02:54:37Z)
• SQS: Bayesian DNN Compression through Sparse Quantized Sub-distributions [18.749300190253624]
  We introduce a unified framework for simultaneous pruning and low-bit quantization via Bayesian variational learning (SQS)<n>In theory, we provide the consistent result of our proposed variational approach to a sparse and quantized deep neural network.
  arXiv  Detail & Related papers  (2025-10-10T04:54:29Z)
• EntroLLM: Entropy Encoded Weight Compression for Efficient Large Language Model Inference on Edge Devices [3.5240021321113204]
  Large Language Models (LLMs) demonstrate exceptional performance across various tasks, but their large storage and computational requirements constrain their deployment on edge devices.<n>We propose EntroLLM, a novel compression framework that integrates mixed quantization with entropy coding to reduce storage overhead while maintaining model accuracy.
  arXiv  Detail & Related papers  (2025-05-05T05:42:14Z)
• ParetoQ: Improving Scaling Laws in Extremely Low-bit LLM Quantization [73.60493264901359]
  We present a unified framework for rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings.<n>We show that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off.<n>Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.
  arXiv  Detail & Related papers  (2025-02-04T18:59:26Z)
• SLiM: One-shot Quantization and Sparsity with Low-rank Approximation for LLM Weight Compression [7.6131620435684875]
  SLIM is a new one-shot compression framework that holistically integrates hardware-friendly quantization, sparsity, and low-rank approximation.<n>SLIM improves model accuracy by up to 5.66% (LLaMA-2-7B) for 2:4 sparsity with 4-bit weight quantization, outperforming prior methods.
  arXiv  Detail & Related papers  (2024-10-12T18:36:07Z)
• 2DQuant: Low-bit Post-Training Quantization for Image Super-Resolution [83.09117439860607]
  Low-bit quantization has become widespread for compressing image super-resolution (SR) models for edge deployment. It is notorious that low-bit quantization degrades the accuracy of SR models compared to their full-precision (FP) counterparts. We present a dual-stage low-bit post-training quantization (PTQ) method for image super-resolution, namely 2DQuant, which achieves efficient and accurate SR under low-bit quantization.
  arXiv  Detail & Related papers  (2024-06-10T06:06:11Z)
• SqueezeLLM: Dense-and-Sparse Quantization [80.32162537942138]
  Main bottleneck for generative inference with LLMs is memory bandwidth, rather than compute, for single batch inference. We introduce SqueezeLLM, a post-training quantization framework that enables lossless compression to ultra-low precisions of up to 3-bit. Our framework incorporates two novel ideas: (i) sensitivity-based non-uniform quantization, which searches for the optimal bit precision assignment based on second-order information; and (ii) the Dense-and-Sparse decomposition that stores outliers and sensitive weight values in an efficient sparse format.
  arXiv  Detail & Related papers  (2023-06-13T08:57:54Z)
• Training with Quantization Noise for Extreme Model Compression [57.51832088938618]
  We tackle the problem of producing compact models, maximizing their accuracy for a given model size. A standard solution is to train networks with Quantization Aware Training, where the weights are quantized during training and the gradients approximated with the Straight-Through Estimator. In this paper, we extend this approach to work beyond int8 fixed-point quantization with extreme compression methods.
  arXiv  Detail & Related papers  (2020-04-15T20:10:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.