# Sliced-Wasserstein Distribution Alignment Loss Improves the Ultra-Low-Bit Quantization of Large Language Models

arXiv: https://arxiv.org/abs/2601.07878 · HTML: https://mlsanity.com/paper/2601.07878/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 34 references that are in the map.
- First posted on arXiv 11 Jan 2026.

## Builds on (most cited first, 27 of 27)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [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)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (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)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [Sliced Wasserstein Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1903.04064/) (2019)
- [EfficientQAT: Efficient Quantization-Aware Training for Large Language Models](https://mlsanity.com/paper/2407.11062/) (2024)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [A Comprehensive Evaluation of Quantization Strategies for Large Language Models](https://mlsanity.com/paper/2402.16775/) (2024)
- [A Comprehensive Study on Quantization Techniques for Large Language Models](https://mlsanity.com/paper/2411.02530/) (2024)
- [Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model](https://mlsanity.com/paper/1804.01947/) (2018)
- [A Survey of Low-bit Large Language Models: Basics, Systems, and Algorithms](https://mlsanity.com/paper/2409.16694/) (2024)
- [ApiQ: Finetuning of 2-Bit Quantized Large Language Model](https://mlsanity.com/paper/2402.05147/) (2024)
- [What Makes Quantization for Large Language Models Hard? An Empirical Study from the Lens of Perturbation](https://mlsanity.com/paper/2403.06408/) (2024)
- [Properties of Discrete Sliced Wasserstein Losses](https://mlsanity.com/paper/2307.10352/) (2023)
- [LowRA: Accurate and Efficient LoRA Fine-Tuning of LLMs under 2 Bits](https://mlsanity.com/paper/2502.08141/) (2025)
- [Enhancing Ultra-Low-Bit Quantization of Large Language Models Through Saliency-Aware Partial Retraining](https://mlsanity.com/paper/2504.13932/) (2025)
- [Discrete Optimization of Min-Max Violation and its Applications Across Computational Sciences](https://mlsanity.com/paper/2508.13437/) (2025)

## Abstract (arXiv)

The benefits of most large language models come with steep and often hidden economic and environmental costs due to their resource usage inefficiency during deployment. Model quantization improves energy and memory efficiency through representing model parameters by lower-precision values. However, compression below 4-bits often distorts activation distributions and degrades performance. We address this challenge by introducing a sliced Wasserstein loss function for distribution-aware calibration in ultra-low-bit post-training quantization. The proposed loss aligns the output distributions of full-precision and quantized models under random linear projections, complementing standard mean-squared error loss without adding any computational overhead during inference. Our proposed loss function can be incorporated with any post-training quantization framework that has a retraining component. We demonstrate the performance gains of our proposed model by incorporating it with two frontier methods known as OmniQuant and TesseraQ. Compared to these two baselines, the proposed loss consistently improves both perplexity and downstream task accuracy across multiple ultra-low-bit settings. Our proposed loss function recovers 4.12-20.37% of the OmniQuant's lost accuracy on the language model LLaMA-2-7B, 0.93-7.65% on OPT-6.7B, and 2.26-6.20% on LLaMA-2-13B. TesseraQ's accuracy degradation is recovered by 3.63-7.63% in relative terms when augmented by our proposed loss function. Taken together, these results demonstrate that distributional alignment provides a simple yet effective performance boost that can push the limits of frontier quantization methods. Our method is available on GitHub to facilitate future progress in ultra-low-bit quantization.