# KurTail : Kurtosis-based LLM Quantization

arXiv: https://arxiv.org/abs/2503.01483 · HTML: https://mlsanity.com/paper/2503.01483/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 43 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 26 of 26)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [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)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (2024)
- [Lessons from the Trenches on Reproducible Evaluation of Language Models](https://mlsanity.com/paper/2405.14782/) (2024)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [OstQuant: Refining Large Language Model Quantization with Orthogonal and Scaling Transformations for Better Distribution Fitting](https://mlsanity.com/paper/2501.13987/) (2025)
- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [Robust Quantization: One Model to Rule Them All](https://mlsanity.com/paper/2002.07686/) (2020)
- [ResQ: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals](https://mlsanity.com/paper/2412.14363/) (2024)

## Built on by (most cited first, 12 of 12)

- [Block Rotation is All You Need for MXFP4 Quantization](https://mlsanity.com/paper/2511.04214/) (2025)
- [ButterflyQuant: Ultra-low-bit LLM Quantization through Learnable Orthogonal Butterfly Transforms](https://mlsanity.com/paper/2509.09679/) (2025)
- [Neural Network Quantization for Microcontrollers: A Comprehensive Survey of Methods, Platforms, and Applications](https://mlsanity.com/paper/2508.15008/) (2025)
- [SINQ: Sinkhorn-Normalized Quantization for Calibration-Free Low-Precision LLM Weights](https://mlsanity.com/paper/2509.22944/) (2025)
- [Beyond Outliers: A Study of Optimizers Under Quantization](https://mlsanity.com/paper/2509.23500/) (2025)
- [Bandwidth-Efficient Adaptive Mixture-of-Experts via Low-Rank Compensation](https://mlsanity.com/paper/2512.17073/) (2025)
- [OffQ: Taming Structured Outliers in LLM Quantization by Offsetting](https://mlsanity.com/paper/2606.07116/) (2026)
- [When Quantization Is Free: An int4 KV Cache That Outruns fp16 on Apple Silicon](https://mlsanity.com/paper/2605.05699/) (2026)
- [When Local Variance Optimality Is Not Enough: RoPE-Aligned Q/K Rotations for Dynamic 4-Bit Quantisation](https://mlsanity.com/paper/2608.13365/) (2026)
- [HBQ: Hierarchical Scaling Block Quantization with Hardware-Efficiency-Aware Design for Accurate LLM Inference](https://mlsanity.com/paper/2609.00450/) (2026)
- [Quantization Error Is Spectrally Flat: A Single Random Probe Is a Calibrated, Data-Free Sensitivity Estimator, with Application to Budget-Targeted Mixed-Precision Quantization](https://mlsanity.com/paper/2609.33923/) (2026)
- [ThinQuant: Scalable Rotation Learning for Weight and Activation Quantization of LLMs](https://mlsanity.com/paper/2609.36120/) (2026)

## Abstract (arXiv)

One of the challenges of quantizing a large language model (LLM) is the presence of outliers. Outliers often make uniform quantization schemes less effective, particularly in extreme cases such as 4-bit quantization. We introduce KurTail, a new post-training quantization (PTQ) scheme that leverages Kurtosis-based rotation to mitigate outliers in the activations of LLMs. Our method optimizes Kurtosis as a measure of tailedness. This approach enables the quantization of weights, activations, and the KV cache in 4 bits. We utilize layer-wise optimization, ensuring memory efficiency. KurTail outperforms existing quantization methods, offering a 13.3% boost in MMLU accuracy and a 15.5% drop in Wiki perplexity compared to QuaRot. It also outperforms SpinQuant with a 2.6% MMLU gain and reduces perplexity by 2.9%, all while reducing the training cost. For comparison, learning the rotation using SpinQuant for Llama3-70B requires at least four NVIDIA H100 80GB GPUs, whereas our method requires only a single GPU, making it a more accessible solution for consumer GPU.