LATMiX: Learnable Affine Transformations for Microscaling Quantization of LLMs

2026-02-04

arXiv.org

AI Summary

This work addresses the significant performance degradation of existing post-training quantization methods when applied to microscaling (MX) formats, primarily caused by the lack of co-optimization between activation distributions and quantization structures. To overcome this limitation, the paper introduces, for the first time, a learnable invertible affine transformation into the MX quantization framework, moving beyond conventional reliance on fixed rotations or Hadamard transforms. By jointly optimizing activation distributions and quantization structures, the proposed approach effectively reduces quantization error at low bit-widths. Theoretical analysis and extensive experiments demonstrate that this method consistently outperforms strong baselines across various model scales and zero-shot benchmarks, achieving sustained accuracy improvements in low-bit MX quantization.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Post-training quantization (PTQ) is a widely used approach for reducing the memory and compute costs of large language models (LLMs). Recent studies have shown that applying invertible transformations to activations can significantly improve quantization robustness by reducing activation outliers; however, existing approaches are largely restricted to rotation or Hadamard-based transformations. Moreover, most studies focused primarily on traditional quantization schemes, whereas modern hardware increasingly supports the microscaling (MX) data format. Attempts to combine both showed severe performance degradation, leading prior work to introduce assumptions on the transformations. In this work, we take a complementary perspective. First, we provide a theoretical analysis of transformations under MX quantization by deriving a bound on the quantization error. Our analysis emphasizes the importance of accounting for both the activation distribution and the underlying quantization structure. Building on this analysis, we propose LATMiX, a method that generalizes outlier reduction to learnable invertible affine transformations optimized using standard deep learning tools. Experiments show consistent improvements in average accuracy for MX low-bit quantization over strong baselines on a wide range of zero-shot benchmarks, across multiple model sizes.

Problem

• post-training quantization
• microscaling
• activation outliers
• invertible transformations
• LLMs

Innovation

• learnable affine transformations
• microscaling quantization
• post-training quantization
• outlier reduction
• LLM quantization