# Gradual Binary Search and Dimension Expansion : A general method for activation quantization in LLMs

arXiv: https://arxiv.org/abs/2504.13989 · HTML: https://mlsanity.com/paper/2504.13989/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 18 Apr 2025.

## Builds on (most cited first, 23 of 23)

- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits](https://mlsanity.com/paper/2402.17764/) (2024)
- [BitNet: Scaling 1-bit Transformers for Large Language Models](https://mlsanity.com/paper/2310.11453/) (2023)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [Defensive Quantization: When Efficiency Meets Robustness](https://mlsanity.com/paper/1904.08444/) (2019)
- [A Survey on Methods and Theories of Quantized Neural Networks](https://mlsanity.com/paper/1808.04752/) (2018)
- [FracBits: Mixed Precision Quantization via Fractional Bit-Widths](https://mlsanity.com/paper/2007.02017/) (2020)
- [Differentiable Model Compression via Pseudo Quantization Noise](https://mlsanity.com/paper/2104.09987/) (2021)
- [Prefixing Attention Sinks can Mitigate Activation Outliers for Large Language Model Quantization](https://mlsanity.com/paper/2406.12016/) (2024)
- [Mitigating the Impact of Outlier Channels for Language Model Quantization with Activation Regularization](https://mlsanity.com/paper/2404.03605/) (2024)
- [DFRot: Achieving Outlier-Free and Massive Activation-Free for Rotated LLMs with Refined Rotation](https://mlsanity.com/paper/2412.00648/) (2024)
- [RoLoRA: Fine-tuning Rotated Outlier-free LLMs for Effective Weight-Activation Quantization](https://mlsanity.com/paper/2407.08044/) (2024)
- [Post-Training Quantization for Re-parameterization via Coarse & Fine Weight Splitting](https://mlsanity.com/paper/2312.10588/) (2023)
- [Improving Quantization with Post-Training Model Expansion](https://mlsanity.com/paper/2503.17513/) (2025)

## Abstract (arXiv)

Large language models (LLMs) have become pivotal in artificial intelligence, demonstrating strong capabilities in reasoning, understanding, and generating data. However, their deployment on edge devices is hindered by their substantial size, often reaching several billion parameters. Quantization is a widely used method to reduce memory usage and inference time, however LLMs present unique challenges due to the prevalence of outliers in their activations. In this work, we leverage the theoretical advantages of Hadamard matrices over random rotation matrices to push the boundaries of quantization in LLMs. We demonstrate that Hadamard matrices are more effective in reducing outliers, which are a significant obstacle in achieving low-bit quantization. Our method based on a gradual binary search enables 3-bit quantization for weights, activations, and key-value (KV) caches, resulting in a 40% increase in accuracy on common benchmarks compared to SoTA methods. We extend the use of rotation matrices to support non-power-of-2 embedding dimensions, similar to the Qwen architecture, by employing the Paley algorithm. We theoretically demonstrates the superiority of Hadamard matrices in reducing outliers.We achieved 3-bit quantization for weights, activations, and KV cache, significantly enhancing model performance. Our experimental results on multiple models family like Mistral, LLaMA, and Qwen demonstrate the effectiveness of our approach, outperforming existing methods and enabling practical 3-bit quantization.