# HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks

arXiv: https://arxiv.org/abs/1911.03852 · HTML: https://mlsanity.com/paper/1911.03852/

## Key facts

- Cited by 261 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2019.

## Built on by (most cited first, 30 of 261)

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [DeepSpeed-MoE: Advancing Mixture-of-Experts Inference and Training to Power Next-Generation AI Scale](https://mlsanity.com/paper/2201.05596/) (2022)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2106.14156/) (2021)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [I-BERT: Integer-only BERT Quantization](https://mlsanity.com/paper/2101.01321/) (2021)
- [QDrop: Randomly Dropping Quantization for Extremely Low-bit Post-Training Quantization](https://mlsanity.com/paper/2203.05740/) (2022)
- [OWQ: Outlier-Aware Weight Quantization for Efficient Fine-Tuning and Inference of Large Language Models](https://mlsanity.com/paper/2306.02272/) (2023)
- [OliVe: Accelerating Large Language Models via Hardware-friendly Outlier-Victim Pair Quantization](https://mlsanity.com/paper/2304.07493/) (2023)
- [Network Quantization with Element-wise Gradient Scaling](https://mlsanity.com/paper/2104.00903/) (2021)
- [A Comprehensive Survey on Model Quantization for Deep Neural Networks in Image Classification](https://mlsanity.com/paper/2205.07877/) (2022)
- [SliM-LLM: Salience-Driven Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2405.14917/) (2024)
- [ActNN: Reducing Training Memory Footprint via 2-Bit Activation Compressed Training](https://mlsanity.com/paper/2104.14129/) (2021)
- [Towards Mixed-Precision Quantization of Neural Networks via Constrained Optimization](https://mlsanity.com/paper/2110.06554/) (2021)
- [NoisyQuant: Noisy Bias-Enhanced Post-Training Activation Quantization for Vision Transformers](https://mlsanity.com/paper/2211.16056/) (2022)
- [Training Transformers with 4-bit Integers](https://mlsanity.com/paper/2306.11987/) (2023)
- [VPTQ: Extreme Low-bit Vector Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2409.17066/) (2024)
- [SQuant: On-the-Fly Data-Free Quantization via Diagonal Hessian Approximation](https://mlsanity.com/paper/2202.07471/) (2022)
- [Mixed-Precision Neural Network Quantization via Learned Layer-wise Importance](https://mlsanity.com/paper/2203.08368/) (2022)
- [ANT: Exploiting Adaptive Numerical Data Type for Low-bit Deep Neural Network Quantization](https://mlsanity.com/paper/2208.14286/) (2022)
- [Hessian-Aware Pruning and Optimal Neural Implant](https://mlsanity.com/paper/2101.08940/) (2021)
- [Differentiable Model Compression via Pseudo Quantization Noise](https://mlsanity.com/paper/2104.09987/) (2021)
- [Mixture Compressor for Mixture-of-Experts LLMs Gains More](https://mlsanity.com/paper/2410.06270/) (2024)
- [OMPQ: Orthogonal Mixed Precision Quantization](https://mlsanity.com/paper/2109.07865/) (2021)
- [Lightweight Deep Learning for Resource-Constrained Environments: A Survey](https://mlsanity.com/paper/2404.07236/) (2024)
- [NIPQ: Noise proxy-based Integrated Pseudo-Quantization](https://mlsanity.com/paper/2206.00820/) (2022)
- [Diversifying the High-level Features for better Adversarial Transferability](https://mlsanity.com/paper/2304.10136/) (2023)
- [APTQ: Attention-aware Post-Training Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2402.14866/) (2024)
- [Applications and Techniques for Fast Machine Learning in Science](https://mlsanity.com/paper/2110.13041/) (2021)

## Abstract (arXiv)

Quantization is an effective method for reducing memory footprint and inference time of Neural Networks, e.g., for efficient inference in the cloud, especially at the edge. However, ultra low precision quantization could lead to significant degradation in model generalization. A promising method to address this is to perform mixed-precision quantization, where more sensitive layers are kept at higher precision. However, the search space for a mixed-precision quantization is exponential in the number of layers. Recent work has proposed HAWQ, a novel Hessian based framework, with the aim of reducing this exponential search space by using second-order information. While promising, this prior work has three major limitations: (i) HAWQV1 only uses the top Hessian eigenvalue as a measure of sensitivity and do not consider the rest of the Hessian spectrum; (ii) HAWQV1 approach only provides relative sensitivity of different layers and therefore requires a manual selection of the mixed-precision setting; and (iii) HAWQV1 does not consider mixed-precision activation quantization. Here, we present HAWQV2 which addresses these shortcomings. For (i), we perform a theoretical analysis showing that a better sensitivity metric is to compute the average of all of the Hessian eigenvalues. For (ii), we develop a Pareto frontier based method for selecting the exact bit precision of different layers without any manual selection. For (iii), we extend the Hessian analysis to mixed-precision activation quantization. We have found this to be very beneficial for object detection. We show that HAWQV2 achieves new state-of-the-art results for a wide range of tasks.