# Adaptive Loss-aware Quantization for Multi-bit Networks

arXiv: https://arxiv.org/abs/1912.08883 · HTML: https://mlsanity.com/paper/1912.08883/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2019.

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

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [A Comprehensive Survey on Model Quantization for Deep Neural Networks in Image Classification](https://mlsanity.com/paper/2205.07877/) (2022)
- [Sharpness-aware Quantization for Deep Neural Networks](https://mlsanity.com/paper/2111.12273/) (2021)
- [Collaborative Multi-Teacher Knowledge Distillation for Learning Low Bit-width Deep Neural Networks](https://mlsanity.com/paper/2210.16103/) (2022)
- [Generalizable Mixed-Precision Quantization via Attribution Rank Preservation](https://mlsanity.com/paper/2108.02720/) (2021)
- [Channel-Wise Mixed-Precision Quantization for Large Language Models](https://mlsanity.com/paper/2410.13056/) (2024)
- [Low-bit Model Quantization for Deep Neural Networks: A Survey](https://mlsanity.com/paper/2505.05530/) (2025)
- [Finding the Task-Optimal Low-Bit Sub-Distribution in Deep Neural Networks](https://mlsanity.com/paper/2112.15139/) (2021)
- [Class-based Quantization for Neural Networks](https://mlsanity.com/paper/2211.14928/) (2022)
- [HGQ: High Granularity Quantization for Real-time Neural Networks on FPGAs](https://mlsanity.com/paper/2405.00645/) (2024)
- [Measuring what Really Matters: Optimizing Neural Networks for TinyML](https://mlsanity.com/paper/2104.10645/) (2021)
- [Early-Exit with Class Exclusion for Efficient Inference of Neural Networks](https://mlsanity.com/paper/2309.13443/) (2023)
- [A Generalized Zero-Shot Quantization of Deep Convolutional Neural Networks via Learned Weights Statistics](https://mlsanity.com/paper/2112.02834/) (2021)
- [Training Compact CNNs for Image Classification using Dynamic-coded Filter Fusion](https://mlsanity.com/paper/2107.06916/) (2021)
- [Radio: Rate-Distortion Optimization for Large Language Model Compression](https://mlsanity.com/paper/2505.03031/) (2025)
- [Automatic Neural Network Pruning that Efficiently Preserves the Model Accuracy](https://mlsanity.com/paper/2111.09635/) (2021)
- [Model compression as constrained optimization, with application to neural nets. Part V: combining compressions](https://mlsanity.com/paper/2107.04380/) (2021)
- [Arrhythmia Classifier Using Convolutional Neural Network with Adaptive Loss-aware Multi-bit Networks Quantization](https://mlsanity.com/paper/2202.12943/) (2022)
- [Learning from Loss Landscape: Generalizable Mixed-Precision Quantization via Adaptive Sharpness-Aware Gradient Aligning](https://mlsanity.com/paper/2505.04877/) (2025)
- [One-Step Forward and Backtrack: Overcoming Zig-Zagging in Loss-Aware Quantization Training](https://mlsanity.com/paper/2401.16760/) (2024)
- [From Algorithm to Hardware: A Survey on Efficient and Safe Deployment of Deep Neural Networks](https://mlsanity.com/paper/2405.06038/) (2024)
- [Foundations of Large Language Model Compression -- Part 1: Weight Quantization](https://mlsanity.com/paper/2409.02026/) (2024)
- [DRESS: Dynamic REal-time Sparse Subnets](https://mlsanity.com/paper/2207.00670/) (2022)
- [Learning Accurate Performance Predictors for Ultrafast Automated Model Compression](https://mlsanity.com/paper/2304.06393/) (2023)
- [Error Diffusion: Post Training Quantization with Block-Scaled Number Formats for Neural Networks](https://mlsanity.com/paper/2410.11203/) (2024)
- [FlexiQ: Adaptive Mixed-Precision Quantization for Latency/Accuracy Trade-Offs in Deep Neural Networks](https://mlsanity.com/paper/2510.02822/) (2025)
- [Quantization of Neural Network Equalizers in Optical Fiber Transmission Experiments](https://mlsanity.com/paper/2310.05950/) (2023)
- [AccEPT: An Acceleration Scheme for Speeding Up Edge Pipeline-parallel Training](https://mlsanity.com/paper/2311.05827/) (2023)
- [PQCAD-DM: Progressive Quantization and Calibration-Assisted Distillation for Extremely Efficient Diffusion Model](https://mlsanity.com/paper/2506.16776/) (2025)
- [Search-Optimized Quantization in Biomedical Ontology Alignment](https://mlsanity.com/paper/2507.13742/) (2025)

## Abstract (arXiv)

We investigate the compression of deep neural networks by quantizing their weights and activations into multiple binary bases, known as multi-bit networks (MBNs), which accelerate the inference and reduce the storage for the deployment on low-resource mobile and embedded platforms. We propose Adaptive Loss-aware Quantization (ALQ), a new MBN quantization pipeline that is able to achieve an average bitwidth below one-bit without notable loss in inference accuracy. Unlike previous MBN quantization solutions that train a quantizer by minimizing the error to reconstruct full precision weights, ALQ directly minimizes the quantization-induced error on the loss function involving neither gradient approximation nor full precision maintenance. ALQ also exploits strategies including adaptive bitwidth, smooth bitwidth reduction, and iterative trained quantization to allow a smaller network size without loss in accuracy. Experiment results on popular image datasets show that ALQ outperforms state-of-the-art compressed networks in terms of both storage and accuracy. Code is available at https://github.com/zqu1992/ALQ