# Where and How to Enhance: Discovering Bit-Width Contribution for Mixed Precision Quantization

arXiv: https://arxiv.org/abs/2508.03002 · HTML: https://mlsanity.com/paper/2508.03002/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 82 of its 122 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Builds on (most cited first, 30 of 82)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [Meta-Learning for Semi-Supervised Few-Shot Classification](https://mlsanity.com/paper/1803.00676/) (2018)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Rethinking Few-Shot Image Classification: a Good Embedding Is All You Need?](https://mlsanity.com/paper/2003.11539/) (2020)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [Decoupled Knowledge Distillation](https://mlsanity.com/paper/2203.08679/) (2022)

## Built on by (most cited first, 1 of 1)

- [Towards Training-free Automatic Proxy Discovery via Large Language Models for Mixed Precision Quantization](https://mlsanity.com/paper/2512.07419/) (2025)

## Abstract (arXiv)

Mixed precision quantization (MPQ) is an effective quantization approach to achieve accuracy-complexity trade-off of neural network, through assigning different bit-widths to network activations and weights in each layer. The typical way of existing MPQ methods is to optimize quantization policies (i.e., bit-width allocation) in a gradient descent manner, termed as Differentiable (DMPQ). At the end of the search, the bit-width associated to the quantization parameters which has the largest value will be selected to form the final mixed precision quantization policy, with the implicit assumption that the values of quantization parameters reflect the operation contribution to the accuracy improvement. While much has been discussed about the MPQ improvement, the bit-width selection process has received little attention. We study this problem and argue that the magnitude of quantization parameters does not necessarily reflect the actual contribution of the bit-width to the task performance. Then, we propose a Shapley-based MPQ (SMPQ) method, which measures the bit-width operation direct contribution on the MPQ task. To reduce computation cost, a Monte Carlo sampling-based approximation strategy is proposed for Shapley computation. Extensive experiments on mainstream benchmarks demonstrate that our SMPQ consistently achieves state-of-the-art performance than gradient-based competitors.