# Vertical Layering of Quantized Neural Networks for Heterogeneous Inference

arXiv: https://arxiv.org/abs/2212.05326 · HTML: https://mlsanity.com/paper/2212.05326/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 65 references that are in the map.
- First posted on arXiv 10 Dec 2022.

## Builds on (most cited first, 30 of 54)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [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)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Single Path One-Shot Neural Architecture Search with Uniform Sampling](https://mlsanity.com/paper/1904.00420/) (2019)
- [Dynamic Neural Networks: A Survey](https://mlsanity.com/paper/2102.04906/) (2021)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [SkipNet: Learning Dynamic Routing in Convolutional Networks](https://mlsanity.com/paper/1711.09485/) (2017)
- [Slimmable Neural Networks](https://mlsanity.com/paper/1812.08928/) (2018)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Trained Ternary Quantization](https://mlsanity.com/paper/1612.01064/) (2016)
- [Compressing Deep Convolutional Networks using Vector Quantization](https://mlsanity.com/paper/1412.6115/) (2014)
- [BlockDrop: Dynamic Inference Paths in Residual Networks](https://mlsanity.com/paper/1711.08393/) (2017)
- [Adaptive Neural Networks for Efficient Inference](https://mlsanity.com/paper/1702.07811/) (2017)

## Built on by (most cited first, 4 of 4)

- [Towards More Diverse and Challenging Pre-training for Point Cloud Learning: Self-Supervised Cross Reconstruction with Decoupled Views](https://mlsanity.com/paper/2509.01250/) (2025)
- [Equipping Vision Foundation Model with Mixture of Experts for Out-of-Distribution Detection](https://mlsanity.com/paper/2510.10584/) (2025)
- [Nearly Lossless Adaptive Bit Switching](https://mlsanity.com/paper/2502.01199/) (2025)
- [Hierarchical Spatial Algorithms for High-Resolution Image Quantization and Feature Extraction](https://mlsanity.com/paper/2510.08449/) (2025)

## Abstract (arXiv)

Although considerable progress has been obtained in neural network quantization for efficient inference, existing methods are not scalable to heterogeneous devices as one dedicated model needs to be trained, transmitted, and stored for one specific hardware setting, incurring considerable costs in model training and maintenance. In this paper, we study a new vertical-layered representation of neural network weights for encapsulating all quantized models into a single one. With this representation, we can theoretically achieve any precision network for on-demand service while only needing to train and maintain one model. To this end, we propose a simple once quantization-aware training (QAT) scheme for obtaining high-performance vertical-layered models. Our design incorporates a cascade downsampling mechanism which allows us to obtain multiple quantized networks from one full precision source model by progressively mapping the higher precision weights to their adjacent lower precision counterparts. Then, with networks of different bit-widths from one source model, multi-objective optimization is employed to train the shared source model weights such that they can be updated simultaneously, considering the performance of all networks. By doing this, the shared weights will be optimized to balance the performance of different quantized models, thus making the weights transferable among different bit widths. Experiments show that the proposed vertical-layered representation and developed once QAT scheme are effective in embodying multiple quantized networks into a single one and allow one-time training, and it delivers comparable performance as that of quantized models tailored to any specific bit-width. Code will be available.