# CTMQ: Cyclic Training of Convolutional Neural Networks with Multiple Quantization Steps

arXiv: https://arxiv.org/abs/2206.12794 · HTML: https://mlsanity.com/paper/2206.12794/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 38 references that are in the map.
- First posted on arXiv 26 Jun 2022.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Quantized Convolutional Neural Networks for Mobile Devices](https://mlsanity.com/paper/1512.06473/) (2015)
- [Binary Neural Networks: A Survey](https://mlsanity.com/paper/2004.03333/) (2020)
- [Integer Quantization for Deep Learning Inference: Principles and Empirical Evaluation](https://mlsanity.com/paper/2004.09602/) (2020)
- [ReActNet: Towards Precise Binary Neural Network with Generalized Activation Functions](https://mlsanity.com/paper/2003.03488/) (2020)
- [Training Deep Neural Networks with 8-bit Floating Point Numbers](https://mlsanity.com/paper/1812.08011/) (2018)
- [Towards Accurate Binary Convolutional Neural Network](https://mlsanity.com/paper/1711.11294/) (2017)
- [Training Binary Neural Networks with Real-to-Binary Convolutions](https://mlsanity.com/paper/2003.11535/) (2020)
- [XNOR-Net++: Improved Binary Neural Networks](https://mlsanity.com/paper/1909.13863/) (2019)
- [Latent Weights Do Not Exist: Rethinking Binarized Neural Network Optimization](https://mlsanity.com/paper/1906.02107/) (2019)
- [ReCU: Reviving the Dead Weights in Binary Neural Networks](https://mlsanity.com/paper/2103.12369/) (2021)
- [BinaryDuo: Reducing Gradient Mismatch in Binary Activation Network by Coupling Binary Activations](https://mlsanity.com/paper/2002.06517/) (2020)
- [MoBiNet: A Mobile Binary Network for Image Classification](https://mlsanity.com/paper/1907.12629/) (2019)
- [Improving Binary Neural Networks through Fully Utilizing Latent Weights](https://mlsanity.com/paper/2110.05850/) (2021)
- [GXNOR-Net: Training deep neural networks with ternary weights and activations without full-precision memory under a unified discretization framework](https://mlsanity.com/paper/1705.09283/) (2017)

## Built on by (most cited first, 2 of 2)

- [Bit-by-Bit: Progressive QAT Strategy with Outlier Channel Splitting for Stable Low-Bit LLMs](https://mlsanity.com/paper/2604.07888/) (2026)
- [PQCAD-DM: Progressive Quantization and Calibration-Assisted Distillation for Extremely Efficient Diffusion Model](https://mlsanity.com/paper/2506.16776/) (2025)

## Abstract (arXiv)

This paper proposes a training method having multiple cyclic training for achieving enhanced performance in low-bit quantized convolutional neural networks (CNNs). Quantization is a popular method for obtaining lightweight CNNs, where the initialization with a pretrained model is widely used to overcome degraded performance in low-resolution quantization. However, large quantization errors between real values and their low-bit quantized ones cause difficulties in achieving acceptable performance for complex networks and large datasets. The proposed training method softly delivers the knowledge of pretrained models to low-bit quantized models in multiple quantization steps. In each quantization step, the trained weights of a model are used to initialize the weights of the next model with the quantization bit depth reduced by one. With small change of the quantization bit depth, the performance gap can be bridged, thus providing better weight initialization. In cyclic training, after training a low-bit quantized model, its trained weights are used in the initialization of its accurate model to be trained. By using better training ability of the accurate model in an iterative manner, the proposed method can produce enhanced trained weights for the low-bit quantized model in each cycle. Notably, the training method can advance Top-1 and Top-5 accuracies of the binarized ResNet-18 on the ImageNet dataset by 5.80% and 6.85%, respectively.