# Quantization and Training of Low Bit-Width Convolutional Neural Networks for Object Detection

arXiv: https://arxiv.org/abs/1612.06052 · HTML: https://mlsanity.com/paper/1612.06052/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2016.

## Built on by (most cited first, 8 of 8)

- [MagR: Weight Magnitude Reduction for Enhancing Post-Training Quantization](https://mlsanity.com/paper/2406.00800/) (2024)
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- [Adaptive Precision Training (AdaPT): A dynamic fixed point quantized training approach for DNNs](https://mlsanity.com/paper/2107.13490/) (2021)
- [CLoQ: Enhancing Fine-Tuning of Quantized LLMs via Calibrated LoRA Initialization](https://mlsanity.com/paper/2501.18475/) (2025)
- [PARQ: Piecewise-Affine Regularized Quantization](https://mlsanity.com/paper/2503.15748/) (2025)
- [Ternary Quantization: A Survey](https://mlsanity.com/paper/2303.01505/) (2023)
- [n-hot: Efficient bit-level sparsity for powers-of-two neural network quantization](https://mlsanity.com/paper/2103.11704/) (2021)

## Abstract (arXiv)

We present LBW-Net, an efficient optimization based method for quantization and training of the low bit-width convolutional neural networks (CNNs). Specifically, we quantize the weights to zero or powers of two by minimizing the Euclidean distance between full-precision weights and quantized weights during backpropagation. We characterize the combinatorial nature of the low bit-width quantization problem. For 2-bit (ternary) CNNs, the quantization of N weights can be done by an exact formula in O(Nlog N) complexity. When the bit-width is three and above, we further propose a semi-analytical thresholding scheme with a single free parameter for quantization that is computationally inexpensive. The free parameter is further determined by network retraining and object detection tests. LBW-Net has several desirable advantages over full-precision CNNs, including considerable memory savings, energy efficiency, and faster deployment. Our experiments on PASCAL VOC dataset show that compared with its 32-bit floating-point counterpart, the performance of the 6-bit LBW-Net is nearly lossless in the object detection tasks, and can even do better in some real world visual scenes, while empirically enjoying more than 4× faster deployment.