# n-hot: Efficient bit-level sparsity for powers-of-two neural network quantization

arXiv: https://arxiv.org/abs/2103.11704 · HTML: https://mlsanity.com/paper/2103.11704/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 47 references that are in the map.
- First posted on arXiv 22 Mar 2021.

## Builds on (most cited first, 30 of 34)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Objects as Points](https://mlsanity.com/paper/1904.07850/) (2019)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [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)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Model compression via distillation and quantization](https://mlsanity.com/paper/1802.05668/) (2018)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [Incremental Network Quantization: Towards Lossless CNNs with Low-Precision Weights](https://mlsanity.com/paper/1702.03044/) (2017)
- [Ternary Weight Networks](https://mlsanity.com/paper/1605.04711/) (2016)
- [Additive Powers-of-Two Quantization: An Efficient Non-uniform Discretization for Neural Networks](https://mlsanity.com/paper/1909.13144/) (2019)
- [Fixed Point Quantization of Deep Convolutional Networks](https://mlsanity.com/paper/1511.06393/) (2015)
- [Scalable Methods for 8-bit Training of Neural Networks](https://mlsanity.com/paper/1805.11046/) (2018)
- [Binarized Neural Networks: Training Deep Neural Networks with Weights and Activations Constrained to +1 or -1](https://mlsanity.com/paper/1602.02830/) (2016)
- [Convolutional Neural Networks using Logarithmic Data Representation](https://mlsanity.com/paper/1603.01025/) (2016)
- [AdderNet: Do We Really Need Multiplications in Deep Learning?](https://mlsanity.com/paper/1912.13200/) (2019)
- [Towards Effective Low-bitwidth Convolutional Neural Networks](https://mlsanity.com/paper/1711.00205/) (2017)
- [Efficient 8-Bit Quantization of Transformer Neural Machine Language Translation Model](https://mlsanity.com/paper/1906.00532/) (2019)
- [Attention-Aware Compositional Network for Person Re-identification](https://mlsanity.com/paper/1805.03344/) (2018)

## Abstract (arXiv)

Powers-of-two (PoT) quantization reduces the number of bit operations of deep neural networks on resource-constrained hardware. However, PoT quantization triggers a severe accuracy drop because of its limited representation ability. Since DNN models have been applied for relatively complex tasks (e.g., classification for large datasets and object detection), improvement in accuracy for the PoT quantization method is required. Although some previous works attempt to improve the accuracy of PoT quantization, there is no work that balances accuracy and computation costs in a memory-efficient way. To address this problem, we propose an efficient PoT quantization scheme. Bit-level sparsity is introduced; weights (or activations) are rounded to values that can be calculated by n shift operations in multiplication. We also allow not only addition but also subtraction as each operation. Moreover, we use a two-stage fine-tuning algorithm to recover the accuracy drop that is triggered by introducing the bit-level sparsity. The experimental results on an object detection model (CenterNet, MobileNet-v2 backbone) on the COCO dataset show that our proposed method suppresses the accuracy drop by 0.3% at most while reducing the number of operations by about 75% and model size by 11.5% compared to the uniform method.