# Hyperspherical Loss-Aware Ternary Quantization

arXiv: https://arxiv.org/abs/2212.12649 · HTML: https://mlsanity.com/paper/2212.12649/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 49 references that are in the map.
- First posted on arXiv 24 Dec 2022.

## Builds on (most cited first, 30 of 40)

- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [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)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [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)
- [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)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Incremental Network Quantization: Towards Lossless CNNs with Low-Precision Weights](https://mlsanity.com/paper/1702.03044/) (2017)
- [Trained Ternary Quantization](https://mlsanity.com/paper/1612.01064/) (2016)
- [Ternary Weight Networks](https://mlsanity.com/paper/1605.04711/) (2016)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Quantization Networks](https://mlsanity.com/paper/1911.09464/) (2019)
- [Hierarchical Multiscale Recurrent Neural Networks](https://mlsanity.com/paper/1609.01704/) (2016)
- [And the Bit Goes Down: Revisiting the Quantization of Neural Networks](https://mlsanity.com/paper/1907.05686/) (2019)
- [Extremely Low Bit Neural Network: Squeeze the Last Bit Out with ADMM](https://mlsanity.com/paper/1707.09870/) (2017)
- [ProxQuant: Quantized Neural Networks via Proximal Operators](https://mlsanity.com/paper/1810.00861/) (2018)

## Abstract (arXiv)

Most of the existing works use projection functions for ternary quantization in discrete space. Scaling factors and thresholds are used in some cases to improve the model accuracy. However, the gradients used for optimization are inaccurate and result in a notable accuracy gap between the full precision and ternary models. To get more accurate gradients, some works gradually increase the discrete portion of the full precision weights in the forward propagation pass, e.g., using temperature-based Sigmoid function. Instead of directly performing ternary quantization in discrete space, we push full precision weights close to ternary ones through regularization term prior to ternary quantization. In addition, inspired by the temperature-based method, we introduce a re-scaling factor to obtain more accurate gradients by simulating the derivatives of Sigmoid function. The experimental results show that our method can significantly improve the accuracy of ternary quantization in both image classification and object detection tasks.