首先定点化的setting分好几种,主要如下所示 (w代表weight,a代表activation,g代表gradient)
最近两年的目前有13篇直接相关的论文,截止到2016年7月
- w定点,a浮点
- Resiliency of Deep Neural Networks under Quantization [Wongyong Sung, Sungho Shin, 2016.01.07, ICLR2016] {5bit在CIFAR10上恢复正确率}
- Fixed Point Quantization of Deep Convolutional Networks [Darryl D.Lin, Sachin S.Talathi, 2016.06.02] {每层定点化策略不同,解析解求出}
- w+a定点
- Hardware-oriented approximation of convolutional neural networks [Philipp Gysel, Mohammad Motamedi, ICLR 2016 Workshop] {ImageNet上8bit-8bit掉0.9%,AlexNet}
- Energy-Efficient ConvNets Through Approximate Computing [Bert Moons, KU leuven, 2016.03.22] {结合硬件的trick可以在ImageNet上4-10bit}
- Going Deeper with Embedded FPGA Platform for Convolutional Neural Network [Jiantao Qiu, Jie Wang, FPGA2016]{ImageNet上8bit-8bit掉1%,AlexNet}
- fine-tune整个网络
- w定点,a+g浮点
- Resiliency of Deep Neural Networks under Quantization [Wongyong Sung, Sungho Shin, 2016.01.07, ICLR2016] {2bit即三值网络在CIFAR10上恢复正确率}
- w+a定点,g浮点
- Fixed Point Quantization of Deep Convolutional Networks [Darryl D.Lin, Sachin S.Talathi, 2016.06.02] {每层定点化策略不同,解析解求出,CIFAR10上fine-tune后4bit-4bit掉1.32%}
- w+a+g定点
- Overcoming Challenges in Fixed Point Training of Deep Convolutional Networks [Darryl D.Lin, Sachin S. Talathi, Qualcomm Research,2016.07.08] {无随机rounding,ImageNet上4bit-16bit-16bit掉7.2%,a和g再小就不收敛}
- DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients [Shuchang Zhou, Zekun Ni, 2016.06.20] {1bit-2bit-4bit, 第一层和最后一层没有量化,ImageNet上掉5.2%}
- w定点,a+g浮点
- fine-tune最高几层
- w+a+g定点
- Overcoming Challenges in Fixed Point Training of Deep Convolutional Networks [Darryl D.Lin, Sachin S. Talathi, Qualcomm Research,2016.07.08] {无随机rounding,ImageNet上4bit-4bit-4bit掉23.3%}
- w+a+g定点
- 分阶段地从低层到高层fine-tune网络
- w+a+g定点
- Overcoming Challenges in Fixed Point Training of Deep Convolutional Networks [Darryl D.Lin, Sachin S. Talathi, Qualcomm Research,2016.07.08] {无随机rounding,ImageNet上4bit-4bit-4bit Top5掉11.5%}
- w+a+g定点
- w定点,a+g浮点
- 二值网络
- BinaryConnect: Training Deep Neural Networks with binary weights during propagations [Matthieu Courbariaux, Yoshua Bengio, 2015.11.02, NIPS] {CIFAR10上8.27%, state-of-art}
- XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks [Mohammad Rastegari, Washington University, 2016.03.16] {ImageNet上39.2%,掉2.8%, AlexNet}
- 三值网络
- Ternary Weight Networks [Fengfu Li, Bin Liu, UCAS, China, 2016.05.16] {ImageNet掉2.3%, ResNet-18B}
- Trained Ternary Quantization [Chenzhuo Zhu, Song Han, Huizi Mao, William J. Dally, ICLR2017] {ResNet上效果更佳}
- 二值网络
- w+a定点,g浮点
- 二值网络
- Binarized Neural Networks: Training Neural Networks with Weights and Activations Constrained to +1 or −1 [Matthieu Courbariaux, Yoshua Bengio, 2016.03.17] {CIFAR10上10.15%}
- XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks [Mohammad Rastegari, Washington University, 2016.03.16] {ImageNet上55.8%, 掉12.4%}
- 二值网络
- w+a+g定点
- Deep Learning with Limited Numerical Precision [ Suyog Gupta, Ankur Agrawal, IBM, 2015.02.09] {随机rounding技巧,CIFAR10上16bit+16bit+16bit复现正确率}
- Training deep neural networks with low precision multiplications [Matthieu Courbariaux, Yoshua Bengio, ICLR 2015 Workshop] {CIFAR10上10bit+10bit+12bit复现正确率}
- DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients [Shuchang Zhou, Zekun Ni, 2016.06.20] {1bit-2bit-4bit, 第一层和最后一层没有量化,ImageNet上掉8.8%}
- Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations [Itay Hubara, Matthieu Courbariaux, 2016.09.22]{1bit-2bit-6bit,ImageNet上超过DoReFa 0.33%}