基于分裂基-2/(2a)FFT算法的卷积神经网络加速性能的研究

伍家松; 达臻; 魏黎明; SENHADJILotfi; 舒华忠

doi:10.11999/JEIT160357

基于分裂基-2/(2a)FFT算法的卷积神经网络加速性能的研究

doi: 10.11999/JEIT160357

基金项目:

国家自然科学基金(61201344, 61271312, 61401085)，高等学校博士学科点专项科研基金(20120092120036)

计量
- 文章访问数: 1895
- HTML全文浏览量: 177
- PDF下载量: 660
- 被引次数: 0
出版历程
- 收稿日期: 2016-04-12
- 修回日期: 2016-12-02
- 刊出日期: 2017-02-19

Acceleration Performance Study of Convolutional Neural Network Based on Split-radix-2/(2a) FFT Algorithms

Funds:

The National Natural Science Foundation of China (61201344, 61271312, 61401085), The Special Research Fund for the Doctoral Program of Higher Education (20120092120036)

摘要

摘要: 卷积神经网络在语音识别和图像识别等众多领域取得了突破性进展，限制其大规模应用的很重要的一个因素就是其计算复杂度，尤其是其中空域线性卷积的计算。利用卷积定理在频域中实现空域线性卷积被认为是一种非常有效的实现方式，该文首先提出一种统一的基于时域抽取方法的分裂基-2/(2a) 1维FFT快速算法，其中a为任意自然数，然后在CPU环境下对提出的FFT算法在一类卷积神经网络中的加速性能进行了比较研究。在MNIST手写数字数据库以及Cifar-10对象识别数据集上的实验表明：利用分裂基-2/4 FFT算法和基-2 FFT算法实现的卷积神经网络相比于空域直接实现的卷积神经网络，精度并不会有损失，并且分裂基-2/4能取得最好的提速效果，在以上两个数据集上分别提速38.56%和72.01%。因此，在频域中实现卷积神经网络的线性卷积操作是一种十分有效的实现方式。
- 信号处理 /
- 深度学习 /
- 卷积神经网络 /
- 快速傅里叶变换
Abstract: Convolution Neural Networks (CNN) make breakthrough progress in many areas recently, such as speech recognition and image recognition. A limiting factor for use of CNN in large-scale application is, until recently, their computational expense, especially the calculation of linear convolution in spatial domain. Convolution theorem provides a very effective way to implement a linear convolution in spatial domain by multiplication in frequency domain. This paper proposes an unified one-dimensional FFT algorithm based on decimation-in-time split- radix-2/(2a), in which a is an arbitrary natural number. The acceleration performance of convolutional neural network is studied by using the proposed FFT algorithm on CPU environment. Experimental results on the MNIST database and Cifar-10 database show great improvement when compared to the direct linear convolution based CNN with no loss in accuracy, and the radix-2/4 FFT gets the best time savings of 38.56% and 72.01% respectively. Therefore, it is a very effective way to realize linear convolution operation in frequency domain.
- Signal processing /
- Deep learning /
- Convolutional Neural Network (CNN) /
- Fast Fourier Transform (FFT)

HTML全文

参考文献(24)

HINTON G E and SALAKHUTDINOV R R. Reducing the dimensionality of data with neural networks[J]. Science, 2006, 313: 504-507. doi: 10.1126/science.1127647.

HINTON G E, OSINDERO S, and TEH Y W. A fast learning algorithm for deep belief nets[J]. Neural Computation, 2006, 18(7): 1527-1554. doi: 10.1162/neco.2006.18.7.1527.

BENGIO Y, COURVILLE A, and VINCENT P. Representation learning: A review and new perspectives[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(8): 1798-1828. doi: 10.1109/TPAMI. 2013.50.

LECUN Y, BENGIO Y, and HINTON G E. Deep learning[J]. Nature, 2015, 521(7553): 436-444. doi: 10.1038/nature14539.

DENG L and YU D. Deep learning: Methods and applications[J]. Foundations and Trends in Signal Processing, 2014, 7(3): 197-387.

LECUN Y, BOTTOU L, BENGIO Y, et al. Gradient-based learning applied to document recognition[J]. Proceedings of the IEEE, 1998, 86(11): 2278-2324. doi: 10.1109/5.726791.

KRIZHEVSKY A, SUTSKEVER I, and HINTON G E. Imagenet classification with deep convolutional neural networks[C]. Advances in Neural Information Processing Systems, Lake Tahoe, NV, USA, 2012: 1097-1105.

SZEGEDY C, LIU W, JIA Y Q, et al.. Going deeper with convolutions[C]. IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA, 2015: 1-9.

JADERBERG M, VEDALDI A, and ZISSERMAN A. Speeding up convolutional neural networks with low rank expansions[J]. Computer Science, 2014, 4(4): XIII.

LIU B, WANG M, FOROOSH H, et al. Sparse Convolutional neural networks[C]. IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, United States, 2015: 806-814.

VASILACHE N, JOHNSON J, MATHIEU M, et al. Fast convolutional nets with fbfft: A GPU performance evaluation [C]. International Conference on Learning Representations, San Diego, CA,USA, 2015: 1-17.

COOLEY J W and TUKEY J W. An algorithm for the machine calculation of complex Fourier series[J]. Mathematics of Computation, 1965, 90(19): 297-301. doi: 10.2307/2003354.

DUHAMEL P and VETTERLI M. Fast Fourier transforms: A tutorial review and a state of the art [J]. Signal Processing, 1990, 19(4): 259-299. doi: 10.1016/0165-1684(90)90158-U.

WINOGRAD S. On computing the discrete Fourier transform[J]. Proceedings of the National Academy of Sciences of the United States of America, 1976, 73(4): 1005-1006. doi: 10.1073/pnas.73.4.1005.

KOLBA D P and PARKS T W. A prime factor algorithm using high-speed convolution[J]. IEEE Transactions on Acoustics Speech Signal Processing, 1977, 25(4): 281-294. doi: 10.1109/TASSP.1977.1162973.

DUHAMEL P and HOLLMANN H. Implementation of Split-radix FFT algorithms for complex, real, and real symmetric data[C]. IEEE International Conference on Acoustics, Speech, and Signal Processing, Tampa, FL, USA, 1985: 285-295.

BOUGUEZEL S, AHMAD M O, and SWAMY M N S. A general class of split-radix FFT algorithms for the computation of the DFT of length-2m [J]. IEEE Transactions on Signal Processing, 2007, 55(8): 4127-4138. doi: 10.1109/ TSP.2007.896110.

BI G, LI G, and LI X. A unified expression for split-radix DFT algorithms[C]. IEEE International Conference on Communications, Circuits and Systems, Chengdu, China, 2010: 323-326.

FARHANG BOROUJENY B and LIM Y C. A comment on the computational complexity of sliding FFT[J]. IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing, 1992, 39(12): 875-876. doi: 10.1109/82. 208583.

PARK C S and KO S J. The hopping discrete Fourier transform[J]. IEEE Signal Processing Magazine, 2014, 31(2): 135-139. doi: 10.1109/MSP.2013.2292891.

GOUK H G and BLAKE A M. Fast sliding window classification with convolutional neural networks[C]. Proceedings of the 29th International Conference on Image and Vision Computing, New Zealand, 2014: 114-118.

RAO K R, KIM D N, and HWANG J J. Fast Fourier Transform: Algorithms and Applications[M]. Berlin: Springer Science Business Media, 2011: 5-6.

FRIGO M and JOHNSON S G. FFTW: An adaptive software architecture for the FFT[C]. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Seattle, WA, USA, 1998: 1381-1384.

SERMANET P, EIGEN D, ZHANG X, et al. Overfeat: Integrated recognition, localization and detection using convolutional networks[OL]. arXiv:1312.6229. 2013: 1-16.

施引文献

资源附件(0)

访问统计