【转】学习笔记：GoogLeNet

原作者：lynnandwei 原文地址：http://blog.csdn.net/lynnandwei/article/details/44458033

GoogLeNet, 2014年ILSVRC挑战赛冠军，将Top5 的错误率降低到6.67%. 一个22层的深度网络，论文在http://arxiv.org/pdf/1409.4842v1.pdf，题目为：Going deeper with convolutions。（每次看这么简洁优雅的题目，就想吐槽国内写paper的 八股文题目）。GoogLeNet这个名字也是挺有意思的，为了像开山鼻祖的LeNet网络致敬，他们选择了这样的名字。

BVLC在caffe中给出了网络的实现：https://github.com/BVLC/caffe/tree/master/models/bvlc_googlenet

模型下载地址：http://dl.caffe.berkeleyvision.org/bvlc_googlenet.caffemodel

从论文里整理了一张这个22个层次的模型的图出来（如果考虑pooling层是27层），先将模型跑了一遍结果，还是那只猫： 

直观输出是如下，觉得挺准确：

[287 281 285 282 283]
['n02127052 lynx, catamount' 'n02123045 tabby, tabby cat'
 'n02124075 Egyptian cat' 'n02123159 tiger cat' 'n02123394 Persian cat']

caffe的实现和原来论文的模型是有不同的：

not training with the relighting data-augmentation;
not training with the scale or aspect-ratio data-augmentation;
uses "xavier" to initialize the weights instead of "gaussian";
quick_solver.prototxt uses a different learning rate decay policy than the original solver.prototxt, that allows a much faster training (60 epochs vs 250 epochs);
The bundled model is the iteration 2,400,000 snapshot (60 epochs) using quick_solver.prototxt

但是准确度还是达到了 a top-1 accuracy 68.7% (31.3% error) and a top-5 accuracy 88.9% (11.1% error)

我们来分析一下这个模型的层次关系:

原始数据，输入为224*224*3

第一层卷积层 conv1 ，pad是3，64个特征，7*7 步长为2，输出特征为 112*112*64，然后进行relu，经过pool1（红色的max pool） 进行pooling 3*3的核，步长为2， [（112 - 3+1）/2]+1 = 56  特征为56*56*64 ， 然后进行norm 

第二层卷积层 conv2， pad是1，3*3，192个特征，输出为56*56*192，然后进行relu，进行norm，经过pool2进行pooling，3*3的核，步长为2 输出为28*28*192 然后进行split 分成四个支线

Setting up pool2/3x3_s2
I0319 23:50:37.405478  5765 net.cpp:103] Top shape: 10 192 28 28 (1505280)
I0319 23:50:37.405484  5765 net.cpp:113] Memory required for data: 174612480
I0319 23:50:37.405495  5765 net.cpp:67] Creating Layer pool2/3x3_s2_pool2/3x3_s2_0_split
I0319 23:50:37.405503  5765 net.cpp:394] pool2/3x3_s2_pool2/3x3_s2_0_split <- pool2/3x3_s2
I0319 23:50:37.405515  5765 net.cpp:356] pool2/3x3_s2_pool2/3x3_s2_0_split -> pool2/3x3_s2_pool2/3x3_s2_0_split_0
I0319 23:50:37.405531  5765 net.cpp:356] pool2/3x3_s2_pool2/3x3_s2_0_split -> pool2/3x3_s2_pool2/3x3_s2_0_split_1
I0319 23:50:37.405545  5765 net.cpp:356] pool2/3x3_s2_pool2/3x3_s2_0_split -> pool2/3x3_s2_pool2/3x3_s2_0_split_2
I0319 23:50:37.405557  5765 net.cpp:356] pool2/3x3_s2_pool2/3x3_s2_0_split -> pool2/3x3_s2_pool2/3x3_s2_0_split_3
I0319 23:50:37.405567  5765 net.cpp:96] Setting up pool2/3x3_s2_pool2/3x3_s2_0_split
I0319 23:50:37.405577  5765 net.cpp:103] Top shape: 10 192 28 28 (1505280)
I0319 23:50:37.405582  5765 net.cpp:103] Top shape: 10 192 28 28 (1505280)
I0319 23:50:37.405587  5765 net.cpp:103] Top shape: 10 192 28 28 (1505280)
I0319 23:50:37.405592  5765 net.cpp:103] Top shape: 10 192 28 28 (1505280)
I0319 23:50:37.405597  5765 net.cpp:113] Memory required for data: 198696960
I0319 23:50:37.405611  5765 net.cpp:67] Creating Layer inception_3a/1x1^M

第三层开始时 inception module ，这个的思想受到使用不同尺度的Gabor过滤器来处理多尺度问题，inception module采用不同尺度的卷积核来处理问题。3a 包含 四个支线：

1： 64个1*1的卷积核（之后进行RULE计算） 变成28*28*64

2： 96个1*1的卷积核 作为3*3卷积核之前的reduce，变成28*28*96， 进行relu计算后，再进行128个3*3的卷积，pad为1， 28*28*128

3：16个1*1的卷积核 作为5*5卷积核之前的reduce，变成28*28*16， 进行relu计算后，再进行32个5*5的卷积，pad为2，变成28*28*32

4：pool层，3*3的核，pad为1，输出还是28*28*192，然后进行32个1*1的卷积，变成28*28*32。

将四个结果进行连接，输出为28*28*256

然后将3a的结果又分成四条支线，开始建立3b的inception module

3b 

1：128个1*1的卷积核（之后进行RULE计算） 变成28*28*128

2：128个1*1的卷积核 作为3*3卷积核之前的reduce，变成28*28*128， 再进行192个3*3的卷积，pad为1， 28*28*192，进行relu计算

3：32个1*1的卷积核 作为5*5卷积核之前的reduce，变成28*28*32， 进行relu计算后，再进行96个5*5的卷积，pad为2，变成28*28*96

4：pool层，3*3的核，pad为1，输出还是28*28*256，然后进行64个1*1的卷积，变成28*28*64。

将四个结果进行连接，输出为28*28*480

同理依次推算，数据变化如下表：

一部分输出结果如下：

I0319 22:27:51.257917 5080 net.cpp:208] This network produces output prob

I0319 22:27:51.258116  5080 net.cpp:467] Collecting Learning Rate and Weight Decay.
I0319 22:27:51.258162  5080 net.cpp:219] Network initialization done.
I0319 22:27:51.258167  5080 net.cpp:220] Memory required for data: 545512320
I0319 22:27:51.345417  5080 net.cpp:702] Ignoring source layer data
I0319 22:27:51.345443  5080 net.cpp:702] Ignoring source layer label_data_1_split
I0319 22:27:51.345448  5080 net.cpp:705] Copying source layer conv1/7x7_s2
I0319 22:27:51.345542  5080 net.cpp:705] Copying source layer conv1/relu_7x7
I0319 22:27:51.345548  5080 net.cpp:705] Copying source layer pool1/3x3_s2
I0319 22:27:51.345553  5080 net.cpp:705] Copying source layer pool1/norm1
I0319 22:27:51.345558  5080 net.cpp:705] Copying source layer conv2/3x3_reduce
I0319 22:27:51.345600  5080 net.cpp:705] Copying source layer conv2/relu_3x3_reduce
I0319 22:27:51.345607  5080 net.cpp:705] Copying source layer conv2/3x3
I0319 22:27:51.346571  5080 net.cpp:705] Copying source layer conv2/relu_3x3
I0319 22:27:51.346580  5080 net.cpp:705] Copying source layer conv2/norm2
I0319 22:27:51.346585  5080 net.cpp:705] Copying source layer pool2/3x3_s2
I0319 22:27:51.346590  5080 net.cpp:705] Copying source layer pool2/3x3_s2_pool2/3x3_s2_0_split
I0319 22:27:51.346595  5080 net.cpp:705] Copying source layer inception_3a/1x1
I0319 22:27:51.346706  5080 net.cpp:705] Copying source layer inception_3a/relu_1x1
I0319 22:27:51.346712  5080 net.cpp:705] Copying source layer inception_3a/3x3_reduce
I0319 22:27:51.346879  5080 net.cpp:705] Copying source layer inception_3a/relu_3x3_reduce
I0319 22:27:51.346885  5080 net.cpp:705] Copying source layer inception_3a/3x3
I0319 22:27:51.347844  5080 net.cpp:705] Copying source layer inception_3a/relu_3x3
I0319 22:27:51.347851  5080 net.cpp:705] Copying source layer inception_3a/5x5_reduce
I0319 22:27:51.347885  5080 net.cpp:705] Copying source layer inception_3a/relu_5x5_reduce
I0319 22:27:51.347892  5080 net.cpp:705] Copying source layer inception_3a/5x5
I0319 22:27:51.348008  5080 net.cpp:705] Copying source layer inception_3a/relu_5x5
I0319 22:27:51.348014  5080 net.cpp:705] Copying source layer inception_3a/pool
I0319 22:27:51.348019  5080 net.cpp:705] Copying source layer inception_3a/pool_proj
I0319 22:27:51.348080  5080 net.cpp:705] Copying source layer inception_3a/relu_pool_proj
I0319 22:27:51.348085  5080 net.cpp:705] Copying source layer inception_3a/output
I0319 22:27:51.348091  5080 net.cpp:705] Copying source layer inception_3a/output_inception_3a/output_0_split
I0319 22:27:51.348096  5080 net.cpp:705] Copying source layer inception_3b/1x1
I0319 22:27:51.348398  5080 net.cpp:705] Copying source layer inception_3b/relu_1x1
I0319 22:27:51.348405  5080 net.cpp:705] Copying source layer inception_3b/3x3_reduce
I0319 22:27:51.348700  5080 net.cpp:705] Copying source layer inception_3b/relu_3x3_reduce
I0319 22:27:51.348707  5080 net.cpp:705] Copying source layer inception_3b/3x3
I0319 22:27:51.350611  5080 net.cpp:705] Copying source layer inception_3b/relu_3x3
I0319 22:27:51.350620  5080 net.cpp:705] Copying source layer inception_3b/5x5_reduce
I0319 22:27:51.350699  5080 net.cpp:705] Copying source layer inception_3b/relu_5x5_reduce
I0319 22:27:51.350705  5080 net.cpp:705] Copying source layer inception_3b/5x5
I0319 22:27:51.351372  5080 net.cpp:705] Copying source layer inception_3b/relu_5x5
I0319 22:27:51.351378  5080 net.cpp:705] Copying source layer inception_3b/pool
I0319 22:27:51.351384  5080 net.cpp:705] Copying source layer inception_3b/pool_proj
I0319 22:27:51.351546  5080 net.cpp:705] Copying source layer inception_3b/relu_pool_proj
I0319 22:27:51.351552  5080 net.cpp:705] Copying source layer inception_3b/output
I0319 22:27:51.351558  5080 net.cpp:705] Copying source layer pool3/3x3_s2
I0319 22:27:51.351563  5080 net.cpp:705] Copying source layer pool3/3x3_s2_pool3/3x3_s2_0_split
I0319 22:27:51.351569  5080 net.cpp:705] Copying source layer inception_4a/1x1
I0319 22:27:51.352367  5080 net.cpp:705] Copying source layer inception_4a/relu_1x1
I0319 22:27:51.352375  5080 net.cpp:705] Copying source layer inception_4a/3x3_reduce
I0319 22:27:51.352782  5080 net.cpp:705] Copying source layer inception_4a/relu_3x3_reduce
I0319 22:27:51.352789  5080 net.cpp:705] Copying source layer inception_4a/3x3
I0319 22:27:51.354333  5080 net.cpp:705] Copying source layer inception_4a/relu_3x3
I0319 22:27:51.354341  5080 net.cpp:705] Copying source layer inception_4a/5x5_reduce
I0319 22:27:51.354420  5080 net.cpp:705] Copying source layer inception_4a/relu_5x5_reduce
I0319 22:27:51.354429  5080 net.cpp:705] Copying source layer inception_4a/5x5
I0319 22:27:51.354601  5080 net.cpp:705] Copying source layer inception_4a/relu_5x5
I0319 22:27:51.354609  5080 net.cpp:705] Copying source layer inception_4a/pool
I0319 22:27:51.354614  5080 net.cpp:705] Copying source layer inception_4a/pool_proj
I0319 22:27:51.354887  5080 net.cpp:705] Copying source layer inception_4a/relu_pool_proj
I0319 22:27:51.354894  5080 net.cpp:705] Copying source layer inception_4a/output
I0319 22:27:51.354900  5080 net.cpp:705] Copying source layer inception_4a/output_inception_4a/output_0_split
I0319 22:27:51.354910  5080 net.cpp:702] Ignoring source layer loss1/ave_pool
I0319 22:27:51.354918  5080 net.cpp:702] Ignoring source layer loss1/conv
I0319 22:27:51.354923  5080 net.cpp:702] Ignoring source layer loss1/relu_conv
I0319 22:27:51.354930  5080 net.cpp:702] Ignoring source layer loss1/fc
I0319 22:27:51.354936  5080 net.cpp:702] Ignoring source layer loss1/relu_fc
I0319 22:27:51.354943  5080 net.cpp:702] Ignoring source layer loss1/drop_fc
I0319 22:27:51.354950  5080 net.cpp:702] Ignoring source layer loss1/classifier
I0319 22:27:51.354956  5080 net.cpp:702] Ignoring source layer loss1/loss
I0319 22:27:51.354962  5080 net.cpp:705] Copying source layer inception_4b/1x1
I0319 22:27:51.355681  5080 net.cpp:705] Copying source layer inception_4b/relu_1x1
I0319 22:27:51.355690  5080 net.cpp:705] Copying source layer inception_4b/3x3_reduce
I0319 22:27:51.356190  5080 net.cpp:705] Copying source layer inception_4b/relu_3x3_reduce
I0319 22:27:51.356199  5080 net.cpp:705] Copying source layer inception_4b/3x3
I0319 22:27:51.358134  5080 net.cpp:705] Copying source layer inception_4b/relu_3x3
I0319 22:27:51.358144  5080 net.cpp:705] Copying source layer inception_4b/5x5_reduce
I0319 22:27:51.358256  5080 net.cpp:705] Copying source layer inception_4b/relu_5x5_reduce
I0319 22:27:51.358263  5080 net.cpp:705] Copying source layer inception_4b/5x5
I0319 22:27:51.358608  5080 net.cpp:705] Copying source layer inception_4b/relu_5x5
I0319 22:27:51.358616  5080 net.cpp:705] Copying source layer inception_4b/pool
I0319 22:27:51.358623  5080 net.cpp:705] Copying source layer inception_4b/pool_proj
I0319 22:27:51.358917  5080 net.cpp:705] Copying source layer inception_4b/relu_pool_proj
I0319 22:27:51.358925  5080 net.cpp:705] Copying source layer inception_4b/output
I0319 22:27:51.358932  5080 net.cpp:705] Copying source layer inception_4b/output_inception_4b/output_0_split
I0319 22:27:51.358937  5080 net.cpp:705] Copying source layer inception_4c/1x1
I0319 22:27:51.359519  5080 net.cpp:705] Copying source layer inception_4c/relu_1x1
I0319 22:27:51.359526  5080 net.cpp:705] Copying source layer inception_4c/3x3_reduce
I0319 22:27:51.360097  5080 net.cpp:705] Copying source layer inception_4c/relu_3x3_reduce
I0319 22:27:51.360105  5080 net.cpp:705] Copying source layer inception_4c/3x3
I0319 22:27:51.362634  5080 net.cpp:705] Copying source layer inception_4c/relu_3x3
I0319 22:27:51.362643  5080 net.cpp:705] Copying source layer inception_4c/5x5_reduce
I0319 22:27:51.362757  5080 net.cpp:705] Copying source layer inception_4c/relu_5x5_reduce
I0319 22:27:51.362764  5080 net.cpp:705] Copying source layer inception_4c/5x5
I0319 22:27:51.363106  5080 net.cpp:705] Copying source layer inception_4c/relu_5x5
I0319 22:27:51.363114  5080 net.cpp:705] Copying source layer inception_4c/pool
I0319 22:27:51.363121  5080 net.cpp:705] Copying source layer inception_4c/pool_proj
I0319 22:27:51.363415  5080 net.cpp:705] Copying source layer inception_4c/relu_pool_proj
I0319 22:27:51.363423  5080 net.cpp:705] Copying source layer inception_4c/output
I0319 22:27:51.363430  5080 net.cpp:705] Copying source layer inception_4c/output_inception_4c/output_0_split
I0319 22:27:51.363436  5080 net.cpp:705] Copying source layer inception_4d/1x1
I0319 22:27:51.363937  5080 net.cpp:705] Copying source layer inception_4d/relu_1x1
I0319 22:27:51.363945  5080 net.cpp:705] Copying source layer inception_4d/3x3_reduce
I0319 22:27:51.364591  5080 net.cpp:705] Copying source layer inception_4d/relu_3x3_reduce
I0319 22:27:51.364600  5080 net.cpp:705] Copying source layer inception_4d/3x3
I0319 22:27:51.367797  5080 net.cpp:705] Copying source layer inception_4d/relu_3x3
I0319 22:27:51.367806  5080 net.cpp:705] Copying source layer inception_4d/5x5_reduce
I0319 22:27:51.367959  5080 net.cpp:705] Copying source layer inception_4d/relu_5x5_reduce
I0319 22:27:51.367966  5080 net.cpp:705] Copying source layer inception_4d/5x5
I0319 22:27:51.368420  5080 net.cpp:705] Copying source layer inception_4d/relu_5x5
I0319 22:27:51.368428  5080 net.cpp:705] Copying source layer inception_4d/pool
I0319 22:27:51.368435  5080 net.cpp:705] Copying source layer inception_4d/pool_proj
I0319 22:27:51.368726  5080 net.cpp:705] Copying source layer inception_4d/relu_pool_proj
I0319 22:27:51.368733  5080 net.cpp:705] Copying source layer inception_4d/output
I0319 22:27:51.368739  5080 net.cpp:705] Copying source layer inception_4d/output_inception_4d/output_0_split
I0319 22:27:51.368748  5080 net.cpp:702] Ignoring source layer loss2/ave_pool
I0319 22:27:51.368755  5080 net.cpp:702] Ignoring source layer loss2/conv
I0319 22:27:51.368762  5080 net.cpp:702] Ignoring source layer loss2/relu_conv
I0319 22:27:51.368768  5080 net.cpp:702] Ignoring source layer loss2/fc
I0319 22:27:51.368774  5080 net.cpp:702] Ignoring source layer loss2/relu_fc
I0319 22:27:51.368780  5080 net.cpp:702] Ignoring source layer loss2/drop_fc
I0319 22:27:51.368788  5080 net.cpp:702] Ignoring source layer loss2/classifier
I0319 22:27:51.368794  5080 net.cpp:702] Ignoring source layer loss2/loss
I0319 22:27:51.368800  5080 net.cpp:705] Copying source layer inception_4e/1x1
I0319 22:27:51.369971  5080 net.cpp:705] Copying source layer inception_4e/relu_1x1
I0319 22:27:51.369981  5080 net.cpp:705] Copying source layer inception_4e/3x3_reduce
I0319 22:27:51.370717  5080 net.cpp:705] Copying source layer inception_4e/relu_3x3_reduce
I0319 22:27:51.370725  5080 net.cpp:705] Copying source layer inception_4e/3x3
I0319 22:27:51.374668  5080 net.cpp:705] Copying source layer inception_4e/relu_3x3
I0319 22:27:51.374678  5080 net.cpp:705] Copying source layer inception_4e/5x5_reduce
I0319 22:27:51.374831  5080 net.cpp:705] Copying source layer inception_4e/relu_5x5_reduce
I0319 22:27:51.374840  5080 net.cpp:705] Copying source layer inception_4e/5x5
I0319 22:27:51.375728  5080 net.cpp:705] Copying source layer inception_4e/relu_5x5
I0319 22:27:51.375737  5080 net.cpp:705] Copying source layer inception_4e/pool
I0319 22:27:51.375744  5080 net.cpp:705] Copying source layer inception_4e/pool_proj
I0319 22:27:51.376332  5080 net.cpp:705] Copying source layer inception_4e/relu_pool_proj
I0319 22:27:51.376340  5080 net.cpp:705] Copying source layer inception_4e/output
I0319 22:27:51.376346  5080 net.cpp:705] Copying source layer pool4/3x3_s2
I0319 22:27:51.376353  5080 net.cpp:705] Copying source layer pool4/3x3_s2_pool4/3x3_s2_0_split
I0319 22:27:51.376359  5080 net.cpp:705] Copying source layer inception_5a/1x1
I0319 22:27:51.378186  5080 net.cpp:705] Copying source layer inception_5a/relu_1x1
I0319 22:27:51.378196  5080 net.cpp:705] Copying source layer inception_5a/3x3_reduce
I0319 22:27:51.379343  5080 net.cpp:705] Copying source layer inception_5a/relu_3x3_reduce
I0319 22:27:51.379353  5080 net.cpp:705] Copying source layer inception_5a/3x3
I0319 22:27:51.383293  5080 net.cpp:705] Copying source layer inception_5a/relu_3x3
I0319 22:27:51.383303  5080 net.cpp:705] Copying source layer inception_5a/5x5_reduce
I0319 22:27:51.383548  5080 net.cpp:705] Copying source layer inception_5a/relu_5x5_reduce
I0319 22:27:51.383558  5080 net.cpp:705] Copying source layer inception_5a/5x5
I0319 22:27:51.384449  5080 net.cpp:705] Copying source layer inception_5a/relu_5x5
I0319 22:27:51.384459  5080 net.cpp:705] Copying source layer inception_5a/pool
I0319 22:27:51.384465  5080 net.cpp:705] Copying source layer inception_5a/pool_proj
I0319 22:27:51.385397  5080 net.cpp:705] Copying source layer inception_5a/relu_pool_proj
I0319 22:27:51.385406  5080 net.cpp:705] Copying source layer inception_5a/output
I0319 22:27:51.385414  5080 net.cpp:705] Copying source layer inception_5a/output_inception_5a/output_0_split
I0319 22:27:51.385421  5080 net.cpp:705] Copying source layer inception_5b/1x1
I0319 22:27:51.388157  5080 net.cpp:705] Copying source layer inception_5b/relu_1x1
I0319 22:27:51.388166  5080 net.cpp:705] Copying source layer inception_5b/3x3_reduce
I0319 22:27:51.389539  5080 net.cpp:705] Copying source layer inception_5b/relu_3x3_reduce
I0319 22:27:51.389549  5080 net.cpp:705] Copying source layer inception_5b/3x3
I0319 22:27:51.395212  5080 net.cpp:705] Copying source layer inception_5b/relu_3x3
I0319 22:27:51.395225  5080 net.cpp:705] Copying source layer inception_5b/5x5_reduce
I0319 22:27:51.395584  5080 net.cpp:705] Copying source layer inception_5b/relu_5x5_reduce
I0319 22:27:51.395594  5080 net.cpp:705] Copying source layer inception_5b/5x5
I0319 22:27:51.396921  5080 net.cpp:705] Copying source layer inception_5b/relu_5x5
I0319 22:27:51.396931  5080 net.cpp:705] Copying source layer inception_5b/pool
I0319 22:27:51.396939  5080 net.cpp:705] Copying source layer inception_5b/pool_proj
I0319 22:27:51.397862  5080 net.cpp:705] Copying source layer inception_5b/relu_pool_proj
I0319 22:27:51.397871  5080 net.cpp:705] Copying source layer inception_5b/output
I0319 22:27:51.397879  5080 net.cpp:705] Copying source layer pool5/7x7_s1
I0319 22:27:51.397886  5080 net.cpp:705] Copying source layer pool5/drop_7x7_s1
I0319 22:27:51.397893  5080 net.cpp:705] Copying source layer loss3/classifier
I0319 22:27:51.406652  5080 net.cpp:702] Ignoring source layer loss3/loss3

材料集合：

http://deeplearning.net/2014/09/19/googles-entry-to-imagenet-2014-challenge/

[1] Imagenet 2014 LSVRC results, http://karpathy.github.io/2014/09/02/what-i-learned-from-competing-against-a-convnet-on-imagenet/,Last retrieved on: 19-09-2014.

[2] Christian Szegedy, Wei Liu, Yangqing Jia, Pierre Sermanet, Scott Reed, Dragomir Anguelov, Dumitru Erhan, Vincent Vanhoucke, Andrew Rabinovich, Going Deeper with Convolutions, Arxiv Link: http://arxiv.org/abs/1409.4842.

[3] GoogLeNet presentation, http://image-net.org/challenges/LSVRC/2014/slides/GoogLeNet.pptx, Last retrieved on: 19-09.2014..

[4] What I learned from competing against a convnet on imagenet, http://karpathy.github.io/2014/09/02/what-i-learned-from-competing-against-a-convnet-on-imagenet/, Last retrieved on: 19-09-2014.

[5] Girshick, Ross, et al. “Rich feature hierarchies for accurate object detection and semantic segmentation.” arXiv preprint arXiv:1311.2524 (2013).

版权声明：本文为博主原创文章，未经博主允许不得转载。