GoogLeNet_BN

参考:

[Going deeper with convolutions]进一步深入卷积操作

批量归一化:通过减轻内部协变量偏移来加速深度网络训练

论文Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift将批量归一化方法作用于卷积神经网络,通过校正每层输入数据的数据分布,从而达到更快的训练目的。在文章最后,添加批量归一化层到GoogLeNet网络,得到了更好的检测效果

参数解析

论文中以表格方式给出了GoogLeNet_BN的参数设置

其相对于GoogLeNet的修改如下:

  1. Inception模块中,$5\times 5$卷积层通过两个$3\times 3$卷积层进行替代。该实现使得网络增加了9个权重层,从而使得参数数量提高了25%,计算耗时增加了30%
  2. 增加了Inception (3c)
  3. Inception模块中,使用平均池化(average pooling)或者最大池化(max pooling
  4. 在各个Inception模块之间不再使用池化层进行操作,而是在Inception 3c/4e模块中使用步长进行减半操作

同时GoogLeNet_BN在第一个卷积层使用了深度乘数为8的可分离卷积,以此来加速计算

Our model employed separable convolution with depth multiplier 8 on the first convolutional layer. This reduces the computational cost while increasing the memory consumption at training time

Note:经过计算后发现,Inception (4c/d/e)的输出深度有错误,应该分别为$608/608/1056$

推导

Inception 3(a/b/c)模块为例,尝试推导修改后的模块实现

假定输入大小为$128\times 192\times 28\times 28$

Inception (3a)

1x1

  • 输入数据体:$128\times 192\times 28\times 28$
  • 卷积核大小为$1\times 1$,步长为$1$,零填充为$0$
  • 滤波器个数:$64$
  • 输出数据体:$128\times 64\times 28\times 28$

3x3

先执行$1\times 1$大小卷积操作

  • 输入数据体:$128\times 192\times 28\times 28$
  • 卷积核大小为$1\times 1$,步长为$1$,零填充为$0$
  • 滤波器个数:$64$
  • 输出数据体:$128\times 64\times 28\times 28$

再执行$3\times 3$大小卷积操作

  • 输入数据体:$128\times 64\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$1$,零填充为$1$
  • 滤波器个数:$64$
  • 输出数据体:$128\times 64\times 28\times 28$

double 3x3

先执行$1\times 1$大小卷积操作

  • 输入数据体:$128\times 192\times 28\times 28$
  • 卷积核大小为$1\times 1$,步长为$1$,零填充为$0$
  • 滤波器个数:$64$
  • 输出数据体:$128\times 64\times 28\times 28$

第一次执行$3\times 3$大小卷积操作

  • 输入数据体:$128\times 64\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$1$,零填充为$1$
  • 滤波器个数:$96$
  • 输出数据体:$128\times 96\times 28\times 28$

第二次执行$3\times 3$大小卷积操作

  • 输入数据体:$128\times 96\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$1$,零填充为$1$
  • 滤波器个数:$96$
  • 输出数据体:$128\times 96\times 28\times 28$

avg pooling

先执行$Average Pooling$操作

  • 输入数据体:$128\times 192\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$1$,零填充为$1$
  • 输出数据体:$128\times 192\times 28\times 28$

再执行$1\times 1$大小卷积操作

  • 输入数据体:$128\times 192\times 28\times 28$
  • 卷积核大小为$1\times 1$,步长为$1$,零填充为$0$
  • 滤波器个数:$32$
  • 输出数据体:$128\times 32\times 28\times 28$

连接

上述4个子模块计算得到了相同的空间尺寸的输出书具体,然后按深度通道进行连接,最后得到$128\times 256\times 28\times 28$大小的输出数据体

Inception (3b)

1x1

  • 输入数据体:$128\times 256\times 28\times 28$
  • 卷积核大小为$1\times 1$,步长为$1$,零填充为$0$
  • 滤波器个数:$64$
  • 输出数据体:$128\times 64\times 28\times 28$

3x3

先执行$1\times 1$大小卷积操作

  • 输入数据体:$128\times 256\times 28\times 28$
  • 卷积核大小为$1\times 1$,步长为$1$,零填充为$0$
  • 滤波器个数:$64$
  • 输出数据体:$128\times 64\times 28\times 28$

再执行$3\times 3$大小卷积操作

  • 输入数据体:$128\times 64\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$1$,零填充为$1$
  • 滤波器个数:$96$
  • 输出数据体:$128\times 96\times 28\times 28$

double 3x3

先执行$1\times 1$大小卷积操作

  • 输入数据体:$128\times 256\times 28\times 28$
  • 卷积核大小为$1\times 1$,步长为$1$,零填充为$0$
  • 滤波器个数:$64$
  • 输出数据体:$128\times 64\times 28\times 28$

第一次执行$3\times 3$大小卷积操作

  • 输入数据体:$128\times 64\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$1$,零填充为$1$
  • 滤波器个数:$96$
  • 输出数据体:$128\times 96\times 28\times 28$

第二次执行$3\times 3$大小卷积操作

  • 输入数据体:$128\times 96\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$1$,零填充为$1$
  • 滤波器个数:$96$
  • 输出数据体:$128\times 96\times 28\times 28$

avg pooling

先执行$Average Pooling$操作

  • 输入数据体:$128\times 256\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$1$,零填充为$1$
  • 输出数据体:$128\times 256\times 28\times 28$

再执行$1\times 1$大小卷积操作

  • 输入数据体:$128\times 256\times 28\times 28$
  • 卷积核大小为$1\times 1$,步长为$1$,零填充为$0$
  • 滤波器个数:$64$
  • 输出数据体:$128\times 64\times 28\times 28$

连接

上述4个子模块计算得到了相同的空间尺寸的输出书具体,然后按深度通道进行连接,最后得到$128\times 320\times 28\times 28$大小的输出数据体

Inception (3c)

其步长为$2$,执行空间尺寸减半操作,所以在此模块中不单独执行$1\times 1$大小卷积层操作

3x3

先执行$1\times 1$大小卷积操作

  • 输入数据体:$128\times 320\times 28\times 28$
  • 卷积核大小为$1\times 1$,步长为$1$,零填充为$0$
  • 滤波器个数:$128$
  • 输出数据体:$128\times 128\times 28\times 28$

再执行$3\times 3$大小卷积操作

  • 输入数据体:$128\times 128\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$2$,零填充为$1$
  • 滤波器个数:$160$
  • 输出数据体:$128\times 160\times 14\times 14$

double 3x3

先执行$1\times 1$大小卷积操作

  • 输入数据体:$128\times 320\times 28\times 28$
  • 卷积核大小为$1\times 1$,步长为$1$,零填充为$0$
  • 滤波器个数:$64$
  • 输出数据体:$128\times 64\times 28\times 28$

第一次执行$3\times 3$大小卷积操作

  • 输入数据体:$128\times 64\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$1$,零填充为$1$
  • 滤波器个数:$96$
  • 输出数据体:$128\times 96\times 28\times 28$

第二次执行$3\times 3$大小卷积操作

  • 输入数据体:$128\times 96\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$2$,零填充为$1$
  • 滤波器个数:$96$
  • 输出数据体:$128\times 96\times 14\times 14$

max pooling

先执行$Max Pooling$操作

  • 输入数据体:$128\times 320\times 28\times 28$
  • 卷积核大小为$3\times 3$,步长为$2$,零填充为$1$
  • 输出数据体:$128\times 320\times 14\times 14$

连接

上述4个子模块计算得到了相同的空间尺寸的输出数据,然后按深度通道进行连接,最后得到$128\times 576\times 28\times 28$大小的输出数据体(???,没有理解stride=2的目的,抑或者是参数表的错误。当前具体实现中不使用stride=2进行减半,还是通过Max Pooling

PyTorch

BasicConv2d

在卷积操作后执行批量归一化

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class BasicConv2d(nn.Module):

def __init__(self, in_channels, out_channels, **kwargs):
super(BasicConv2d, self).__init__()
self.conv = nn.Conv2d(in_channels, out_channels, bias=False, **kwargs)
self.bn = nn.BatchNorm2d(out_channels, eps=0.001)

def forward(self, x):
x = self.conv(x)
# x = self.bn(x)
return F.relu(x, inplace=True)

Inception

  1. $1\times 1$大小卷积层可能不存在
  2. 修改$5\times 5$卷积操作为两个$3\times 3$卷积操作
  3. 根据输入选择最大池化或者平均池化操作
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class Inception(nn.Module):
__constants__ = ['branch2', 'branch3', 'branch4']

def __init__(self, in_channels, ch1x1, ch3x3red, ch3x3, dch3x3red, dch3x3, pool_proj,
conv_block=None, stride_num=1, pool_type='max'):
super(Inception, self).__init__()
if conv_block is None:
conv_block = BasicConv2d
if ch1x1 == 0:
self.branch1 = None
else:
self.branch1 = conv_block(in_channels, ch1x1, kernel_size=1, stride=1, padding=0)

self.branch2 = nn.Sequential(
conv_block(in_channels, ch3x3red, kernel_size=1, stride=1, padding=0),
conv_block(ch3x3red, ch3x3, kernel_size=3, stride=stride_num, padding=1)
)

self.branch3 = nn.Sequential(
conv_block(in_channels, dch3x3red, kernel_size=1, stride=1, padding=0),
conv_block(dch3x3red, dch3x3, kernel_size=5, stride=stride_num, padding=1),
conv_block(dch3x3, dch3x3, kernel_size=5, stride=stride_num, padding=1),
)

if pool_proj != 0:
if pool_type == 'max':
self.branch4 = nn.Sequential(
nn.MaxPool2d(kernel_size=3, stride=stride_num, padding=1, ceil_mode=True),
conv_block(in_channels, pool_proj, kernel_size=1, stride=1, padding=0)
)
else:
# avg pooling
self.branch4 = nn.Sequential(
nn.AvgPool2d(kernel_size=3, stride=1, padding=1, ceil_mode=True),
conv_block(in_channels, pool_proj, kernel_size=1, stride=1, padding=0)
)
else:
# only max pooling
self.branch4 = nn.MaxPool2d(kernel_size=3, stride=stride_num, padding=1, ceil_mode=True)

def _forward(self, x):
branch2 = self.branch2(x)
branch3 = self.branch3(x)
branch4 = self.branch4(x)

if self.branch1 is not None:
branch1 = self.branch1(x)
outputs = [branch1, branch2, branch3, branch4]
else:
outputs = [branch2, branch3, branch4]
return outputs

def forward(self, x):
outputs = self._forward(x)
return torch.cat(outputs, 1)

GoogLeNet_BN

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class GoogLeNet_BN(nn.Module):
__constants__ = ['aux_logits', 'transform_input']

def __init__(self, num_classes=1000, aux_logits=True, transform_input=False, init_weights=True,
blocks=None):
"""
GoogLeNet实现
:param num_classes: 输出类别数
:param aux_logits: 是否使用辅助分类器
:param transform_input:
:param init_weights:
:param blocks:
"""
super(GoogLeNet_BN, self).__init__()
if blocks is None:
blocks = [BasicConv2d, Inception, InceptionAux]
assert len(blocks) == 3
conv_block = blocks[0]
inception_block = blocks[1]
inception_aux_block = blocks[2]

self.aux_logits = aux_logits
self.transform_input = transform_input

self.conv1 = conv_block(3, 64, kernel_size=7, stride=2, padding=3)
self.maxpool1 = nn.MaxPool2d(3, stride=2, padding=0, ceil_mode=True)
self.conv2 = conv_block(64, 64, kernel_size=1, stride=1, padding=0)
self.conv3 = conv_block(64, 192, kernel_size=3, stride=1, padding=1)
self.maxpool2 = nn.MaxPool2d(3, stride=2, padding=0, ceil_mode=True)

self.inception3a = inception_block(192, 64, 64, 64, 64, 96, 32, pool_type='avg')
self.inception3b = inception_block(256, 64, 64, 96, 64, 96, 64, pool_type='avg')
self.inception3c = inception_block(320, 0, 128, 160, 64, 96, 0, pool_type='max')
self.maxpool3 = nn.MaxPool2d(3, stride=2, ceil_mode=True)

self.inception4a = inception_block(576, 224, 64, 96, 96, 128, 128, pool_type='avg')
self.inception4b = inception_block(576, 192, 96, 128, 96, 128, 128, pool_type='avg')
self.inception4c = inception_block(576, 160, 128, 160, 128, 160, 128, pool_type='avg')
self.inception4d = inception_block(608, 96, 128, 192, 160, 192, 128, pool_type='avg')
self.inception4e = inception_block(608, 0, 128, 192, 192, 256, 0, pool_type='max')
self.maxpool4 = nn.MaxPool2d(2, stride=2, ceil_mode=True)

self.inception5a = inception_block(1056, 352, 192, 320, 160, 224, 128, pool_type='avg')
self.inception5b = inception_block(1024, 352, 192, 320, 192, 224, 128, pool_type='max')

if aux_logits:
# 辅助分类器
# inception (4a) 输出 14x14x576
self.aux1 = inception_aux_block(576, num_classes)
# inception (4d) 输出 14x14x608
self.aux2 = inception_aux_block(608, num_classes)

self.avgpool = nn.AdaptiveAvgPool2d((1, 1))
self.dropout = nn.Dropout(0.2)
self.fc = nn.Linear(1024, num_classes)

if init_weights:
self._initialize_weights()

def _initialize_weights(self):
for m in self.modules():
if isinstance(m, nn.Conv2d) or isinstance(m, nn.Linear):
import scipy.stats as stats
X = stats.truncnorm(-2, 2, scale=0.01)
values = torch.as_tensor(X.rvs(m.weight.numel()), dtype=m.weight.dtype)
values = values.view(m.weight.size())
with torch.no_grad():
m.weight.copy_(values)
elif isinstance(m, nn.BatchNorm2d):
nn.init.constant_(m.weight, 1)
nn.init.constant_(m.bias, 0)

def _transform_input(self, x):
# type: (Tensor) -> Tensor
if self.transform_input:
x_ch0 = torch.unsqueeze(x[:, 0], 1) * (0.229 / 0.5) + (0.485 - 0.5) / 0.5
x_ch1 = torch.unsqueeze(x[:, 1], 1) * (0.224 / 0.5) + (0.456 - 0.5) / 0.5
x_ch2 = torch.unsqueeze(x[:, 2], 1) * (0.225 / 0.5) + (0.406 - 0.5) / 0.5
x = torch.cat((x_ch0, x_ch1, x_ch2), 1)
return x

def _forward(self, x):
# type: (Tensor) -> Tuple[Tensor, Optional[Tensor], Optional[Tensor]]
# N x 3 x 224 x 224
x = self.conv1(x)
# N x 64 x 112 x 112
x = self.maxpool1(x)
# N x 64 x 56 x 56
x = self.conv2(x)
# N x 64 x 56 x 56
x = self.conv3(x)
# N x 192 x 56 x 56
x = self.maxpool2(x)

# N x 192 x 28 x 28
x = self.inception3a(x)
# N x 256 x 28 x 28
x = self.inception3b(x)
# N x 320 x 28 x 28
x = self.inception3c(x)
# N x 576 x 28 x 28
x = self.maxpool3(x)
# N x 576 x 14 x 14
x = self.inception4a(x)
# N x 576 x 14 x 14
aux_defined = self.training and self.aux_logits
if aux_defined:
aux1 = self.aux1(x)
else:
aux1 = None

x = self.inception4b(x)
# N x 576 x 14 x 14
x = self.inception4c(x)
# N x 608 x 14 x 14
x = self.inception4d(x)
# N x 608 x 14 x 14
if aux_defined:
aux2 = self.aux2(x)
else:
aux2 = None

x = self.inception4e(x)
# N x 1056 x 14 x 14
x = self.maxpool4(x)
# N x 1024 x 7 x 7
x = self.inception5a(x)
# N x 1024 x 7 x 7
x = self.inception5b(x)
# N x 1024 x 7 x 7

x = self.avgpool(x)
# N x 1024 x 1 x 1
x = torch.flatten(x, 1)
# N x 1024
x = self.dropout(x)
x = self.fc(x)
# N x 1000 (num_classes)
return x, aux2, aux1

def forward(self, x):
x = self._transform_input(x)
x, aux1, aux2 = self._forward(x)
aux_defined = self.training and self.aux_logits
if aux_defined:
# 训练阶段返回3个分类器结果
return x, aux2, aux1
else:
# 测试阶段仅使用最后一个分类器
return x

测试

比较GoogLeNet_BNGoogLeNet.具体测试代码参考test_googlenet_bn.py

参数个数

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[googlenet_bn] param num: 17683640
[googlenet] param num: 13370744
num_googlenet_bn / num_googlenet: 1.32

GoogLeNet1768万个参数,GoogLeNet1337万个,两者相差1.32

测试时间

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[googlenet_bn] time: 0.0596
[googlenet] time: 0.0602
time_googlenet / time_googlenet_bn: 1.010

计算100次测试图像平均使用时间:

  1. GoogLeNet_BN:0.0596
  2. GoogLeNet:0.0602

两者的计算时间相近

训练

比对GoogLeNet_BNGoogLeNet训练,训练参数如下:

  1. 数据集:PASCAL VOC 07+1220类共40058个训练样本和12032个测试样本
  2. 批量大小:128
  3. 优化器:Adam,学习率为1e-3
  4. 随步长衰减:每隔8轮衰减4%,学习因子为0.96
  5. 迭代次数:100

训练100次结果如下:

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{'train': 40058, 'test': 12032}
Epoch 0/99
----------
train Loss: 4.2452 Acc: 0.2644
test Loss: 2.4459 Acc: 0.3763
Epoch 1/99
----------
...
...
----------
train Loss: 0.9129 Acc: 0.8467
test Loss: 0.9284 Acc: 0.7454
Epoch 98/99
----------
train Loss: 0.8963 Acc: 0.8524
test Loss: 0.9539 Acc: 0.7406
Epoch 99/99
----------
train Loss: 0.8869 Acc: 0.8526
test Loss: 0.9968 Acc: 0.7409
Training complete in 194m 38s
Best test Acc: 0.747839
train googlenet_bn done

Epoch 0/99
----------
train Loss: 4.2141 Acc: 0.2787
test Loss: 2.4076 Acc: 0.3763
Epoch 1/99
----------
train Loss: 3.9860 Acc: 0.3354
test Loss: 2.2959 Acc: 0.3969
Epoch 2/99
----------
...
...
----------
train Loss: 0.9720 Acc: 0.8304
test Loss: 0.9777 Acc: 0.7278
Epoch 98/99
----------
train Loss: 0.9744 Acc: 0.8279
test Loss: 0.9249 Acc: 0.7358
Epoch 99/99
----------
train Loss: 0.9632 Acc: 0.8336
test Loss: 0.9337 Acc: 0.7350
Training complete in 152m 5s
Best test Acc: 0.742852
train googlenet done

100轮迭代后,GoogLeNet_BN实现了74.78%的最好测试精度;GoogLeNet实现了74.23%的最好测试精度

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