In [1]:
import numpy as np
def convolution(img, kernel, padding=1, stride=1):
"""
img: input image with one channel
kernel: convolution kernel
"""
h, w = img.shape
kernel_size = kernel.shape[0]
# height and width of image with padding
ph, pw = h + 2 * padding, w + 2 * padding
padding_img = np.zeros((ph, pw))
padding_img[padding:h + padding, padding:w + padding] = img
# height and width of output image
result_h = (h + 2 * padding - kernel_size) // stride + 1
result_w = (w + 2 * padding - kernel_size) // stride + 1
result = np.zeros((result_h, result_w))
# convolution
x, y = 0, 0
for i in range(0, ph - kernel_size + 1, stride):
for j in range(0, pw - kernel_size + 1, stride):
roi = padding_img[i:i+kernel_size, j:j+kernel_size]
result[x, y] = np.sum(roi * kernel)
y += 1
y = 0
x += 1
return result
下面在图像上简单一下测试我们的conv函数,这里使用3*3的高斯核对下面的图像进行滤波.
In [2]:
from PIL import Image
import matplotlib.pyplot as plt
img = Image.open('pics/lena.jpg').convert('L')
plt.imshow(img, cmap='gray')
Out[2]:
In [3]:
# a Laplace kernel
laplace_kernel = np.array([[-1, -1, -1],
[-1, 8, -1],
[-1, -1, -1]])
# Gauss kernel with kernel_size=3
gauss_kernel3 = (1/ 16) * np.array([[1, 2, 1],
[2, 4, 2],
[1, 2, 1]])
# Gauss kernel with kernel_size=5
gauss_kernel5 = (1/ 84) * np.array([[1, 2, 3, 2, 1],
[2, 5, 6, 5, 2],
[3, 6, 8, 6, 3],
[2, 5, 6, 5, 2],
[1, 2, 3, 2, 1]])
fig, ax = plt.subplots(1, 3, figsize=(12, 8))
laplace_img = convolution(np.array(img), laplace_kernel, padding=1, stride=1)
ax[0].imshow(Image.fromarray(laplace_img), cmap='gray')
ax[0].set_title('laplace')
gauss3_img = convolution(np.array(img), gauss_kernel3, padding=1, stride=1)
ax[1].imshow(Image.fromarray(gauss3_img), cmap='gray')
ax[1].set_title('gauss kernel_size=3')
gauss5_img = convolution(np.array(img), gauss_kernel5, padding=2, stride=1)
ax[2].imshow(Image.fromarray(gauss5_img), cmap='gray')
ax[2].set_title('gauss kernel_size=5')
Out[3]:
上面我们实现了实现了对单通道输入单通道输出的卷积.在CNN中,一般使用到的都是多通道输入多通道输出的卷积,要实现多通道的卷积, 我们只需要对循环调用上面的conv函数即可.
In [4]:
def myconv2d(features, weights, padding=0, stride=1):
"""
features: input, in_channel * h * w
weights: kernel, out_channel * in_channel * kernel_size * kernel_size
return output with out_channel
"""
in_channel, h, w = features.shape
out_channel, _, kernel_size, _ = weights.shape
# height and width of output image
output_h = (h + 2 * padding - kernel_size) // stride + 1
output_w = (w + 2 * padding - kernel_size) // stride + 1
output = np.zeros((out_channel, output_h, output_w))
# call convolution out_channel * in_channel times
for i in range(out_channel):
weight = weights[i]
for j in range(in_channel):
feature_map = features[j]
kernel = weight[j]
output[i] += convolution(feature_map, kernel, padding, stride)
return output
接下来, 让我们测试我们写好的myconv2d函数.
In [5]:
input_data=[
[[0,0,2,2,0,1],
[0,2,2,0,0,2],
[1,1,0,2,0,0],
[2,2,1,1,0,0],
[2,0,1,2,0,1],
[2,0,2,1,0,1]],
[[2,0,2,1,1,1],
[0,1,0,0,2,2],
[1,0,0,2,1,0],
[1,1,1,1,1,1],
[1,0,1,1,1,2],
[2,1,2,1,0,2]]
]
weights_data=[[
[[ 0, 1, 0],
[ 1, 1, 1],
[ 0, 1, 0]],
[[-1, -1, -1],
[ -1, 8, -1],
[ -1, -1, -1]]
]]
# numpy array
input_data = np.array(input_data)
weights_data = np.array(weights_data)
# show the result
print(myconv2d(input_data, weights_data, padding=3, stride=3))
在Pytorch中,已经为我们提供了卷积和卷积层的实现.使用同样的input和weights,以及stride,padding,pytorch的卷积的结果应该和我们的一样.可以在下面的代码中进行验证.
In [6]:
import torch
import torch.nn.functional as F
input_tensor = torch.tensor(input_data).unsqueeze(0).float()
F.conv2d(input_tensor, weight=torch.tensor(weights_data).float(), bias=None, stride=3, padding=3)
Out[6]:
In [7]:
def convolutionV2(img, kernel, padding=(0,0), stride=(1,1)):
h, w = img.shape
kh, kw = kernel.shape
# height and width of image with padding
ph, pw = h + 2 * padding[0], w + 2 * padding[1]
padding_img = np.zeros((ph, pw))
padding_img[padding[0]:h + padding[0], padding[1]:w + padding[1]] = img
# height and width of output image
result_h = (h + 2 * padding[0] - kh) // stride[0] + 1
result_w = (w + 2 * padding[1] - kw) // stride[1] + 1
result = np.zeros((result_h, result_w))
# convolution
x, y = 0, 0
for i in range(0, ph - kh + 1, stride[0]):
for j in range(0, pw - kw + 1, stride[1]):
roi = padding_img[i:i+kh, j:j+kw]
result[x, y] = np.sum(roi * kernel)
y += 1
y = 0
x += 1
return result
In [8]:
# test input
test_input = np.array([[1, 1, 2, 1],
[0, 1, 0, 2],
[2, 2, 0, 2],
[2, 2, 2, 1],
[2, 3, 2, 3]])
test_kernel = np.array([[1, 0], [0, 1], [0, 0]])
# output
print(convolutionV2(test_input, test_kernel, padding=(1, 0), stride=(1, 1)))
print(convolutionV2(test_input, test_kernel, padding=(2, 1), stride=(1, 2)))
In [9]:
import torch
import torch.nn as nn
x = torch.randn(1, 1, 32, 32)
conv_layer = nn.Conv2d(in_channels=1, out_channels=3, kernel_size=3, stride=1, padding=0)
y = conv_layer(x)
print(x.shape)
print(y.shape)
请问:
答:
In [10]:
x = torch.randn(1, 1, 32, 32)
conv_layer = nn.Conv2d(in_channels=1, out_channels=3, kernel_size=5, stride=2, padding=2)
y = conv_layer(x)
print(x.shape)
print(y.shape)
In [11]:
# input N * C * H * W
x = torch.randn(1, 1, 4, 4)
# maxpool
maxpool = nn.MaxPool2d(kernel_size=2, stride=2)
y = maxpool(x)
# avgpool
avgpool = nn.AvgPool2d(kernel_size=2, stride=2)
z = avgpool(x)
#avgpool
print(x)
print(y)
print(z)
我们可以选择在cpu或gpu上来训练我们的模型.
实验室提供了4卡的gpu服务器,要查看各个gpu设备的使用情况,可以在服务器上的jupyter主页点击new->terminal,在terminal中输入nvidia-smi即可查看每张卡的使用情况.如下图.
在本次实验中我们将代码中的torch.device('cuda:0')的0更换成所需的设备id即可选择在相应的gpu设备上运行程序.
In [12]:
import torch
import torch.nn as nn
import torch.utils.data as Data
import torchvision
class MyCNN(nn.Module):
def __init__(self, image_size, num_classes):
super(MyCNN, self).__init__()
# conv1: Conv2d -> BN -> ReLU -> MaxPool
self.conv1 = nn.Sequential(
nn.Conv2d(in_channels=3, out_channels=16, kernel_size=3, stride=1, padding=1),
nn.BatchNorm2d(16),
nn.ReLU(),
nn.MaxPool2d(kernel_size=2, stride=2),
)
# conv2: Conv2d -> BN -> ReLU -> MaxPool
self.conv2 = nn.Sequential(
nn.Conv2d(in_channels=16, out_channels=32, kernel_size=3, stride=1, padding=1),
nn.BatchNorm2d(32),
nn.ReLU(),
nn.MaxPool2d(kernel_size=2, stride=2),
)
# fully connected layer
self.fc = nn.Linear(32 * (image_size // 4) * (image_size // 4), num_classes)
def forward(self, x):
"""
input: N * 3 * image_size * image_size
output: N * num_classes
"""
x = self.conv1(x)
x = self.conv2(x)
# view(x.size(0), -1): change tensor size from (N ,H , W) to (N, H*W)
x = x.view(x.size(0), -1)
output = self.fc(x)
return output
这样,一个简单的CNN模型就写好了.与前面的课堂内容相似,我们需要对完成网络进行训练与评估的代码.
In [8]:
def train(model, train_loader, loss_func, optimizer, device):
"""
train model using loss_fn and optimizer in an epoch.
model: CNN networks
train_loader: a Dataloader object with training data
loss_func: loss function
device: train on cpu or gpu device
"""
total_loss = 0
# train the model using minibatch
for i, (images, targets) in enumerate(train_loader):
images = images.to(device)
targets = targets.to(device)
# forward
outputs = model(images)
loss = loss_func(outputs, targets)
# backward and optimize
optimizer.zero_grad()
loss.backward()
optimizer.step()
total_loss += loss.item()
# every 100 iteration, print loss
if (i + 1) % 100 == 0:
print ("Step [{}/{}] Train Loss: {:.4f}"
.format(i+1, len(train_loader), loss.item()))
return total_loss / len(train_loader)
In [10]:
def evaluate(model, val_loader, device):
"""
model: CNN networks
val_loader: a Dataloader object with validation data
device: evaluate on cpu or gpu device
return classification accuracy of the model on val dataset
"""
# evaluate the model
model.eval()
# context-manager that disabled gradient computation
with torch.no_grad():
correct = 0
total = 0
for i, (images, targets) in enumerate(val_loader):
# device: cpu or gpu
images = images.to(device)
targets = targets.to(device)
outputs = model(images)
# return the maximum value of each row of the input tensor in the
# given dimension dim, the second return vale is the index location
# of each maxium value found(argmax)
_, predicted = torch.max(outputs.data, dim=1)
correct += (predicted == targets).sum().item()
total += targets.size(0)
accuracy = correct / total
print('Accuracy on Test Set: {:.4f} %'.format(100 * accuracy))
return accuracy
In [15]:
def save_model(model, save_path):
# save model
torch.save(model.state_dict(), save_path)
In [11]:
import matplotlib.pyplot as plt
def show_curve(ys, title):
"""
plot curlve for Loss and Accuacy
Args:
ys: loss or acc list
title: loss or accuracy
"""
x = np.array(range(len(ys)))
y = np.array(ys)
plt.plot(x, y, c='b')
plt.axis()
plt.title('{} curve'.format(title))
plt.xlabel('epoch')
plt.ylabel('{}'.format(title))
plt.show()
In [2]:
import torch
import torch.nn as nn
import torchvision
import torchvision.transforms as transforms
# mean and std of cifar10 in 3 channels
cifar10_mean = (0.49, 0.48, 0.45)
cifar10_std = (0.25, 0.24, 0.26)
# define transform operations of train dataset
train_transform = transforms.Compose([
# data augmentation
transforms.Pad(4),
transforms.RandomHorizontalFlip(),
transforms.RandomCrop(32),
transforms.ToTensor(),
transforms.Normalize(cifar10_mean, cifar10_std)])
test_transform = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize(cifar10_mean, cifar10_std)])
# torchvision.datasets provide CIFAR-10 dataset for classification
train_dataset = torchvision.datasets.CIFAR10(root='./data/',
train=True,
transform=train_transform,
download=True)
test_dataset = torchvision.datasets.CIFAR10(root='./data/',
train=False,
transform=test_transform)
# Data loader: provides single- or multi-process iterators over the dataset.
train_loader = torch.utils.data.DataLoader(dataset=train_dataset,
batch_size=100,
shuffle=True)
test_loader = torch.utils.data.DataLoader(dataset=test_dataset,
batch_size=100,
shuffle=False)
训练过程中使用交叉熵(cross-entropy)损失函数与Adam优化器来训练我们的分类器网络. 阅读下面的代码并在To-Do处,根据之前所学的知识,补充前向传播和反向传播的代码来实现分类网络的训练.
In [3]:
def fit(model, num_epochs, optimizer, device):
"""
train and evaluate an classifier num_epochs times.
We use optimizer and cross entropy loss to train the model.
Args:
model: CNN network
num_epochs: the number of training epochs
optimizer: optimize the loss function
"""
# loss and optimizer
loss_func = nn.CrossEntropyLoss()
model.to(device)
loss_func.to(device)
# log train loss and test accuracy
losses = []
accs = []
for epoch in range(num_epochs):
print('Epoch {}/{}:'.format(epoch + 1, num_epochs))
# train step
loss = train(model, train_loader, loss_func, optimizer, device)
losses.append(loss)
# evaluate step
accuracy = evaluate(model, test_loader, device)
accs.append(accuracy)
# show curve
show_curve(losses, "train loss")
show_curve(accs, "test accuracy")
In [19]:
# hyper parameters
num_epochs = 10
lr = 0.01
image_size = 32
num_classes = 10
In [20]:
# declare and define an objet of MyCNN
mycnn = MyCNN(image_size, num_classes)
print(mycnn)
In [21]:
# Device configuration, cpu, cuda:0/1/2/3 available
device = torch.device('cuda:0')
optimizer = torch.optim.Adam(mycnn.parameters(), lr=lr)
# start training on cifar10 dataset
fit(mycnn, num_epochs, optimizer, device)
现在,试在To-Do补充代码完成下面的forward函数来完成ResidualBlock的实现,并运行它.
In [4]:
# 3x3 convolution
def conv3x3(in_channels, out_channels, stride=1):
return nn.Conv2d(in_channels, out_channels, kernel_size=3,
stride=stride, padding=1, bias=False)
# Residual block
class ResidualBlock(nn.Module):
def __init__(self, in_channels, out_channels, stride=1, downsample=None):
super(ResidualBlock, self).__init__()
self.conv1 = conv3x3(in_channels, out_channels, stride)
self.bn1 = nn.BatchNorm2d(out_channels)
self.relu = nn.ReLU(inplace=True)
self.conv2 = conv3x3(out_channels, out_channels)
self.bn2 = nn.BatchNorm2d(out_channels)
self.downsample = downsample
def forward(self, x):
"""
Defines the computation performed at every call.
x: N * C * H * W
"""
residual = x
# if the size of input x changes, using downsample to change the size of residual
if self.downsample:
residual = self.downsample(x)
out = self.conv1(x)
out = self.bn1(out)
out = self.relu(out)
out = self.conv2(out)
out = self.bn2(out)
out += residual
out = self.relu(out)
return out
下面是一份针对cifar10数据集的ResNet的实现.
它先通过一个conv3x3,然后经过3个包含多个残差模块的layer(一个layer可能包括多个ResidualBlock, 由传入的layers列表中的数字决定), 然后经过一个全局平均池化层,最后通过一个线性层.
In [5]:
class ResNet(nn.Module):
def __init__(self, block, layers, num_classes=10):
"""
block: ResidualBlock or other block
layers: a list with 3 positive num.
"""
super(ResNet, self).__init__()
self.in_channels = 16
self.conv = conv3x3(3, 16)
self.bn = nn.BatchNorm2d(16)
self.relu = nn.ReLU(inplace=True)
# layer1: image size 32
self.layer1 = self.make_layer(block, 16, num_blocks=layers[0])
# layer2: image size 32 -> 16
self.layer2 = self.make_layer(block, 32, num_blocks=layers[1], stride=2)
# layer1: image size 16 -> 8
self.layer3 = self.make_layer(block, 64, num_blocks=layers[2], stride=2)
# global avg pool: image size 8 -> 1
self.avg_pool = nn.AvgPool2d(8)
self.fc = nn.Linear(64, num_classes)
def make_layer(self, block, out_channels, num_blocks, stride=1):
"""
make a layer with num_blocks blocks.
"""
downsample = None
if (stride != 1) or (self.in_channels != out_channels):
# use Conv2d with stride to downsample
downsample = nn.Sequential(
conv3x3(self.in_channels, out_channels, stride=stride),
nn.BatchNorm2d(out_channels))
# first block with downsample
layers = []
layers.append(block(self.in_channels, out_channels, stride, downsample))
self.in_channels = out_channels
# add num_blocks - 1 blocks
for i in range(1, num_blocks):
layers.append(block(out_channels, out_channels))
# return a layer containing layers
return nn.Sequential(*layers)
def forward(self, x):
out = self.conv(x)
out = self.bn(out)
out = self.relu(out)
out = self.layer1(out)
out = self.layer2(out)
out = self.layer3(out)
out = self.avg_pool(out)
# view: here change output size from 4 dimensions to 2 dimensions
out = out.view(out.size(0), -1)
out = self.fc(out)
return out
In [6]:
resnet = ResNet(ResidualBlock, [2, 2, 2])
print(resnet)
使用fit函数训练实现的ResNet,观察结果变化.
In [25]:
# Hyper-parameters
num_epochs = 10
lr = 0.001
# Device configuration
device = torch.device('cuda:0')
# optimizer
optimizer = torch.optim.Adam(resnet.parameters(), lr=lr)
fit(resnet, num_epochs, optimizer, device)
In [14]:
resnet = ResNet(ResidualBlock, [2, 2, 2])
num_epochs = 10
lr = 0.0009
device = torch.device('cuda:0')
optimizer = torch.optim.Adam(resnet.parameters(), lr=lr)
fit(resnet, num_epochs, optimizer, device)
In [49]:
from torch import nn
class SELayer(nn.Module):
def __init__(self, channel, reduction=16):
super(SELayer, self).__init__()
# The output of AdaptiveAvgPool2d is of size H x W, for any input size.
self.avg_pool = nn.AdaptiveAvgPool2d((1, 1))
self.fc1 = nn.Linear(channel, channel // reduction)
self.fc2 = nn.Linear(channel // reduction, channel)
self.sigmoid = nn.Sigmoid()
def forward(self, x):
b, c, _, _ = x.shape
out = self.avg_pool(x).view(b, c)
out = self.fc1(out)
out = self.fc2(out)
out = self.sigmoid(out).view(b, c, 1, 1)
return out * x
In [50]:
class SEResidualBlock(nn.Module):
def __init__(self, in_channels, out_channels, stride=1, downsample=None, reduction=16):
super(SEResidualBlock, self).__init__()
self.conv1 = conv3x3(in_channels, out_channels, stride)
self.bn1 = nn.BatchNorm2d(out_channels)
self.relu = nn.ReLU(inplace=True)
self.conv2 = conv3x3(out_channels, out_channels)
self.bn2 = nn.BatchNorm2d(out_channels)
self.se = SELayer(out_channels, reduction)
self.downsample = downsample
def forward(self, x):
residual = x
if self.downsample:
residual = self.downsample(x)
out = self.conv1(x)
out = self.bn1(out)
out = self.relu(out)
out = self.conv2(out)
out = self.bn2(out)
out = self.se(out)
out += residual
out = self.relu(out)
return out
In [51]:
se_resnet = ResNet(SEResidualBlock, [2, 2, 2])
print(se_resnet)
In [52]:
# Hyper-parameters
num_epochs = 10
lr = 0.001
# Device configuration
device = torch.device('cuda:0')
# optimizer
optimizer = torch.optim.Adam(se_resnet.parameters(), lr=lr)
fit(se_resnet, num_epochs, optimizer, device)
In [53]:
import math
class VGG(nn.Module):
def __init__(self, cfg):
super(VGG, self).__init__()
self.features = self._make_layers(cfg)
# linear layer
self.classifier = nn.Linear(512, 10)
def forward(self, x):
out = self.features(x)
out = out.view(out.size(0), -1)
out = self.classifier(out)
return out
def _make_layers(self, cfg):
"""
cfg: a list define layers this layer contains
'M': MaxPool, number: Conv2d(out_channels=number) -> BN -> ReLU
"""
layers = []
in_channels = 3
for x in cfg:
if x == 'M':
layers += [nn.MaxPool2d(kernel_size=2, stride=2)]
else:
layers += [nn.Conv2d(in_channels, x, kernel_size=3, padding=1),
nn.BatchNorm2d(x),
nn.ReLU(inplace=True)]
in_channels = x
layers += [nn.AvgPool2d(kernel_size=1, stride=1)]
return nn.Sequential(*layers)
In [54]:
cfg = {
'VGG11': [64, 'M', 128, 'M', 256, 256, 'M', 512, 512, 'M', 512, 512, 'M'],
'VGG13': [64, 64, 'M', 128, 128, 'M', 256, 256, 'M', 512, 512, 'M', 512, 512, 'M'],
'VGG16': [64, 64, 'M', 128, 128, 'M', 256, 256, 256, 'M', 512, 512, 512, 'M', 512, 512, 512, 'M'],
'VGG19': [64, 64, 'M', 128, 128, 'M', 256, 256, 256, 256, 'M', 512, 512, 512, 512, 'M', 512, 512, 512, 512, 'M'],
}
vggnet = VGG(cfg['VGG11'])
print(vggnet)
In [55]:
# Hyper-parameters
num_epochs = 10
lr = 1e-3
# Device configuration
device = torch.device('cuda:0')
# optimizer
optimizer = torch.optim.Adam(vggnet.parameters(), lr=lr)
fit(vggnet, num_epochs, optimizer, device)