機器學習 | PyTorch簡明教程下篇
作者：周末程序猿
接著上篇《PyTorch簡明教程上篇》，繼續學習多層感知機，卷積神經網絡和LSTMNet。
接著上篇《PyTorch簡明教程上篇》，繼續學習多層感知機，卷積神經網絡和LSTMNet。
1、多層感知機
多層感知機通過在網絡中加入一個或多個隱藏層來克服線性模型的限制，是一個簡單的神經網絡，也是深度學習的重要基礎，具體圖如下：
import numpy as np
import torch
from torch.autograd import Variable
from torch import optim
from data_util import load_mnist
def build_model(input_dim, output_dim):
return torch.nn.Sequential(
torch.nn.Linear(input_dim, 512, bias=False),
torch.nn.ReLU(),
torch.nn.Dropout(0.2),
torch.nn.Linear(512, 512, bias=False),
torch.nn.ReLU(),
torch.nn.Dropout(0.2),
torch.nn.Linear(512, output_dim, bias=False),
)
def train(model, loss, optimizer, x_val, y_val):
model.train()
optimizer.zero_grad()
fx = model.forward(x_val)
output = loss.forward(fx, y_val)
output.backward()
optimizer.step()
return output.item()
def predict(model, x_val):
model.eval()
output = model.forward(x_val)
return output.data.numpy().argmax(axis=1)
def main():
torch.manual_seed(42)
trX, teX, trY, teY = load_mnist(notallow=False)
trX = torch.from_numpy(trX).float()
teX = torch.from_numpy(teX).float()
trY = torch.tensor(trY)
n_examples, n_features = trX.size()
n_classes = 10
model = build_model(n_features, n_classes)
loss = torch.nn.CrossEntropyLoss(reductinotallow='mean')
optimizer = optim.Adam(model.parameters())
batch_size = 100
for i in range(100):
cost = 0.
num_batches = n_examples // batch_size
for k in range(num_batches):
start, end = k * batch_size, (k + 1) * batch_size
cost += train(model, loss, optimizer,
trX[start:end], trY[start:end])
predY = predict(model, teX)
print("Epoch %d, cost = %f, acc = %.2f%%"
% (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))
if __name__ == "__main__":
main()（1）以上代碼和單層神經網絡的代碼類似，區別是build_model構建一個包含三個線性層和兩個ReLU激活函數的神經網絡模型：
- 向模型中添加第一個線性層，該層的輸入特征數量為input_dim，輸出特征數量為512；
- 接著添加一個ReLU激活函數和一個Dropout層，用于增強模型的非線性能力和防止過擬合；
- 向模型中添加第二個線性層，該層的輸入特征數量為512，輸出特征數量為512；
- 接著添加一個ReLU激活函數和一個Dropout層；
- 向模型中添加第三個線性層，該層的輸入特征數量為512，輸出特征數量為output_dim，即模型的輸出類別數量；
（2）什么是ReLU激活函數？ReLU（Rectified Linear Unit，修正線性單元）激活函數是深度學習和神經網絡中常用的一種激活函數，ReLU函數的數學表達式為：f(x) = max(0, x)，其中x是輸入值。ReLU函數的特點是當輸入值小于等于0時，輸出為0；當輸入值大于0時，輸出等于輸入值。簡單來說，ReLU函數就是將負數部分抑制為0，正數部分保持不變。ReLU激活函數在神經網絡中的作用是引入非線性因素，使得神經網絡能夠擬合復雜的非線性關系，同時，ReLU函數相對于其他激活函數（如Sigmoid或Tanh）具有計算速度快、收斂速度快等優點；
（3）什么是Dropout層？Dropout層是一種在神經網絡中用于防止過擬合的技術。在訓練過程中，Dropout層會隨機地將一部分神經元的輸出置為0，即"丟棄"這些神經元，這樣做的目的是為了減少神經元之間的相互依賴，從而提高網絡的泛化能力；
（4）print("Epoch %d, cost = %f, acc = %.2f%%" % (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))最后打印當前訓練的輪次，損失值和acc，上述的代碼輸出如下：
...
Epoch 91, cost = 0.011129, acc = 98.45%
Epoch 92, cost = 0.007644, acc = 98.58%
Epoch 93, cost = 0.011872, acc = 98.61%
Epoch 94, cost = 0.010658, acc = 98.58%
Epoch 95, cost = 0.007274, acc = 98.54%
Epoch 96, cost = 0.008183, acc = 98.43%
Epoch 97, cost = 0.009999, acc = 98.33%
Epoch 98, cost = 0.011613, acc = 98.36%
Epoch 99, cost = 0.007391, acc = 98.51%
Epoch 100, cost = 0.011122, acc = 98.59%可以看出最后相同的數據分類，準確率比單層神經網絡要高（98.59% > 97.68%）。
2、卷積神經網絡
卷積神經網絡（CNN）是一種深度學習算法，如果輸入一個矩陣，CNN能夠區分出重要的部分和不重要的部分（分配權重），相比較其他分類任務，CNN對數據預處理的要求不是很高，只要經過足夠的訓練，就可以學習到矩陣中的特征，如下圖：
import numpy as np
import torch
from torch.autograd import Variable
from torch import optim
from data_util import load_mnist
class ConvNet(torch.nn.Module):
def __init__(self, output_dim):
super(ConvNet, self).__init__()
self.conv = torch.nn.Sequential()
self.conv.add_module("conv_1", torch.nn.Conv2d(1, 10, kernel_size=5))
self.conv.add_module("maxpool_1", torch.nn.MaxPool2d(kernel_size=2))
self.conv.add_module("relu_1", torch.nn.ReLU())
self.conv.add_module("conv_2", torch.nn.Conv2d(10, 20, kernel_size=5))
self.conv.add_module("dropout_2", torch.nn.Dropout())
self.conv.add_module("maxpool_2", torch.nn.MaxPool2d(kernel_size=2))
self.conv.add_module("relu_2", torch.nn.ReLU())
self.fc = torch.nn.Sequential()
self.fc.add_module("fc1", torch.nn.Linear(320, 50))
self.fc.add_module("relu_3", torch.nn.ReLU())
self.fc.add_module("dropout_3", torch.nn.Dropout())
self.fc.add_module("fc2", torch.nn.Linear(50, output_dim))
def forward(self, x):
x = self.conv.forward(x)
x = x.view(-1, 320)
return self.fc.forward(x)
def train(model, loss, optimizer, x_val, y_val):
model.train()
optimizer.zero_grad()
fx = model.forward(x_val)
output = loss.forward(fx, y_val)
output.backward()
optimizer.step()
return output.item()
def predict(model, x_val):
model.eval()
output = model.forward(x_val)
return output.data.numpy().argmax(axis=1)
def main():
torch.manual_seed(42)
trX, teX, trY, teY = load_mnist(notallow=False)
trX = trX.reshape(-1, 1, 28, 28)
teX = teX.reshape(-1, 1, 28, 28)
trX = torch.from_numpy(trX).float()
teX = torch.from_numpy(teX).float()
trY = torch.tensor(trY)
n_examples = len(trX)
n_classes = 10
model = ConvNet(output_dim=n_classes)
loss = torch.nn.CrossEntropyLoss(reductinotallow='mean')
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)
batch_size = 100
for i in range(100):
cost = 0.
num_batches = n_examples // batch_size
for k in range(num_batches):
start, end = k * batch_size, (k + 1) * batch_size
cost += train(model, loss, optimizer,
trX[start:end], trY[start:end])
predY = predict(model, teX)
print("Epoch %d, cost = %f, acc = %.2f%%"
% (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))
if __name__ == "__main__":
main()（1）以上代碼定義了一個名為ConvNet的類，它繼承自torch.nn.Module類，表示一個卷積神經網絡，在__init__方法中定義了兩個子模塊conv和fc，分別表示卷積層和全連接層。在conv子模塊中，我們定義了兩個卷積層（torch.nn.Conv2d）、兩個最大池化層（torch.nn.MaxPool2d）、兩個ReLU激活函數（torch.nn.ReLU）和一個Dropout層（torch.nn.Dropout）。在fc子模塊中，定義了兩個線性層（torch.nn.Linear）、一個ReLU激活函數和一個Dropout層；
（2）定義池化層的目的？池化層（Pooling layer）是CNN中的一個重要組成部分。池化層的主要目的有以下幾點：
- 降低維度：池化層通過對輸入特征圖（Feature maps）進行局部區域的下采樣操作，降低了特征圖的尺寸。這樣可以減少后續層中的參數數量，降低計算復雜度，加速訓練過程；
- 平移不變性：池化層可以提高網絡對輸入圖像的平移不變性。當圖像中的某個特征發生小幅度平移時，池化層的輸出仍然具有相似的特征表示。這有助于提高模型的泛化能力，使其能夠在不同位置和尺度下識別相同的特征；
- 防止過擬合：通過減少特征圖的尺寸，池化層可以降低模型的參數數量，從而降低過擬合的風險；
- 增強特征表達：池化操作可以聚合局部區域內的特征，從而強化和突出更重要的特征信息。常見的池化操作有最大池化（Max Pooling）和平均池化（Average Pooling），分別表示在局部區域內取最大值或平均值作為輸出；
（3）print("Epoch %d, cost = %f, acc = %.2f%%" % (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))最后打印當前訓練的輪次，損失值和acc，上述的代碼輸出如下：
...
Epoch 91, cost = 0.047302, acc = 99.22%
Epoch 92, cost = 0.049026, acc = 99.22%
Epoch 93, cost = 0.048953, acc = 99.13%
Epoch 94, cost = 0.045235, acc = 99.12%
Epoch 95, cost = 0.045136, acc = 99.14%
Epoch 96, cost = 0.048240, acc = 99.02%
Epoch 97, cost = 0.049063, acc = 99.21%
Epoch 98, cost = 0.045373, acc = 99.23%
Epoch 99, cost = 0.046127, acc = 99.12%
Epoch 100, cost = 0.046864, acc = 99.10%可以看出最后相同的數據分類，準確率比多層感知機要高（99.10% > 98.59%）。
3、LSTMNet
LSTMNet是使用長短時記憶網絡（Long Short-Term Memory, LSTM）構建的神經網絡，核心思想是引入了一個名為"記憶單元"的結構，該結構可以在一定程度上保留長期依賴信息，LSTM中的每個單元包括一個輸入門（input gate）、一個遺忘門（forget gate）和一個輸出門（output gate），這些門的作用是控制信息在記憶單元中的流動，以便網絡可以學習何時存儲、更新或輸出有用的信息。
import numpy as np
import torch
from torch import optim, nn
from data_util import load_mnist
class LSTMNet(torch.nn.Module):
def __init__(self, input_dim, hidden_dim, output_dim):
super(LSTMNet, self).__init__()
self.hidden_dim = hidden_dim
self.lstm = nn.LSTM(input_dim, hidden_dim)
self.linear = nn.Linear(hidden_dim, output_dim, bias=False)
def forward(self, x):
batch_size = x.size()[1]
h0 = torch.zeros([1, batch_size, self.hidden_dim])
c0 = torch.zeros([1, batch_size, self.hidden_dim])
fx, _ = self.lstm.forward(x, (h0, c0))
return self.linear.forward(fx[-1])
def train(model, loss, optimizer, x_val, y_val):
model.train()
optimizer.zero_grad()
fx = model.forward(x_val)
output = loss.forward(fx, y_val)
output.backward()
optimizer.step()
return output.item()
def predict(model, x_val):
model.eval()
output = model.forward(x_val)
return output.data.numpy().argmax(axis=1)
def main():
torch.manual_seed(42)
trX, teX, trY, teY = load_mnist(notallow=False)
train_size = len(trY)
n_classes = 10
seq_length = 28
input_dim = 28
hidden_dim = 128
batch_size = 100
epochs = 100
trX = trX.reshape(-1, seq_length, input_dim)
teX = teX.reshape(-1, seq_length, input_dim)
trX = np.swapaxes(trX, 0, 1)
teX = np.swapaxes(teX, 0, 1)
trX = torch.from_numpy(trX).float()
teX = torch.from_numpy(teX).float()
trY = torch.tensor(trY)
model = LSTMNet(input_dim, hidden_dim, n_classes)
loss = torch.nn.CrossEntropyLoss(reductinotallow='mean')
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)
for i in range(epochs):
cost = 0.
num_batches = train_size // batch_size
for k in range(num_batches):
start, end = k * batch_size, (k + 1) * batch_size
cost += train(model, loss, optimizer,
trX[:, start:end, :], trY[start:end])
predY = predict(model, teX)
print("Epoch %d, cost = %f, acc = %.2f%%" %
(i + 1, cost / num_batches, 100. * np.mean(predY == teY)))
if __name__ == "__main__":
main()（1）以上這段代碼通用的部分就不解釋了，具體說LSTMNet類：
- self.lstm = nn.LSTM(input_dim, hidden_dim)創建一個LSTM層，輸入維度為input_dim，隱藏層維度為hidden_dim；
- self.linear = nn.Linear(hidden_dim, output_dim, bias=False)創建一個線性層（全連接層），輸入維度為hidden_dim，輸出維度為output_dim，并設置不使用偏置項（bias）；
- h0 = torch.zeros([1, batch_size, self.hidden_dim])初始化LSTM層的隱藏狀態h0，全零張量，形狀為[1, batch_size, hidden_dim]；
- c0 = torch.zeros([1, batch_size, self.hidden_dim])初始化LSTM層的細胞狀態c0，全零張量，形狀為[1, batch_size, hidden_dim]；
- fx, _ = self.lstm.forward(x, (h0, c0))將輸入數據x以及初始隱藏狀態h0和細胞狀態c0傳入LSTM層，得到LSTM層的輸出fx；
- return self.linear.forward(fx[-1])將LSTM層的輸出傳入線性層進行計算，得到最終輸出。這里fx[-1]表示取LSTM層輸出的最后一個時間步的數據；
（2）print("Epoch %d, cost = %f, acc = %.2f%%" % (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))最后打印當前訓練的輪次，損失值和acc，上述的代碼輸出如下：
Epoch 91, cost = 0.000468, acc = 98.57%
Epoch 92, cost = 0.000452, acc = 98.57%
Epoch 93, cost = 0.000437, acc = 98.58%
Epoch 94, cost = 0.000422, acc = 98.57%
Epoch 95, cost = 0.000409, acc = 98.58%
Epoch 96, cost = 0.000396, acc = 98.58%
Epoch 97, cost = 0.000384, acc = 98.57%
Epoch 98, cost = 0.000372, acc = 98.56%
Epoch 99, cost = 0.000360, acc = 98.55%
Epoch 100, cost = 0.000349, acc = 98.55%4、輔助代碼
兩篇文章的from data_util import load_mnist的data_util.py代碼如下：
import gzip
import os
import urllib.request as request
from os import path
import numpy as np
DATASET_DIR = 'datasets/'
MNIST_FILES = ["train-images-idx3-ubyte.gz", "train-labels-idx1-ubyte.gz",
"t10k-images-idx3-ubyte.gz", "t10k-labels-idx1-ubyte.gz"]
def download_file(url, local_path):
dir_path = path.dirname(local_path)
if not path.exists(dir_path):
print("Creating the directory '%s' ..." % dir_path)
os.makedirs(dir_path)
print("Downloading from '%s' ..." % url)
request.urlretrieve(url, local_path)
def download_mnist(local_path):
url_root = "http://yann.lecun.com/exdb/mnist/"
for f_name in MNIST_FILES:
f_path = os.path.join(local_path, f_name)
if not path.exists(f_path):
download_file(url_root + f_name, f_path)
def one_hot(x, n):
if type(x) == list:
x = np.array(x)
x = x.flatten()
o_h = np.zeros((len(x), n))
o_h[np.arange(len(x)), x] = 1
return o_h
def load_mnist(ntrain=60000, ntest=10000, notallow=True):
data_dir = os.path.join(DATASET_DIR, 'mnist/')
if not path.exists(data_dir):
download_mnist(data_dir)
else:
# check all files
checks = [path.exists(os.path.join(data_dir, f)) for f in MNIST_FILES]
if not np.all(checks):
download_mnist(data_dir)
with gzip.open(os.path.join(data_dir, 'train-images-idx3-ubyte.gz')) as fd:
buf = fd.read()
loaded = np.frombuffer(buf, dtype=np.uint8)
trX = loaded[16:].reshape((60000, 28 * 28)).astype(float)
with gzip.open(os.path.join(data_dir, 'train-labels-idx1-ubyte.gz')) as fd:
buf = fd.read()
loaded = np.frombuffer(buf, dtype=np.uint8)
trY = loaded[8:].reshape((60000))
with gzip.open(os.path.join(data_dir, 't10k-images-idx3-ubyte.gz')) as fd:
buf = fd.read()
loaded = np.frombuffer(buf, dtype=np.uint8)
teX = loaded[16:].reshape((10000, 28 * 28)).astype(float)
with gzip.open(os.path.join(data_dir, 't10k-labels-idx1-ubyte.gz')) as fd:
buf = fd.read()
loaded = np.frombuffer(buf, dtype=np.uint8)
teY = loaded[8:].reshape((10000))
trX /= 255.
teX /= 255.
trX = trX[:ntrain]
trY = trY[:ntrain]
teX = teX[:ntest]
teY = teY[:ntest]
if onehot:
trY = one_hot(trY, 10)
teY = one_hot(teY, 10)
else:
trY = np.asarray(trY)
teY = np.asarray(teY)
return trX, teX, trY, teY責任編輯：華軒
來源：
周末程序猿
