接著上篇《PyTorch簡明教程上篇》，繼續學習多層感知機，卷積神經網路和LSTMNet。
1、多層感知機
多層感知機是一種簡單的神經網絡，也是深度學習的重要基礎。它透過在網路中添加一個或多個隱藏層來克服線性模型的限制。具體的圖示如下：
import numpy as npimport torchfrom torch.autograd import Variablefrom torch import optimfrom data_util import load_mnistdef 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 = 10model = build_model(n_features, n_classes)loss = torch.nn.CrossEntropyLoss(reductinotallow='mean')optimizer = optim.Adam(model.parameters())batch_size = 100for i in range(100):cost = 0.num_batches = n_examples // batch_sizefor k in range(num_batches):start, end = k * batch_size, (k + 1) * batch_sizecost += 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()登入後複製
（1）以上程式碼和單層神經網路的程式碼類似，差異在於build_model建構一個包含三個線性層和兩個ReLU激活函數的神經網路模型：
- 在模型中加入第一個線性層，該層的輸入特徵數為input_dim，輸出特徵數量為512；
- 接著增加一個ReLU激活函數和一個Dropout層，用於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，該層的輸入特徵數量為512，輸出特徵數量為512;
- 接著加入一個ReLU激活函數和一個Dropout層；
- #在模型中加入第三個線性層，該層的輸入特徵數為512，輸出特徵數為output_dim ，即模型的輸出類別數；
（2）什麼是ReLU激活函數？ ReLU（Rectified Linear Unit，修正線性單元）活化函數是深度學習和神經網路中常用的一種活化函數，ReLU函數的數學表達式為：f(x) = max(0, x)，其中x是輸入值。 ReLU函數的特性是當輸入值小於等於0時，輸出為0；當輸入值大於0時，輸出等於輸入值。簡單來說，ReLU函數就是將負數部分抑制為0，正數部分不變。 ReLU活化函數在神經網路中的作用是引入非線性因素，使得神經網路能夠擬合複雜的非線性關係，同時，ReLU函數相對於其他活化函數（如Sigmoid或Tanh）具有計算速度快、收斂速度快等優點；
（3）什麼是Dropout層？ Dropout層是一種在神經網路中用來防止過度擬合的技術。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，從而提高網路的泛化能力;
（4）print("Epoch %d, cost = %f, acc = %.2f%%" % (i 1, cost / num_batches, 100. * np.mean(predY == teY )))最後列印目前訓練的輪次，損失值和acc，上述的程式碼輸出如下：
...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%
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可以看出最後相同的資料分類，準確率比單層神經網路高（98.59% > 97.68%）。
2、卷積神經網路
卷積神經網路（CNN）是一種深度學習演算法。當輸入矩陣時，CNN可以對其中的重要和不重要部分進行區分（分配權重）。相較於其他分類任務，CNN對資料預處理的要求並不高，只要經過充分的訓練，就能夠學習到矩陣的特性。下圖展示了這個過程：
import numpy as npimport torchfrom torch.autograd import Variablefrom torch import optimfrom data_util import load_mnistclass 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 = 10model = ConvNet(output_dim=n_classes)loss = torch.nn.CrossEntropyLoss(reductinotallow='mean')optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.9)batch_size = 100for i in range(100):cost = 0.num_batches = n_examples // batch_sizefor k in range(num_batches):start, end = k * batch_size, (k + 1) * batch_sizecost += 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()登入後複製
（1）以上程式碼定義了一個名為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組conv和fc，分別表示卷積層和全連接層。在conv子模組中，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子模組中，定義了兩個線性層（torch.nn.Linear）、一個ReLU激活函數和一個Dropout層；
池化層在CNN中扮演著重要的角色，其主要目的有以下幾點：
- 降低维度：池化层通过对输入特征图（Feature maps）进行局部区域的下采样操作，降低了特征图的尺寸。这样可以减少后续层中的参数数量，降低计算复杂度，加速训练过程；
- 平移不变性：池化层可以提高网络对输入图像的平移不变性。当图像中的某个特征发生小幅度平移时，池化层的输出仍然具有相似的特征表示。这有助于提高模型的泛化能力，使其能够在不同位置和尺度下识别相同的特征；
- 防止过拟合：通过减少特征图的尺寸，池化层可以降低模型的参数数量，从而降低过拟合的风险；
- 增强特征表达：池化操作可以聚合局部区域内的特征，从而强化和突出更重要的特征信息。常见的池化操作有最大池化（Max Pooling）和平均池化（Average Pooling），分别表示在局部区域内取最大值或平均值作为输出；
（3）print("Epoch %d, cost = %f, acc = %.2f%%" % (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))最后打印当前训练的轮次，损失值和acc，上述的代码输出如下：
...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%
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可以看出最后相同的数据分类，准确率比多层感知机要高（99.10% > 98.59%）。
3、LSTMNet
LSTMNet是使用长短时记忆网络（Long Short-Term Memory, LSTM）构建的神经网络，核心思想是引入了一个名为"记忆单元"的结构，该结构可以在一定程度上保留长期依赖信息，LSTM中的每个单元包括一个输入门（input gate）、一个遗忘门（forget gate）和一个输出门（output gate），这些门的作用是控制信息在记忆单元中的流动，以便网络可以学习何时存储、更新或输出有用的信息。
import numpy as npimport torchfrom torch import optim, nnfrom data_util import load_mnistclass LSTMNet(torch.nn.Module):def __init__(self, input_dim, hidden_dim, output_dim):super(LSTMNet, self).__init__()self.hidden_dim = hidden_dimself.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 = 10seq_length = 28input_dim = 28hidden_dim = 128batch_size = 100epochs = 100trX = 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_sizefor k in range(num_batches):start, end = k * batch_size, (k + 1) * batch_sizecost += 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()登入後複製
（1）以上这段代码通用的部分就不解释了，具体说LSTMNet类：
- self.lstm = nn.LSTM(input_dim, hidden_dim)创建一个LSTM层，输入维度为input_dim，隐藏层维度为hidden_dim；
- self.linear = nn.Linear(hidden_dim, output_dim, bias=False)创建一个线性层（全连接层），输入维度为hidden_dim，输出维度为output_dim，并设置不使用偏置项（bias）；
- h0 = torch.zeros([1, batch_size, self.hidden_dim])初始化LSTM层的隐藏状态h0，全零张量，形状为[1, batch_size, hidden_dim]；
- c0 = torch.zeros([1, batch_size, self.hidden_dim])初始化LSTM层的细胞状态c0，全零张量，形状为[1, batch_size, hidden_dim]；
- fx, _ = self.lstm.forward(x, (h0, c0))将输入数据x以及初始隐藏状态h0和细胞状态c0传入LSTM层，得到LSTM层的输出fx；
- return self.linear.forward(fx[-1])将LSTM层的输出传入线性层进行计算，得到最终输出。这里fx[-1]表示取LSTM层输出的最后一个时间步的数据；
（2）print("第%d轮，损失值=%f，准确率=%.2f%%" % (i + 1, cost / num_batches, 100. * np.mean(predY == teY)))。打印出当前训练轮次的信息，其中包括损失值和准确率，以上代码的输出结果如下：
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%
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4、辅助代码
两篇文章的from data_util import load_mnist的data_util.py代码如下：
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("创建目录'%s' ..." % dir_path)
os.makedirs(dir_path)
print("从'%s'下载中 ..." % 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:
# 检查所有文件
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登入後複製
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