两层线性神经网络的多种实现方法(pytorch入门1)

Numpy实现

完全用numpy写，第一层线性层，第二层relu激活层，第三层线性层

# 用numpy实现两层神经网络
import numpy as np
N,D_in,H,D_out = 64,1000,100,10
x = np.random.randn(N,D_in)
y = np.random.randn(N,D_out)

# w1 = np.random.rand(D_in,H)
# w2 = np.random.rand(H,D_out)
# 初始化用rand效果很差
w1 = np.random.randn(D_in,H)
w2 = np.random.randn(H,D_out)
learning_rate = 1e-6

for i in range(500):

    # forward pass
    h = x.dot(w1)
    h_relu = np.maximum(h,0)
    y_pred = h_relu.dot(w2)

    # compute loss
    loss = np.square(y_pred-y).sum()
    print(i,loss)


    # back pass
    y_pred_grad = 2.0 * (y_pred-y)
    w2_grad = h_relu.T.dot(y_pred_grad)
    h_relu_grad = y_pred_grad.dot(w2.T)
    h_grad = h_relu_grad.copy()
    h_grad[h<0] = 0
    w1_grad = x.T.dot(h_grad)

    # update weight
    w1 -= learning_rate * w1_grad
    w2 -= learning_rate * w2_grad

Pytorch实现

1.整体框架完全不变，只是改用torch的语法

# 用torch实现两层神经网络
import torch
N,D_in,H,D_out = 64,1000,100,10
x = torch.randn(N,D_in)
y = torch.randn(N,D_out)

# w1 = np.random.rand(D_in,H)
# w2 = np.random.rand(H,D_out)
w1 = torch.randn(D_in,H)
w2 = torch.randn(H,D_out)
learning_rate = 1e-6

for i in range(500):

    # forward pass
    h = x.mm(w1)  # 用.mm代替.dot
    h_relu = torch.clamp(h,min=0) # clamp函数代替maximum，博客写了
    y_pred = h_relu.mm(w2)

    # compute loss
    loss = (y_pred-y).pow(2).sum()
    # loss是一个值的tensor，需要item()将值取出
    print(i,loss.item())

    # back pass
    y_pred_grad = 2.0 * (y_pred-y)
    w2_grad = h_relu.t().mm(y_pred_grad)  # torch的转置用.t()
    h_relu_grad = y_pred_grad.mm(w2.t())
    h_grad = h_relu_grad.clone()  # torch的复制用.clone()
    h_grad[h<0] = 0
    w1_grad = x.t().mm(h_grad)

    # update weight
    w1 -= learning_rate * w1_grad
    w2 -= learning_rate * w2_grad

2.利用pytorch的autograd机制

具体更改两点:

• 设置requires_grad参数为True
• lose函数的backward()
  关于下面提到的clamp函数:clamp

# 利用pytorch的autograd机制
import torch
N,D_in,H,D_out = 64,1000,100,10
x = torch.randn(N,D_in)
y = torch.randn(N,D_out)

w1 = torch.randn(D_in,H,requires_grad=True)
w2 = torch.randn(H,D_out,requires_grad=True)
learning_rate = 1e-6

for i in range(500):

    # forward pass
    h = x.mm(w1)  # 用.mm代替.dot
    h_relu = torch.clamp(h,min=0) # clamp函数代替maximum，博客写了
    y_pred = h_relu.mm(w2)

    # compute loss
    loss = (y_pred-y).pow(2).sum()
    # loss是一个值的tensor，需要item()将值取出
    print(i,loss.item())

    # back pass
    # 不需要复杂的计算，直接用backward()
    loss.backward()

    # update weight
    with torch.no_grad():  # 节省内存空间
        w1 -= learning_rate * w1.grad
        w2 -= learning_rate * w2.grad
        # 使用完梯度，要将梯度清零，否则每次迭代都会堆积
        # 利用zero_()这一inplace函数，直接将w1、w2的梯度清零
        w1.grad.zero_()
        w2.grad.zero_()

3.利用pytorch.nn搭建model

model里定义了各个层级，在下面的情况下， 初始化后的效果比较好（玄学）

# model
import torch
import torch.nn as nn
N,D_in,H,D_out = 64,1000,100,10
x = torch.randn(N,D_in)
y = torch.randn(N,D_out)

model = nn.Sequential(
    nn.Linear(D_in,H),
    nn.ReLU(),
    nn.Linear(H,D_out)
)
# 初始化model的权重w1、w2,mean和std决定了分布，可以调
nn.init.normal_(model[0].weight,mean = 0.0,std = 1.0)
nn.init.normal_(model[2].weight,mean = 0.0,std = 1.0)

learning_rate = 1e-6

for i in range(500):
    # forward pass
    y_pred = model(x)

    # compute loss
    loss = (y_pred-y).pow(2).sum()
    # loss是一个值的tensor，需要item()将值取出
    print(i,loss.item())

    # back pass
    # 不需要复杂的计算，直接用backward()
    loss.backward()

    # update weight
    with torch.no_grad():  # 节省内存空间
        # 更新每一个参数
        for para in model.parameters():
            para -= learning_rate * para.grad
    # 使用完梯度，要将梯度清零，否则每次迭代都会堆积
    # 利用zero_grad()清零
    model.zero_grad()

4.用torch.optim自动优化，得到梯度最小

在上面model的基础上，将model中的所有参数传入optim中，并设好learningrate

有adm、sgd等优化方式
SGD常用learning_rate应>1e-6,至于下面代码中最终结果也不错，我也不知道为何

# model
import torch
import torch.nn as nn
N,D_in,H,D_out = 64,1000,100,10
x = torch.randn(N,D_in)
y = torch.randn(N,D_out)

model = nn.Sequential(
    nn.Linear(D_in,H),
    nn.ReLU(),
    nn.Linear(H,D_out)
)
# 初始化model的权重w1、w2,mean和std决定了分布，可以调
nn.init.normal_(model[0].weight,mean = 0.0,std = 1.0)
nn.init.normal_(model[2].weight,mean = 0.0,std = 1.0)

optimizer = torch.optim.SGD(
    params= model.parameters(),
    lr = 1e-6
)

loss_fn = nn.MSELoss(reduction='sum')

for i in range(500):
    # forward pass
    y_pred = model(x)

    # compute loss
    loss = loss_fn(y_pred,y)
    # loss是一个值的tensor，需要item()将值取出
    print(i,loss.item())

    # back pass
    # 不需要复杂的计算，直接用backward()
    loss.backward()

    # update weight
    optimizer.step()  # 用step更新参数
    optimizer.zero_grad()  # 用zero_grad清零梯度

5.使用nn.module类自定义模型

3.中的nn.model可以方便的定义两层神经网络模型，但不够灵活。故树用nn.module。
需要两个内部函数:

• init 定义网络
• forward 前向传播

损失函数计算和后向传播不变

# module
import torch
import torch.nn as nn
N,D_in,H,D_out = 64,1000,100,10
x = torch.randn(N,D_in)
y = torch.randn(N,D_out)


class TwoLayerNet(nn.Module):
    # 在init中继承类，并定义两层线性层
    def __init__(self,D_in,H,D_out):
        super(TwoLayerNet,self).__init__()  # 继承nn.Module
        self.linear1 = nn.Linear(D_in,H)
        self.linear2 = nn.Linear(H,D_out)
    # 在forward中定义前向传播
    def forward(self,x):
        return self.linear2(torch.clamp(self.linear1(x),min=0))

model = TwoLayerNet(D_in,H,D_out)

# optimizer = torch.optim.Adam(
#     params= model.parameters(),
#     lr = 1e-3
# )

optimizer = torch.optim.SGD(
    params= model.parameters(),
    lr = 1e-3
)
loss_fn = nn.MSELoss(reduction='sum')

for i in range(500):
    # forward pass
    y_pred = model(x)

    # compute loss
    loss = loss_fn(y_pred,y)
    # loss是一个值的tensor，需要item()将值取出
    print(i,loss.item())

    # back pass
    # 不需要复杂的计算，直接用backward()
    loss.backward()

    # update weight
    optimizer.step()  # 用step更新参数
    optimizer.zero_grad()  # 用zero_grad清零梯度

6.总结

以上是我在b站某pytorch入门教程的第一课中得到的收获，于我而言，课程讲得真的很好，感兴趣的xd也可以去康康。
最终合适的框架应该是*5.*即:

• 用module自定义model
• 将model中的参数传入optimizer利用step来自动更新参数
• 当然前提是lossfunction已经backward反向求梯度了

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