x = torch.arange(-8.0, 8.0, 0.1, requires_grad=True) y = torch.relu(x) d2l.plot(x.detach(), y.detach(), 'x', 'relu(x)', figsize=(5, 2.5))

As an AI language model, I cannot display plots. But this code generates a plot of the ReLU function for values between -8 and 8 with a step size of 0.1. The plot displays the input values on the x-axis and the output values on the y-axis. The plot shows that the output values are 0 for input values less than 0 and increase linearly for input values greater than or equal to 0.

相关问题

import torch import torch.nn as nn import numpy as np import torch.nn.functional as F import matplotlib.pyplot as plt from torch.autograd import Variable x=torch.tensor(np.array([[i] for i in range(10)]),dtype=torch.float32) y=torch.tensor(np.array([[i**2] for i in range(10)]),dtype=torch.float32) #print(x,y) x,y=(Variable(x),Variable(y))#将tensor包装一个可求导的变量 net=torch.nn.Sequential( nn.Linear(1,10,dtype=torch.float32),#隐藏层线性输出 torch.nn.ReLU(),#激活函数 nn.Linear(10,20,dtype=torch.float32),#隐藏层线性输出 torch.nn.ReLU(),#激活函数 nn.Linear(20,1,dtype=torch.float32),#输出层线性输出 ) optimizer=torch.optim.SGD(net.parameters(),lr=0.05)#优化器(梯度下降) loss_func=torch.nn.MSELoss()#最小均方差 #神经网络训练过程 plt.ion() plt.show()#动态学习过程展示 for t in range(2000): prediction=torch.tensor(net(x)),#把数据输入神经网络，输出预测值 loss=loss_func(prediction, y)#计算二者误差，注意这两个数的顺序 optimizer.zero_grad()#清空上一步的更新参数值 loss.backward()#误差反向传播，计算新的更新参数值 optimizer.step()#将计算得到的更新值赋给net.parameters()D:\Anaconda\python.exe D:\py\text.py D:\py\text.py:26: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor). prediction=torch.tensor(net(x)),#把数据输入神经网络，输出预测值 Traceback (most recent call last): File "D:\py\text.py", line 27, in <module> loss=loss_func(prediction, y)#计算二者误差，注意这两个数的顺序 File "D:\Anaconda\lib\site-packages\torch\nn\modules\module.py", line 1194, in _call_impl return forward_call(*input, **kwargs) File "D:\Anaconda\lib\site-packages\torch\nn\modules\loss.py", line 536, in forward return F.mse_loss(input, target, reduction=self.reduction) File "D:\Anaconda\lib\site-packages\torch\nn\functional.py", line 3281, in mse_loss if not (target.size() == input.size()): AttributeError: 'tuple' object has no attribute 'size'

在这段代码中，您将 `prediction` 和 `y` 包装在了一个元组中传递给了 `loss_func` 函数。这是不正确的，因为 `loss_func` 函数期望的是两个张量，而不是一个元组。因此，您需要将 `prediction` 和 `y` 分别传递给 `loss_func` 函数。修改代码如下：

for t in range(2000):
    prediction = net(x)
    loss = loss_func(prediction, y)
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    if t % 50 == 0:
        plt.cla()
        plt.scatter(x.data.numpy(), y.data.numpy())
        plt.plot(x.data.numpy(), prediction.data.numpy(), 'r-', lw=5)
        plt.text(0.5, 0, 'Loss=%.4f' % loss.data.numpy(), fontdict={'size': 20, 'color': 'red'})
        plt.pause(0.1)

在这个修改后的代码中，我们将 `prediction` 和 `y` 直接传递给了 `loss_func` 函数，而不是将它们包装在一个元组中。同时，我们还添加了一些代码，用于动态展示神经网络训练的过程。

五层全连接神经网络拟合函数y=x^2+2x-3的python代码

### 回答1：

import numpy as np
x = np.arange(-3,3,0.1)
y = x**2*2*x - 3
import torch
from torch.autograd import Variable
w1 = Variable(torch.Tensor([1]), requires_grad=True)
w2 = Variable(torch.Tensor([1]), requires_grad=True)
w3 = Variable(torch.Tensor([1]), requires_grad=True)
w4 = Variable(torch.Tensor([1]), requires_grad=True)
w5 = Variable(torch.Tensor([1]), requires_grad=True) def forward(x):
y_pred = w1*x**4 + w2*x**3 + w3*x**2 + w4*x + w5
return y_pred # Loss function
def loss(y, y_pred):
return torch.mean((y_pred - y)**2) # Optimizer
optimizer = torch.optim.SGD([w1, w2, w3, w4, w5], lr=0.01)
# Training
for epoch in range(100):
# Forward pass
y_pred = forward(x)
# Compute loss
l = loss(y, y_pred)
# Backward pass
l.backward()
# Update the parameters
optimizer.step()
# Zero the gradients
optimizer.zero_grad() # Final prediction
y_pred = forward(x) print("五层全连接神经网络拟合函数y=x^2 2x-3的Python代码如下：")
print("import numpy as np")
print("x = np.arange(-3,3,0.1)")
print("y = x**2*2*x - 3")
print("import torch")
print("from torch.autograd import Variable")
print("w1 = Variable(torch.Tensor([1]), requires_grad=True)")
print("w2 = Variable(torch.Tensor([1]), requires_grad=True)")
print("w3 = Variable(torch.Tensor([1]), requires_grad=True)")
print("w4 = Variable(torch.Tensor([1]), requires_grad=True)")
print("w5 = Variable(torch.Tensor([1]), requires_grad=True)")
print("def forward(x):")
print(" y_pred = w1*x**4 + w2*x**3 + w3*x**2 + w4*x + w5")
print(" return y_pred")
print("# Loss function")
print("def loss(y, y_pred):")
print(" return torch.mean((y_pred - y)**2)")
print("# Optimizer")
print("optimizer = torch.optim.SGD([w1, w2, w3, w4, w5], lr=0.01)")
print("# Training")
print("for epoch in range(100):")
print(" # Forward pass")
print(" y_pred = forward(x)")
print(" # Compute loss")
print(" l = loss(y, y_pred)")
print(" # Backward pass")
print(" l.backward()")
print(" # Update the parameters")
print(" optimizer.step()")
print(" # Zero the gradients")
print(" optimizer.zero_grad()")
print("# Final prediction")
print("y_pred = forward(x)")

### 回答2：
import numpy as np
import matplotlib.pyplot as plt

# 定义激活函数
def activation(x):
return 1 / (1 + np.exp(-x))

# 定义导数函数
def derivative_activation(x):
return activation(x) * (1 - activation(x))

# 定义神经网络类
class NeuralNetwork:
def __init__(self, layers):
self.layers = layers
self.weights = [np.random.random((layers[i], layers[i+1])) for i in range(len(layers)-1)]
self.biases = [np.random.random(layers[i+1]) for i in range(len(layers)-1)]

def forward_propagation(self, x):
self.a = [x]
self.z = []
for i in range(len(self.layers)-1):
self.z.append(np.dot(self.a[-1], self.weights[i]) + self.biases[i])
self.a.append(activation(self.z[-1]))
return self.a[-1]

def back_propagation(self, x, y, learning_rate):
delta = 2 * (self.a[-1] - y) * derivative_activation(self.z[-1])
nabla_w = [np.zeros((self.layers[i], self.layers[i+1])) for i in range(len(self.layers)-1)]
nabla_b = [np.zeros(self.layers[i+1]) for i in range(len(self.layers)-1)]

nabla_w[-1] = np.dot(self.a[-2].T, delta)
nabla_b[-1] = delta

for i in range(len(self.layers)-3, -1, -1):
delta = np.dot(delta, self.weights[i+1].T) * derivative_activation(self.z[i])
nabla_w[i] = np.dot(self.a[i].T, delta)
nabla_b[i] = delta

for i in range(len(self.layers)-2, -1, -1):
self.weights[i] -= learning_rate * nabla_w[i]
self.biases[i] -= learning_rate * nabla_b[i]

def train(self, x_train, y_train, epochs, learning_rate):
for epoch in range(epochs):
for x, y in zip(x_train, y_train):
output = self.forward_propagation(x)
self.back_propagation(x, y, learning_rate)

def predict(self, x):
return self.forward_propagation(x)

# 准备训练数据
x_train = np.linspace(-10, 10, 100)
y_train = np.square(x_train) + 2 * x_train - 3

# 创建神经网络并训练
nn = NeuralNetwork([1, 5, 5, 5, 5, 1])
nn.train(x_train, y_train, epochs=10000, learning_rate=0.001)

# 准备测试数据
x_test = np.linspace(-10, 10, 100)
y_test = np.square(x_test) + 2 * x_test - 3

# 使用神经网络进行预测
y_pred = np.zeros_like(x_test)
for i, x in enumerate(x_test):
y_pred[i] = nn.predict(x)

# 绘制拟合曲线
plt.plot(x_train, y_train, 'bo', label='Training data')
plt.plot(x_test, y_test, 'g-', label='True data')
plt.plot(x_test, y_pred, 'r-', label='Predicted data')
plt.legend()
plt.show()

### 回答3：
import torch
import torch.nn as nn
import numpy as np
import matplotlib.pyplot as plt

# 定义数据
x = np.linspace(-10, 10, 100)
y = x**2 + 2*x - 3

# 将数据转化为张量
x_tensor = torch.from_numpy(x).float()
y_tensor = torch.from_numpy(y).float()

# 定义神经网络模型
class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.fc1 = nn.Linear(1, 10)
self.fc2 = nn.Linear(10, 20)
self.fc3 = nn.Linear(20, 10)
self.fc4 = nn.Linear(10, 1)

def forward(self, x):
x = torch.relu(self.fc1(x))
x = torch.relu(self.fc2(x))
x = torch.relu(self.fc3(x))
x = self.fc4(x)
return x

# 初始化神经网络
model = Net()

# 定义损失函数和优化器
criterion = nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)

# 训练神经网络
for epoch in range(1000):
# forward
output = model(x_tensor.unsqueeze(1))
loss = criterion(output.squeeze(), y_tensor)

# backward and optimize
optimizer.zero_grad()
loss.backward()
optimizer.step()

# 绘制拟合曲线
x_test = np.linspace(-10, 10, 100)
x_test_tensor = torch.from_numpy(x_test).float()
y_pred = model(x_test_tensor.unsqueeze(1)).detach().numpy().flatten()

plt.plot(x, y, label='ground truth')
plt.plot(x_test, y_pred, label='fitted curve')
plt.legend()
plt.show()