人工智能基础作业3

一、使用pytorch复现课上例题

# https://blog.csdn.net/qq_41033011/article/details/109325070
# https://github.com/Darwlr/Deep_learning/blob/master/06%20Pytorch%E5%AE%9E%E7%8E%B0%E5%8F%8D%E5%90%91%E4%BC%A0%E6%92%AD.ipynb
# torch.nn.Sigmoid(h_in)

import torch

x1, x2 = torch.Tensor([0.5]), torch.Tensor([0.3])
y1, y2 = torch.Tensor([0.23]), torch.Tensor([-0.07])
print("=====输入值：x1, x2；真实输出值：y1, y2=====")
print(x1, x2, y1, y2)
w1, w2, w3, w4, w5, w6, w7, w8 = torch.Tensor([0.2]), torch.Tensor([-0.4]), torch.Tensor([0.5]), torch.Tensor(
    [0.6]), torch.Tensor([0.1]), torch.Tensor([-0.5]), torch.Tensor([-0.3]), torch.Tensor([0.8])  # 权重初始值
w1.requires_grad = True
w2.requires_grad = True
w3.requires_grad = True
w4.requires_grad = True
w5.requires_grad = True
w6.requires_grad = True
w7.requires_grad = True
w8.requires_grad = True


def sigmoid(z):
    a = 1 / (1 + torch.exp(-z))
    return a


def forward_propagate(x1, x2):
    in_h1 = w1 * x1 + w3 * x2
    out_h1 = sigmoid(in_h1)  # out_h1 = torch.sigmoid(in_h1)
    in_h2 = w2 * x1 + w4 * x2
    out_h2 = sigmoid(in_h2)  # out_h2 = torch.sigmoid(in_h2)

    in_o1 = w5 * out_h1 + w7 * out_h2
    out_o1 = sigmoid(in_o1)  # out_o1 = torch.sigmoid(in_o1)
    in_o2 = w6 * out_h1 + w8 * out_h2
    out_o2 = sigmoid(in_o2)  # out_o2 = torch.sigmoid(in_o2)

    print("正向计算：o1 ,o2")
    print(out_o1.data, out_o2.data)

    return out_o1, out_o2


def loss_fuction(x1, x2, y1, y2):  # 损失函数
    y1_pred, y2_pred = forward_propagate(x1, x2)  # 前向传播
    loss = (1 / 2) * (y1_pred - y1) ** 2 + (1 / 2) * (y2_pred - y2) ** 2  # 考虑 ： t.nn.MSELoss()
    print("损失函数（均方误差）：", loss.item())
    return loss


def update_w(w1, w2, w3, w4, w5, w6, w7, w8):
    # 步长
    step = 1
    w1.data = w1.data - step * w1.grad.data
    w2.data = w2.data - step * w2.grad.data
    w3.data = w3.data - step * w3.grad.data
    w4.data = w4.data - step * w4.grad.data
    w5.data = w5.data - step * w5.grad.data
    w6.data = w6.data - step * w6.grad.data
    w7.data = w7.data - step * w7.grad.data
    w8.data = w8.data - step * w8.grad.data
    w1.grad.data.zero_()  # 注意：将w中所有梯度清零
    w2.grad.data.zero_()
    w3.grad.data.zero_()
    w4.grad.data.zero_()
    w5.grad.data.zero_()
    w6.grad.data.zero_()
    w7.grad.data.zero_()
    w8.grad.data.zero_()
    return w1, w2, w3, w4, w5, w6, w7, w8


if __name__ == "__main__":

    print("=====更新前的权值=====")
    print(w1.data, w2.data, w3.data, w4.data, w5.data, w6.data, w7.data, w8.data)

    for i in range(10):
        print("n=====第" + str(i) + "轮=====")
        L = loss_fuction(x1, x2, y1, y2)  # 前向传播，求 Loss，构建计算图
        L.backward()  # 自动求梯度，不需要人工编程实现。反向传播，求出计算图中所有梯度存入w中
        print("grad W: ", round(w1.grad.item(), 2), round(w2.grad.item(), 2), round(w3.grad.item(), 2),
              round(w4.grad.item(), 2), round(w5.grad.item(), 2), round(w6.grad.item(), 2), round(w7.grad.item(), 2),
              round(w8.grad.item(), 2))
        w1, w2, w3, w4, w5, w6, w7, w8 = update_w(w1, w2, w3, w4, w5, w6, w7, w8)

    print("更新后的权值")
    print(w1.data, w2.data, w3.data, w4.data, w5.data, w6.data, w7.data, w8.data)

二、对比【作业3】和【作业2】的程序，观察两种方法结果是否相同？如果不同，哪个正确

PyTorch第一反向传播求得的梯度
手动计算第一轮反向传播求得的梯度

通过比较实验结果发现两次实验结果不同。手动计算和使用PyTorch计算的权重向量的梯度值中w1和w3互为相反数，其他相同。

三、【作业2】程序更新（保留【作业2中】的错误答案，留作对比。新程序到作业3。）

作业二

四、对比【作业2】与【作业3】的反向传播的实现方法。总结并陈述。

PyTorch是一个成熟的机械学习库，能够简化极大的简化神经网络模型中的反向传播求各个参数的梯度问题，与之相比手动操作容易出错。手动计算可以计算简单模型，但是当模型隐藏层很多时，手动计算效率低且易错，建议使用PyTorch。

五、激活函数Sigmoid用PyTorch自带函数torch.sigmoid()，观察、总结并陈述。

替换后代码：

# https://blog.csdn.net/qq_41033011/article/details/109325070
# https://github.com/Darwlr/Deep_learning/blob/master/06%20Pytorch%E5%AE%9E%E7%8E%B0%E5%8F%8D%E5%90%91%E4%BC%A0%E6%92%AD.ipynb
# torch.nn.Sigmoid(h_in)

import torch

x1, x2 = torch.Tensor([0.5]), torch.Tensor([0.3])
y1, y2 = torch.Tensor([0.23]), torch.Tensor([-0.07])
print("=====输入值：x1, x2；真实输出值：y1, y2=====")
print(x1, x2, y1, y2)
w1, w2, w3, w4, w5, w6, w7, w8 = torch.Tensor([0.2]), torch.Tensor([-0.4]), torch.Tensor([0.5]), torch.Tensor(
    [0.6]), torch.Tensor([0.1]), torch.Tensor([-0.5]), torch.Tensor([-0.3]), torch.Tensor([0.8])  # 权重初始值
w1.requires_grad = True
w2.requires_grad = True
w3.requires_grad = True
w4.requires_grad = True
w5.requires_grad = True
w6.requires_grad = True
w7.requires_grad = True
w8.requires_grad = True

def forward_propagate(x1, x2):
    in_h1 = w1 * x1 + w3 * x2
    out_h1 = torch.sigmoid(in_h1)
    in_h2 = w2 * x1 + w4 * x2
    out_h2 = torch.sigmoid(in_h2)

    in_o1 = w5 * out_h1 + w7 * out_h2
    out_o1 = torch.sigmoid(in_o1)
    in_o2 = w6 * out_h1 + w8 * out_h2
    out_o2 = torch.sigmoid(in_o2)

    print("正向计算：o1 ,o2")
    print(out_o1.data, out_o2.data)

    return out_o1, out_o2



def loss_fuction(x1, x2, y1, y2):  # 损失函数
    y1_pred, y2_pred = forward_propagate(x1, x2)  # 前向传播
    loss = (1 / 2) * (y1_pred - y1) ** 2 + (1 / 2) * (y2_pred - y2) ** 2  # 考虑 ： t.nn.MSELoss()
    print("损失函数（均方误差）：", loss.item())
    return loss


def update_w(w1, w2, w3, w4, w5, w6, w7, w8):
    # 步长
    step = 1
    w1.data = w1.data - step * w1.grad.data
    w2.data = w2.data - step * w2.grad.data
    w3.data = w3.data - step * w3.grad.data
    w4.data = w4.data - step * w4.grad.data
    w5.data = w5.data - step * w5.grad.data
    w6.data = w6.data - step * w6.grad.data
    w7.data = w7.data - step * w7.grad.data
    w8.data = w8.data - step * w8.grad.data
    w1.grad.data.zero_()  # 注意：将w中所有梯度清零
    w2.grad.data.zero_()
    w3.grad.data.zero_()
    w4.grad.data.zero_()
    w5.grad.data.zero_()
    w6.grad.data.zero_()
    w7.grad.data.zero_()
    w8.grad.data.zero_()
    return w1, w2, w3, w4, w5, w6, w7, w8


if __name__ == "__main__":

    print("=====更新前的权值=====")
    print(w1.data, w2.data, w3.data, w4.data, w5.data, w6.data, w7.data, w8.data)

    for i in range(10):
        print("n=====第" + str(i) + "轮=====")
        L = loss_fuction(x1, x2, y1, y2)  # 前向传播，求 Loss，构建计算图
        L.backward()  # 自动求梯度，不需要人工编程实现。反向传播，求出计算图中所有梯度存入w中
        print("grad W: ", round(w1.grad.item(), 2), round(w2.grad.item(), 2), round(w3.grad.item(), 2),
              round(w4.grad.item(), 2), round(w5.grad.item(), 2), round(w6.grad.item(), 2), round(w7.grad.item(), 2),
              round(w8.grad.item(), 2))
        w1, w2, w3, w4, w5, w6, w7, w8 = update_w(w1, w2, w3, w4, w5, w6, w7, w8)

    print("更新后的权值")
    print(w1.data, w2.data, w3.data, w4.data, w5.data, w6.data, w7.data, w8.data)

运行结果：

六、激活函数Sigmoid改变为Relu，观察、总结并陈述。

把激活函数改为：

def forward_propagate(x1, x2):
    in_h1 = w1 * x1 + w3 * x2
    out_h1 = torch.relu(in_h1)
    in_h2 = w2 * x1 + w4 * x2
    out_h2 = torch.relu(in_h2)


    in_o1 = w5 * out_h1 + w7 * out_h2
    out_o1 = torch.relu(in_o1)
    in_o2 = w6 * out_h1 + w8 * out_h2
    out_o2 = torch.relu(in_o2)

    print("正向计算：o1 ,o2")
    print(out_o1.data, out_o2.data)

    return out_o1, out_o2

运行结果为：

七、损失函数MSE用PyTorch自带函数 t.nn.MSELoss()替代，观察、总结并陈述。

把损失函数改为：

def loss_fuction(x1, x2, y1, y2):  # 损失函数
    # torch.nn.CrossEntropyLoss交叉熵
    y1_pred, y2_pred = forward_propagate(x1, x2)  # 前向传播
    loss_f = torch.nn.MSELoss()
    # loss_f = torch.nn.CrossEntropyLoss交叉熵
    y_pred = torch.cat((y1_pred, y2_pred), dim=0)
    y = torch.cat((y1, y2), dim=0)
    loss = loss_f(y_pred,y)
    print("损失函数（均方误差）：", loss.item())
    return loss

在计算之前要将所有预测值合并成一个张量，所有实际值合并成一个张量，再使用torch.nn.MSELoss()计算结果
部分计算结果：

八、损失函数MSE改变为交叉熵，观察、总结并陈述。

修改计算损失函数代码为：

def loss_fuction(x1, x2, y1, y2):  # 损失函数
    # torch.nn.CrossEntropyLoss交叉熵
    y1_pred, y2_pred = forward_propagate(x1, x2)  # 前向传播
    # loss_f = torch.nn.MSELoss()
    loss_f = torch.nn.CrossEntropyLoss
    y_pred = torch.cat((y1_pred, y2_pred), dim=0)
    y = torch.cat((y1, y2), dim=0)
    loss = loss_f(y_pred,y)
    print("损失函数（均方误差）：", loss.item())
    return loss

九、改变步长，训练次数，观察、总结并陈述

def update_w(w1, w2, w3, w4, w5, w6, w7, w8): 
    step = 1 #步长，令step = 1,10,50,100
    w1.data = w1.data - step * w1.grad.data
    w2.data = w2.data - step * w2.grad.data
    w3.data = w3.data - step * w3.grad.data
    w4.data = w4.data - step * w4.grad.data
    w5.data = w5.data - step * w5.grad.data
    w6.data = w6.data - step * w6.grad.data
    w7.data = w7.data - step * w7.grad.data
    w8.data = w8.data - step * w8.grad.data
    w1.grad.data.zero_()  # 注意：将w中所有梯度清零
    w2.grad.data.zero_()
    w3.grad.data.zero_()
    w4.grad.data.zero_()
    w5.grad.data.zero_()
    w6.grad.data.zero_()
    w7.grad.data.zero_()
    w8.grad.data.zero_()
    return w1, w2, w3, w4, w5, w6, w7, w8

步长为1：

步长为5：

步长为10：

十、权值w1-w8初始值换为随机数，对比【作业2】指定权值结果，观察、总结并陈述。

使用随机生成的初始步长

# w1, w2, w3, w4, w5, w6, w7, w8 = torch.Tensor([0.2]), torch.Tensor([-0.4]), torch.Tensor([0.5]), torch.Tensor(
#     [0.6]), torch.Tensor([0.1]), torch.Tensor([-0.5]), torch.Tensor([-0.3]), torch.Tensor([0.8])
w1, w2, w3, w4, w5, w6, w7, w8 = torch.randn(1), torch.randn(1), torch.randn(1), torch.randn(1), 
    torch.randn(1), torch.randn(1), torch.randn(1), torch.randn(1)

生成的随机权重值

十、全面总结反向传播原理和编码实现，认真写心得体会

代码实现：

# https://blog.csdn.net/qq_41033011/article/details/109325070
# https://github.com/Darwlr/Deep_learning/blob/master/06%20Pytorch%E5%AE%9E%E7%8E%B0%E5%8F%8D%E5%90%91%E4%BC%A0%E6%92%AD.ipynb
# torch.nn.Sigmoid(h_in)

import torch

x1, x2 = torch.Tensor([0.5]), torch.Tensor([0.3])
y1, y2 = torch.Tensor([0.23]), torch.Tensor([-0.07])
print("=====输入值：x1, x2；真实输出值：y1, y2=====")
print(x1, x2, y1, y2)
w1, w2, w3, w4, w5, w6, w7, w8 = torch.Tensor([0.2]), torch.Tensor([-0.4]), torch.Tensor([0.5]), torch.Tensor(
    [0.6]), torch.Tensor([0.1]), torch.Tensor([-0.5]), torch.Tensor([-0.3]), torch.Tensor([0.8])  # 权重初始值
w1.requires_grad = True
w2.requires_grad = True
w3.requires_grad = True
w4.requires_grad = True
w5.requires_grad = True
w6.requires_grad = True
w7.requires_grad = True
w8.requires_grad = True

def forward_propagate(x1, x2):
    in_h1 = w1 * x1 + w3 * x2
    out_h1 = torch.relu(in_h1)
    in_h2 = w2 * x1 + w4 * x2
    out_h2 = torch.relu(in_h2)


    in_o1 = w5 * out_h1 + w7 * out_h2
    out_o1 = torch.relu(in_o1)
    in_o2 = w6 * out_h1 + w8 * out_h2
    out_o2 = torch.relu(in_o2)

    print("正向计算：o1 ,o2")
    print(out_o1.data, out_o2.data)

    return out_o1, out_o2


def loss_fuction(x1, x2, y1, y2):  # 损失函数
    # torch.nn.CrossEntropyLoss交叉熵
    y1_pred, y2_pred = forward_propagate(x1, x2)  # 前向传播
    # loss_f = torch.nn.MSELoss()
    loss_f = torch.nn.CrossEntropyLoss
    y_pred = torch.cat((y1_pred, y2_pred), dim=0)
    y = torch.cat((y1, y2), dim=0)
    loss = loss_f(y_pred,y)
    print("损失函数（均方误差）：", loss.item())
    return loss

def update_w(w1, w2, w3, w4, w5, w6, w7, w8):
    step = 1 #步长，令step = 1,10,50,100
    w1.data = w1.data - step * w1.grad.data
    w2.data = w2.data - step * w2.grad.data
    w3.data = w3.data - step * w3.grad.data
    w4.data = w4.data - step * w4.grad.data
    w5.data = w5.data - step * w5.grad.data
    w6.data = w6.data - step * w6.grad.data
    w7.data = w7.data - step * w7.grad.data
    w8.data = w8.data - step * w8.grad.data
    w1.grad.data.zero_()  # 注意：将w中所有梯度清零
    w2.grad.data.zero_()
    w3.grad.data.zero_()
    w4.grad.data.zero_()
    w5.grad.data.zero_()
    w6.grad.data.zero_()
    w7.grad.data.zero_()
    w8.grad.data.zero_()
    return w1, w2, w3, w4, w5, w6, w7, w8


if __name__ == "__main__":

    print("=====更新前的权值=====")
    print(w1.data, w2.data, w3.data, w4.data, w5.data, w6.data, w7.data, w8.data)

    for i in range(10):
        print("n=====第" + str(i) + "轮=====")
        L = loss_fuction(x1, x2, y1, y2)  # 前向传播，求 Loss，构建计算图
        L.backward()  # 自动求梯度，不需要人工编程实现。反向传播，求出计算图中所有梯度存入w中
        print("grad W: ", round(w1.grad.item(), 2), round(w2.grad.item(), 2), round(w3.grad.item(), 2),
              round(w4.grad.item(), 2), round(w5.grad.item(), 2), round(w6.grad.item(), 2), round(w7.grad.item(), 2),
              round(w8.grad.item(), 2))
        w1, w2, w3, w4, w5, w6, w7, w8 = update_w(w1, w2, w3, w4, w5, w6, w7, w8)

    print("更新后的权值")
    print(w1.data, w2.data, w3.data, w4.data, w5.data, w6.data, w7.data, w8.data)

总结：
PyTorch是一个很完备的机械学习库，使用PyTorch完成反向传播过程中各个权重的梯度计算即快有准确，而且PyTorch还包含了多种封装好的损失函数计算函数，是神经网络模型中十分好用的工具库。
反向传播是为了梯度下降做准备，实现方法就是计算损失函数对传播路径上每一个权重的偏导数，可以使用PyTorch实现来提高编码效率的准确性。

人工智能基础 作业3

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