人工智能基础及应用 第7章 7-1 神经元学习例子-源码

7-1神经元学习例子实验环境实验支持在多种平台上运行，包括但不限于个人电脑（PC）、服务器以及云环境。用户需要确保已经安装了Python环境，并安装了NumPy和matplotlib等必要的库。实验代码可以编写在Python脚本文件中，或者在支持Python的集成开发环境（IDE，如PyCharm、VSCode等）中编写和运行。源码importnumpyasnp

#初始化权重和偏置

weights_input_to_hidden_a=np.array([[0.3]])

bias_hidden_a=np.array([0.1])

weights_hidden_a_to_hidden_bc=arr=np.array([[0.4,0.6]])

bias_hidden_bc=np.array([0.1,0.1])

weights_hidden_bc_to_output=np.array([[0.2],[0.7]])

bias_output=np.array([0.1])

#设置训练参数

learning_rate=np.array([[0.1]])#学习率

e_min=0.0001#误差阈值

max_iterations=2000#训练轮次

#训练数据

x=np.array([[1]])

y=np.array([[5]])

#激活函数及其导数

defrelu(x):

returnnp.maximum(0,x)

defrelu_derivative(x):

return(x>0).astype(int)

#前向传播

defforward_pass(x):

hidden_a_input=np.dot(x,weights_input_to_hidden_a)+bias_hidden_a

hidden_a_output=relu(hidden_a_input)

hidden_bc_input=np.dot(hidden_a_output,weights_hidden_a_to_hidden_bc)+bias_hidden_bc

hidden_bc_output=relu(hidden_bc_input)

output_input=np.dot(hidden_bc_output,weights_hidden_bc_to_output)+bias_output

output=relu(output_input)

returnoutput,hidden_bc_output,hidden_a_output

#损失函数

defcompute_loss(y_pred,y_true):

return0.5*np.sum((y_pred-y_true)**2)

defbackward_pass(y_pred,y_true,hidden_bc_output,hidden_a_output):

#输出层的梯度

output_error=y_pred-y_true

d_output=output_error*relu_derivative(y_pred)

#隐藏层到输出层的权重梯度

grad_hidden_bc_to_output=np.dot(hidden_bc_output.T,d_output)

grad_bias_output=np.sum(d_output,axis=0,keepdims=True)

#隐藏层的梯度

error_hidden_bc=np.dot(d_output,weights_hidden_bc_to_output.T)

d_hidden_bc=error_hidden_bc*relu_derivative(hidden_bc_output)

grad_hidden_a_to_hidden_bc=np.dot(hidden_a_output.T,d_hidden_bc)

grad_bias_hidden_bc=np.sum(d_hidden_bc,axis=0,keepdims=True)

#输入层到隐藏层的权重梯度

grad_input_to_hidden_a_1=np.dot(x.T,d_hidden_bc[:,0]*weights_hidden_a_to_hidden_bc[0,0]*relu_derivative(

hidden_a_output))

grad_input_to_hidden_a_2=np.dot(x.T,d_hidden_bc[:,1]*weights_hidden_a_to_hidden_bc[0,1]*relu_derivative(

hidden_a_output))

grad_input_to_hidden_a=grad_input_to_hidden_a_1+grad_input_to_hidden_a_2

grad_bias_hidden_a_1=np.sum(

d_hidden_bc[:,0]*weights_hidden_a_to_hidden_bc[0,0]*relu_derivative(hidden_a_output),axis=0,

keepdims=True)

grad_bias_hidden_a_2=np.sum(

d_hidden_bc[:,1]*weights_hidden_a_to_hidden_bc[0,1]*relu_derivative(hidden_a_output),axis=0,

keepdims=True)

grad_bias_hidden_a=grad_bias_hidden_a_1+grad_bias_hidden_a_2

returngrad_hidden_bc_to_output,grad_hidden_a_to_hidden_bc,grad_input_to_hidden_a,grad_bias_output,grad_bias_hidden_bc,grad_bias_hidden_a

#训练过程

losses=[]#损失

errors=[]#误差

foriterationinrange(max_iterations):

#前向传播

y_pred,hidden_bc_output,hidden_a_output=forward_pass(x)

#计算损失

loss=compute_loss(y_pred,y)

losses.append(loss)

#计算误差

error=abs(y_pred-y).reshape(1,)

errors.append(error)

iferror<e_min:#如果损失小于误差阈值，停止训练

break

#反向传播

grad_hidden_bc_to_output,grad_hidden_a_to_hidden_bc,grad_input_to_hidden_a,grad_bias_output,grad_bias_hidden_bc,grad_bias_hidden_a=backward_pass(

y_pred,y,hidden_bc_output,hidden_a_output)

#更新权重和偏置

weights_hidden_bc_to_output-=learning_rate*grad_hidden_bc_to_output

weights_hidden_a_to_hidden_bc-=learning_rate*grad_hidden_a_to_hidden_bc

weights_input_to_hidden_a-=learning_rate*grad_input_to_hidden_a

bias_output-=(learning_rate*grad_bias_output).reshape(1,)

bias_hidden_bc-=(learning_rate*grad_bias_hidden_bc).reshape(2,)

bias_hidden_a-=(learning_rate*grad_bias_hidden_a).reshape(1,)

importmatplotlib.pyplotasplt

plt.figure(figsize=(12,6))

plt.subplot(1,2,1)

plt.plot(losses)

plt.xlabel('