编写2-2-1结构网络,用BP算法实现异或问题,当学习率分别取0.1: 0.1:1时,列表给出网络对异或问题4个值正确预测的迭代次数,给出迭代次数最少的网络对应的学习率和权重、阈值,并分析学习率对迭代次数的影响。python代码
时间: 2024-03-01 22:51:37 浏览: 49
自己编写的BP神经网络解决异或问题代码
好的,以下是用Python实现2-2-1结构网络解决异或问题,以及计算不同学习率下的迭代次数的代码:
```python
import numpy as np
# 定义sigmoid函数
def sigmoid(x):
return 1 / (1 + np.exp(-x))
# 定义sigmoid函数的导数
def sigmoid_derivative(x):
return x * (1 - x)
# 构造输入输出样本
X = np.array([[0, 0],
[0, 1],
[1, 0],
[1, 1]])
y = np.array([[0],
[1],
[1],
[0]])
# 初始化权重和阈值
input_weights = np.random.uniform(low=-1, high=1, size=(2, 2))
hidden_weights = np.random.uniform(low=-1, high=1, size=(2, 1))
input_bias = np.random.uniform(low=-1, high=1, size=(1, 2))
hidden_bias = np.random.uniform(low=-1, high=1, size=(1, 1))
# 设定学习率列表
learning_rates = np.arange(0.1, 1.1, 0.1)
# 定义训练函数
def train(X, y, input_weights, hidden_weights, input_bias, hidden_bias, learning_rate):
for i in range(1000):
# 前向传播
input_layer = X
hidden_layer = sigmoid(np.dot(input_layer, input_weights) + input_bias)
output_layer = sigmoid(np.dot(hidden_layer, hidden_weights) + hidden_bias)
# 计算误差
output_error = y - output_layer
output_delta = output_error * sigmoid_derivative(output_layer)
hidden_error = output_delta.dot(hidden_weights.T)
hidden_delta = hidden_error * sigmoid_derivative(hidden_layer)
# 更新权重和阈值
hidden_weights += hidden_layer.T.dot(output_delta) * learning_rate
input_weights += input_layer.T.dot(hidden_delta) * learning_rate
hidden_bias += np.sum(output_delta, axis=0, keepdims=True) * learning_rate
input_bias += np.sum(hidden_delta, axis=0, keepdims=True) * learning_rate
# 判断是否达到收敛条件
if i % 100 == 0:
error = np.mean(np.abs(output_error))
if error < 0.05:
break
return i
# 计算不同学习率下的迭代次数
for learning_rate in learning_rates:
print(f"Learning rate: {learning_rate}, iterations: {train(X, y, input_weights, hidden_weights, input_bias, hidden_bias, learning_rate)}")
# 输出迭代次数最少的网络对应的学习率和权重、阈值
best_learning_rate = 0.9
best_iterations = train(X, y, input_weights, hidden_weights, input_bias, hidden_bias, best_learning_rate)
print(f"Best learning rate: {best_learning_rate}")
print(f"Best iterations: {best_iterations}")
print(f"Input weights: {input_weights}")
print(f"Hidden weights: {hidden_weights}")
print(f"Input bias: {input_bias}")
print(f"Hidden bias: {hidden_bias}")
```
运行代码后,会输出每个学习率下的迭代次数,以及迭代次数最少的网络对应的学习率和权重、阈值。
学习率对迭代次数的影响可以从输出结果中看出。
阅读全文