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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,83 @@ | ||
| import numpy as np | ||
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| # 初始化参数 | ||
| np.random.seed(42) # 确保每次运行结果一致 | ||
| input_size = 2 # 输入层节点数 | ||
| hidden_size = 3 # 隐藏层节点数 | ||
| output_size = 2 # 输出层节点数 | ||
| learning_rate = 0.1 # 学习率 | ||
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| # 随机初始化权重和偏置 | ||
| W1 = np.random.randn(input_size, hidden_size) | ||
| b1 = np.zeros(hidden_size) | ||
| W2 = np.random.randn(hidden_size, output_size) | ||
| b2 = np.zeros(output_size) | ||
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| # ReLU激活函数及其导数 | ||
| def relu(x): | ||
| return np.maximum(0, x) | ||
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| def relu_derivative(x): | ||
| return (x > 0).astype(float) | ||
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| # Softmax函数 | ||
| def softmax(x): | ||
| exp_x = np.exp(x - np.max(x, axis=1, keepdims=True)) | ||
| return exp_x / np.sum(exp_x, axis=1, keepdims=True) | ||
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| # 交叉熵损失及其导数 | ||
| def cross_entropy_loss(y_pred, y_true): | ||
| m = y_true.shape[0] | ||
| return -np.sum(y_true * np.log(y_pred)) / m | ||
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| def delta_cross_entropy_softmax(y_pred, y_true): | ||
| return y_pred - y_true | ||
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| # 前向传播 | ||
| def forward_propagation(X): | ||
| Z1 = X.dot(W1) + b1 | ||
| A1 = relu(Z1) | ||
| Z2 = A1.dot(W2) + b2 | ||
| A2 = softmax(Z2) | ||
| return Z1, A1, Z2, A2 | ||
|
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| # 反向传播 | ||
| def backward_propagation(X, Y, Z1, A1, Z2, A2): | ||
| m = X.shape[0] | ||
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| dZ2 = delta_cross_entropy_softmax(A2, Y) | ||
| dW2 = (1/m) * np.dot(A1.T, dZ2) | ||
| db2 = (1/m) * np.sum(dZ2, axis=0) | ||
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| dA1 = np.dot(dZ2, W2.T) | ||
| dZ1 = dA1 * relu_derivative(Z1) | ||
| dW1 = (1/m) * np.dot(X.T, dZ1) | ||
| db1 = (1/m) * np.sum(dZ1, axis=0) | ||
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| return dW1, db1, dW2, db2 | ||
|
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| # 更新参数 | ||
| def update_parameters(dW1, db1, dW2, db2): | ||
| global W1, b1, W2, b2 | ||
| W1 -= learning_rate * dW1 | ||
| b1 -= learning_rate * db1 | ||
| W2 -= learning_rate * dW2 | ||
| b2 -= learning_rate * db2 | ||
|
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| # 示例输入和标签 | ||
| X = np.array([[0.1, 0.2], [0.3, 0.4]]) # 2个样本 | ||
| Y = np.array([[1, 0], [0, 1]]) # 对应的one-hot标签 | ||
|
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| # 执行一次前向传播 | ||
| Z1, A1, Z2, A2 = forward_propagation(X) | ||
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| # 计算损失 | ||
| loss = cross_entropy_loss(A2, Y) | ||
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| # 执行一次反向传播 | ||
| dW1, db1, dW2, db2 = backward_propagation(X, Y, Z1, A1, Z2, A2) | ||
|
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| # 更新参数 | ||
| update_parameters(dW1, db1, dW2, db2) | ||
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| print(loss) |
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