numpy手写两层神经网络

使用中间隐藏层使用sigmoid激活函数，输出层使用softmax。反向算梯度的时候把loss和softmax一起算了

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import numpy as np

def train(X,target):

    #定义超参数：W1,W2分别为两层网络的权重，lr学习率

    inputchannels,hiddenchannels,outputchannels=5,20,3

    W1=np.random.randn(inputchannels+1,hiddenchannels)

    W2=np.random.randn(hiddenchannels+1,outputchannels)

    X_hat = np.insert(X, 0, values=1, axis=1)

    _,batch_size = X.shape

    lr=0.1

    #开始训练

    for i in range(1000):

        g=1

        #forward

        X1 = X_hat @ W1  #8*6 6*20->8*20

        activate_X1 = 1 / (1 + np.exp(-X1))

        X2_hat = np.insert(activate_X1, 0, values=1, axis=1)

        X2 = X2_hat @ W2  #8*21 21*3 -> 8*3

        activate_X2 = np.exp(X2) / np.sum(np.exp(X2), axis=1, keepdims=True)

        loss = -np.sum(target * np.log(activate_X2)) / batch_size

        #backward

        delta_g = (g * activate_X2 - target) / batch_size 

        delta_W2 = X2_hat.T @ delta_g 

        delta_X2_hat = delta_g @ W2.T

        delta_X1 = delta_X2_hat[:,1:] * (activate_X1 * (1 - activate_X1)) 

        delta_W1 = X_hat.T @ delta_X1 

        #更新参数

        W1 = W1 - delta_W1 *lr

        W2 = W2 - delta_W2 *lr

        if (i + 1) % 100 == 0 or i % 5 == 0 and (i / 5) < 3:

            print(f"Iter: {i}, Loss: {loss:.3f}")

    return W1,W2

def test(X_test,W1,W2):

    X_hat = np.insert(X_test, 0, values=1, axis=1)

    X1 = X_hat @ W1 

    activate_X1 = 1 / (1 + np.exp(-X1))

    X2_hat = np.insert(activate_X1, 0, values=1, axis=1)

    X2 = X2_hat @ W2 

    probability = np.exp(X2) / np.sum(np.exp(X2), axis=1, keepdims=True)

    return probability