?實現四層神經網絡，如下圖：

反向傳播原理：

“反向傳播算法”過程及公式推導（超直觀好懂的Backpropagation）_aift的專欄-CSDN博客_反向傳播算法

使用SGD(小批量隨機梯度下降)

import numpy as np import torchvisiondef tanh(x):s1 = np.exp(x) - np.exp(-x)s2 = np.exp(x) + np.exp(-x)s = s1 / s2return s# 標簽one-hot處理 def onehot(targets, num):result = np.zeros((num, 10))for i in range(num):result[i][targets[i]] = 1return result# sigmoid def sigmoid(x):return 1 / (1 + np.exp(-x))# sigmoid的一階導數 def Dsigmoid(x):return sigmoid(x)*(1-sigmoid(x))class NN(object):def __init__(self, l0, l1, l2, l3, batch_size=6):self.lr = 0.4 # 學習率self.batch_size = batch_sizeself.W1 = np.random.randn(l0, l1) * 0.01 # 初始化self.b1 = np.random.randn(l1) * 0.01self.W2 = np.random.randn(l1, l2) * 0.01self.b2 = np.random.randn(l2) * 0.01self.W3 = np.random.randn(l2, l3) * 0.01self.b3 = np.random.randn(l3) * 0.01# 前向傳播def forward(self, X, y):self.X = X # m x 784self.z1 = np.dot(X, self.W1) + self.b1 # m x 200, 等于中間層層數self.a1 = sigmoid(self.z1) # m x 200# self.z2 = np.dot(self.a1, self.W2) + self.b2 # m x 30# self.a2 = sigmoid(self.z2) # m x 30self.z2 = np.dot(self.a1, self.W2) + self.b2 # m x 10self.a2 = sigmoid(self.z2)self.z3 = np.dot(self.a2, self.W3) + self.b3 self.a3 = sigmoid(self.z3) loss = np.sum((self.a3 - y) * (self.a3 - y)) / 6 # 均方差self.d3 = (self.a3 - y) * Dsigmoid(self.z3) # 用于反向傳播return loss, self.a3# 反向傳播def backward(self):dW3 = np.dot(self.a2.T, self.d3) / self.batch_size db3 = np.sum(self.d3, axis=0) / self.batch_size d2 = np.dot(self.d3, self.W3.T) * Dsigmoid(self.z2) # 用于反向傳播dW2 = np.dot(self.a1.T, d2) / self.batch_sizedb2 = np.sum(d2, axis=0) / self.batch_sized1 = np.dot(d2, self.W2.T) * Dsigmoid(self.z1)dW1 = np.dot(self.X.T, d1) / self.batch_size # 784x 200db1 = np.sum(d1, axis=0) / self.batch_size # 200self.W3 -= self.lr * dW3self.b3 -= self.lr * db3self.W2 -= self.lr * dW2self.b2 -= self.lr * db2self.W1 -= self.lr * dW1self.b1 -= self.lr * db1def train():nn = NN(784, 200, 30, 10)for epoch in range(10):for i in range(0, 60000, nn.batch_size):X = train_data.data[i:i+nn.batch_size]Y = train_data.targets[i:i+nn.batch_size]loss, _ = nn.forward(X, Y)print("epocj:", epoch, "-", i, ":", "{:.3f}".format(loss) )nn.backward()np.savez("data.npz", w1=nn.W1, b1=nn.b1, w2=nn.W2, b2=nn.b2, w3=nn.W3, b3=nn.b3)def test():r = np.load("data.npz")nn = NN(784, 200, 30, 10)nn.W1 = r["w1"]nn.b1 = r["b1"]nn.W2 = r["w2"]nn.b2 = r["b2"]nn.W3 = r["w3"]nn.b3 = r["b3"]_, result = nn.forward(test_data.data, test_data.targets2)result = np.argmax(result, axis=1)precison = np.sum(result==test_data.targets) / 10000print("Precison:", precison)if __name__ == '__main__':# Mnist手寫數字集train_data = torchvision.datasets.MNIST(root='data/', train=True, download=True)test_data = torchvision.datasets.MNIST(root='data/', train=False)train_data.data = train_data.data.numpy() # [60000,28,28]train_data.targets = train_data.targets.numpy() # [60000]test_data.data = test_data.data.numpy() # [10000,28,28]test_data.targets = test_data.targets.numpy() # [10000]# 輸入向量處理train_data.data = train_data.data.reshape(60000, 28 * 28) / 255. # (60000, 784)test_data.data = test_data.data.reshape(10000, 28 * 28) / 255.# 標簽one-hot處理train_data.targets = onehot(train_data.targets, 60000) # (60000, 10)test_data.targets2 = onehot(test_data.targets, 10000) # 用于前向傳播train()test()

模型的精度達到97%?

總結

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