用Python从0到1实现一个神经网络(附代码)！

1.介绍了神经网络的基本结构——神经元；

2.在神经元中使用S型激活函数；

3.神经网络就是连接在一起的神经元；

4.构建了一个数据集，输入（或特征）是体重和身高，输出（或标签）是性别；

5.学习了损失函数和均方差损失；

6.训练网络就是最小化其损失；

7.用反向传播方法计算偏导；

8.用随机梯度下降法训练网络。

砖块：神 经元

import numpy as np def sigmoid (x) : # 我们的激活函数: f(x) = 1 / (1 + e^(-x)) return 1 / ( 1 + np.exp(-x)) class Neuron : def __init__ ( self , weights, bias) : self .weights = weights self .bias = bias def feedforward ( self , inputs) : # 加权输入，加入偏置，然后使用激活函数 total = np.dot( self .weights, inputs) + self .bias return sigmoid(total) weights = np.array([ 0 , 1 ]) # w1 = 0, w2 = 1 bias = 4 # b = 4 n = Neuron(weights, bias) x = np.array([ 2 , 3 ]) # x1 = 2, x2 = 3 print(n.feedforward(x)) # 0.9990889488055994

import numpy as np # ... code from previous section here class OurNeuralNetwork : ’’’ A neural network with: - 2 inputs - a hidden layer with 2 neurons (h1, h2) - an output layer with 1 neuron (o1) Each neuron has the same weights and bias: - w = [0, 1] - b = 0 ’’’ def __init__ (self) : weights = np.array([ 0 , 1 ]) bias = 0 # 这里是来自前一节的神经元类 self.h1 = Neuron(weights, bias) self.h2 = Neuron(weights, bias) self.o1 = Neuron(weights, bias) def feedforward (self, x) : out_h1 = self.h1.feedforward(x) out_h2 = self.h2.feedforward(x) # o1的输入是h1和h2的输出 out_o1 = self.o1.feedforward(np.array([out_h1, out_h2])) return out_o1 network = OurNeuralNetwork() x = np.array([ 2 , 3 ]) print(network.feedforward(x)) # 0.7216325609518421

import numpy as np def mse_loss (y_true, y_pred) : # y_true and y_pred are numpy arrays of the same length. return ((y_true - y_pred) ** 2 ).mean() y_true = np.array([ 1 , 0 , 0 , 1 ]) y_pred = np.array([ 0 , 0 , 0 , 0 ]) print(mse_loss(y_true, y_pred)) # 0.5

import numpy as np def sigmoid (x) : # Sigmoid activation function: f(x) = 1 / (1 + e^(-x)) return 1 / ( 1 + np.exp(-x)) def deriv_sigmoid (x) : # Derivative of sigmoid: f’(x) = f(x) * (1 - f(x)) fx = sigmoid(x) return fx * ( 1 - fx) def mse_loss (y_true, y_pred) : # y_true和y_pred是相同长度的numpy数组。 return ((y_true - y_pred) ** 2 ).mean() class OurNeuralNetwork : ’’ ’ A neural network with: - 2 inputs - a hidden layer with 2 neurons (h1, h2) - an output layer with 1 neuron (o1) *** 免责声明 ***: 下面的代码是为了简单和演示，而不是最佳的。 真正的神经网络代码与此完全不同。不要使用此代码。 相反，读/运行它来理解这个特定的网络是如何工作的。 ’ ’’ def __init__ ( self ) : # 权重，Weights self .w1 = np.random.normal() self .w2 = np.random.normal() self .w3 = np.random.normal() self .w4 = np.random.normal() self .w5 = np.random.normal() self .w6 = np.random.normal() # 截距项，Biases self .b1 = np.random.normal() self .b2 = np.random.normal() self .b3 = np.random.normal() def feedforward ( self , x) : # X是一个有2个元素的数字数组。 h1 = sigmoid( self .w1 * x[ 0 ] + self .w2 * x[ 1 ] + self .b1) h2 = sigmoid( self .w3 * x[ 0 ] + self .w4 * x[ 1 ] + self .b2) o1 = sigmoid( self .w5 * h1 + self .w6 * h2 + self .b3) return o1 def train ( self , data, all_y_trues) : ’’ ’ - data is a (n x 2) numpy array, n = # of samples in the dataset. - all_y_trues is a numpy array with n elements. Elements in all_y_trues correspond to those in data. ’ ’’ learn_rate = 0 . 1 epochs = 1000 # 遍历整个数据集的次数 for epoch in range(epochs): for x, y_true in zip(data, all_y_trues): # --- 做一个前馈(稍后我们将需要这些值) sum_h1 = self .w1 * x[ 0 ] + self .w2 * x[ 1 ] + self .b1 h1 = sigmoid(sum_h1) sum_h2 = self .w3 * x[ 0 ] + self .w4 * x[ 1 ] + self .b2 h2 = sigmoid(sum_h2) sum_o1 = self .w5 * h1 + self .w6 * h2 + self .b3 o1 = sigmoid(sum_o1) y_pred = o1 # --- 计算偏导数。 # --- Naming: d_L_d_w1 represents "partial L / partial w1" d_L_d_ypred = - 2 * (y_true - y_pred) # Neuron o1 d_ypred_d_w5 = h1 * deriv_sigmoid(sum_o1) d_ypred_d_w6 = h2 * deriv_sigmoid(sum_o1) d_ypred_d_b3 = deriv_sigmoid(sum_o1) d_ypred_d_h1 = self .w5 * deriv_sigmoid(sum_o1) d_ypred_d_h2 = self .w6 * deriv_sigmoid(sum_o1) # Neuron h1 d_h1_d_w1 = x[ 0 ] * deriv_sigmoid(sum_h1) d_h1_d_w2 = x[ 1 ] * deriv_sigmoid(sum_h1) d_h1_d_b1 = deriv_sigmoid(sum_h1) # Neuron h2 d_h2_d_w3 = x[ 0 ] * deriv_sigmoid(sum_h2) d_h2_d_w4 = x[ 1 ] * deriv_sigmoid(sum_h2) d_h2_d_b2 = deriv_sigmoid(sum_h2) # --- 更新权重和偏差 # Neuron h1 self .w1 -= learn_rate * d_L_d_ypred * d_ypred_d_h1 * d_h1_d_w1 self .w2 -= learn_rate * d_L_d_ypred * d_ypred_d_h1 * d_h1_d_w2 self .b1 -= learn_rate * d_L_d_ypred * d_ypred_d_h1 * d_h1_d_b1 # Neuron h2 self .w3 -= learn_rate * d_L_d_ypred * d_ypred_d_h2 * d_h2_d_w3 self .w4 -= learn_rate * d_L_d_ypred * d_ypred_d_h2 * d_h2_d_w4 self .b2 -= learn_rate * d_L_d_ypred * d_ypred_d_h2 * d_h2_d_b2 # Neuron o1 self .w5 -= learn_rate * d_L_d_ypred * d_ypred_d_w5 self .w6 -= learn_rate * d_L_d_ypred * d_ypred_d_w6 self .b3 -= learn_rate * d_L_d_ypred * d_ypred_d_b3 # --- 在每次epoch结束时计算总损失 if epoch % 10 == 0 : y_preds = np.apply_along_axis( self .feedforward, 1 , data) loss = mse_loss(all_y_trues, y_preds) print( "Epoch %d loss: %.3f" % (epoch, loss)) # 定义数据集 data = np.array([ [- 2 , - 1 ], # Alice [ 25 , 6 ], # Bob [ 17 , 4 ], # Charlie [- 15 , - 6 ], # Diana ]) all_y_trues = np.array([ 1 , # Alice 0 , # Bob 0 , # Charlie 1 , # Diana ]) # 训练我们的神经网络! network = OurNeuralNetwork() network.train(data, all_y_trues)

# 做一些预测 emily = np. array ([ -7 , -3 ]) # 128 磅, 63 英寸 frank = np. array ([ 20 , 2 ]) # 155 磅, 68 英寸 print ( "Emily: %.3f" % network.feedforward(emily)) # 0.951 - F print ( "Frank: %.3f" % network.feedforward(frank)) # 0.039 - M