【python】小型神经网络的搭建

 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 and y_pred are numpy arrays of the same length.
   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)
 
   *** DISCLAIMER ***:
   The code below is intended to be simple and educational, NOT optimal.
   Real neural net code looks nothing like this. DO NOT use this code.
   Instead, read/run it to understand how this specific network works.
   '''
   def __init__(self):
     # 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()
 
     # Biases
     self.b1 = np.random.normal()
     self.b2 = np.random.normal()
     self.b3 = np.random.normal()
 
   def feedforward(self, x):
     # x is a numpy array with 2 elements.
     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 # number of times to loop through the entire dataset
 
     for epoch in range(epochs):
       for x, y_true in zip(data, all_y_trues):
         # --- Do a feedforward (we'll need these values later)
         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
 
         # --- Calculate partial derivatives.
         # --- 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)
 
         # --- Update weights and biases
         # 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
 
       # --- Calculate total loss at the end of each epoch
       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: %.8f" % (epoch, loss))
 
 # Define dataset
 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
 ])
 
 # Train our neural network!
 network = OurNeuralNetwork()
 network.train(data, all_y_trues)

tz@croplab,HZAU

2019/6/19