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神经网络——浅浅的做个笔记

发布时间:2022/9/10 20:12:09

我们来看一个小示例

 

 

 把男人定义为1,女人定义为0

 

 

 输入身高和体重,来预测男人和女人,因此有两个输入,一个输出,我们不妨设两个隐藏层

 

代码如下:

 


   import numpy as np


   def sigmoid(x):
  # Sigmoid activation function: f(x) = 1 / (1 + e^(-x))
   return 1 / (1 + np.exp(-x))


# 求导
def deriv_sigmoid(x):
  # Derivative of sigmoid: f'(x) = f(x) * (1 - f(x))
  fx = sigmoid(x)
  return fx * (1 - fx)
# 损失函数
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()
# 神经网络
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.
    '''
#学习率
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: %.3f" % (epoch, loss)) # Define dataset data = np.array([ [-2, -1], # Alice [25, 6], # Bob [17, 4], # Charlie [-15, -6], # Diana ]) all_y_trues = np.array([ 0, # Alice 1, # Bob 1, # Charlie 0, # Diana ]) # Train our neural network! network = OurNeuralNetwork() network.train(data, all_y_trues) # Make some predictions emily = np.array([-7, -3]) # 128 pounds, 63 inches frank = np.array([20, 2]) # 155 pounds, 68 inches print("Emily: %.3f" % network.feedforward(emily)) print("Frank: %.3f" % network.feedforward(frank))


Emily: 0.035
Frank: 0.961
 

 

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