Python 实现一个全连接的神经网络

class NeuralNetwork(object):
  def __init__(self):
    pass
  def forward(self,x):
    # 返回前向传播的 Z 也就是 w 和 b 线性组合，输入激活函数前的值
    # 返回激活函数输出值 A
    # z_s , a_s
    pass
  def backward(self,y,z_s,a_s):
    #返回前向传播中学习参数的导数 dw db
    pass
  def train(self,x,y,batch_size=10,epochs=100,lr=0.001):
    pass

  def __init__(self,layers = [2 , 10, 1], activations=['sigmoid', 'sigmoid']):
    assert(len(layers) == len(activations)+1)
    self.layers = layers
    self.activations = activations
    self.weights = []
    self.biases = []
    for i in range(len(layers)-1):
      self.weights.append(np.random.randn(layers[i+1], layers[i]))
      self.biases.append(np.random.randn(layers[i+1], 1))

for i in range(len(layers)-1):
  self.weights.append(np.random.randn(layers[i+1], layers[i]))
  self.biases.append(np.random.randn(layers[i+1], 1))

def feedforward(self, x):
  # 返回前向传播的值
  a = np.copy(x)
  z_s = []
  a_s = [a]
  for i in range(len(self.weights)):
      activation_function = self.getActivationFunction(self.activations[i])
      z_s.append(self.weights[i].dot(a) + self.biases[i])
      a = activation_function(z_s[-1])
      a_s.append(a)
  return (z_s, a_s)

  @staticmethod
  def getActivationFunction(name):
        if(name == 'sigmoid'):
            return lambda x : np.exp(x)/(1+np.exp(x))
        elif(name == 'linear'):
            return lambda x : x
        elif(name == 'relu'):
            def relu(x):
                y = np.copy(x)
                y[y<0] = 0
                return y
            return relu
        else:
            print('Unknown activation function. linear is used')
            return lambda x: x

[@staticmethod]
def getDerivitiveActivationFunction(name):
    if(name == 'sigmoid'):
        sig = lambda x : np.exp(x)/(1+np.exp(x))
        return lambda x :sig(x)*(1-sig(x))
    elif(name == 'linear'):
        return lambda x: 1
    elif(name == 'relu'):
        def relu_diff(x):
            y = np.copy(x)
            y[y>=0] = 1
            y[y<0] = 0
            return y
        return relu_diff
    else:
        print('Unknown activation function. linear is used')
        return lambda x: 1

  def backpropagation(self,y, z_s, a_s):
      dw = []  # dC/dW
      db = []  # dC/dB
      deltas = [None] * len(self.weights)  # delta = dC/dZ 计算每一层的误差
      # 最后一层误差

      deltas[-1] = ((y-a_s[-1])*(self.getDerivitiveActivationFunction(self.activations[-1]))(z_s[-1]))
      # 反向传播
      for i in reversed(range(len(deltas)-1)):
          deltas[i] = self.weights[i+1].T.dot(deltas[i+1])*(self.getDerivitiveActivationFunction(self.activations[i])(z_s[i]))
      #a= [print(d.shape) for d in deltas]
      batch_size = y.shape[1]
      db = [d.dot(np.ones((batch_size,1)))/float(batch_size) for d in deltas]
      dw = [d.dot(a_s[i].T)/float(batch_size) for i,d in enumerate(deltas)]
      # 返回权重(weight)矩阵 and 偏置向量(biases)
      return dw, db

batch_size = y.shape[1]
db = [d.dot(np.ones((batch_size,1)))/float(batch_size) for d in deltas]
dw = [d.dot(a_s[i].T)/float(batch_size) for i,d in enumerate(deltas)]

  def train(self, x, y, batch_size=10, epochs=100, lr = 0.01):
# update weights and biases based on the output
      for e in range(epochs): 
          i=0
          while(i<len(y)):
              x_batch = x[i:i+batch_size]
              y_batch = y[i:i+batch_size]
              i = i+batch_size
              z_s, a_s = self.feedforward(x_batch)
              dw, db = self.backpropagation(y_batch, z_s, a_s)
              self.weights = [w+lr*dweight for w,dweight in  zip(self.weights, dw)]
              self.biases = [w+lr*dbias for w,dbias in  zip(self.biases, db)]
              # print("loss = {}".format(np.linalg.norm(a_s[-1]-y_batch) ))