1、__init__

代码：

    def __init_(self, sizes):
        self.num_layers = len(sizes)
        self.sizes = sizes
        self.biases = [ np.random.randn(y, 1) for y in sizes[1:] ]
        self.weights = [ np.random.randn(y, x) for x, y in zip(sizes[:-1], sizes[1:]) ] 

疑问：biases 和 weights 代码背后的生成过程

知识补充：np.random.randn(m, n)

• in:

      a = np.random.randn(3, 1)
      print(a)
  

• out:

      array([[-1.16708562],
             [-1.3747519 ],
             [ 1.53180853]])
  

解析：self.biases = [ np.random.randn(y, 1) for y in sizes[1:] ]

• in

      net = [3, 3, 4, 1]
      a = [np.random.randn(y, 1) for y in net[1:]]
      print(a)
  

• out:

      biases:
      [array([[-1.28584926],
              [-0.10648672],
              [ 0.96696939]]), 第二层
       array([[ 0.18739769],
              [ 0.31517292],
              [-0.93142655],
              [-1.34400024]]), 第三层
       array([[1.02909078]])]  第四层
  

解析：self.weights = [ np.random.randn(y, x) for x, y in zip(sizes[:-1], sizes[1:]) ]

• 易知：

      zip(sizes[:-1], sizes[1:]) == [(3, 3), (3, 4), (4, 1)]
  

• 结果应为：

      [
          np.random.randn(3, 3),
          np.random.randn(3, 4)，
          np.random.randn(4, 1)
      ]
  

• in

      a = [np.random.randn(y, x) for x, y in [(3, 3), (3, 4), (4, 1)]]
      a
  

• out

      [array([[ 0.92428425,  1.30627121,  0.33581147],
              [-2.20627075, -0.93125026, -0.30980836],
              [ 1.39007824, -2.07998321, -0.25047032]]),
       array([[-0.31758724, -1.98424497,  0.02881466],
              [ 0.37809777, -0.32856453, -0.07872715],
              [ 0.76281222,  2.61967303, -0.34342589],
              [-0.99639051, -0.9156387 , -0.78856185]]),
       array([[-1.17977103, -1.35824605, -1.02660058, -0.52706551]])]
  

1、sigmoid

代码：

def sigmoid(z):
    return 1.0 / (1.0 + np.exp(-z))

补充：np.exp()

• in:

    a = np.exp(1)
    a

• out:

2.718281828459045