创建神经网络来确定 XOR 门

Question

I am trying to create aa simple neural network that determines an XOR gate in Python for my class assignment, but I keep getting an error. Below is my code and corresponding error:

logic_inputs = np.array(logic_inputs)
logic_inputs

class Layer():

    def __init__(self, W, b):
        self.m = W.shape[0]
        self.n = W.shape[1]
        self.W = W
        self.b = b

   def activate(self, X):
       z = np.dot(X, self.W) + self.b
       return sigmoid(z)

W1 = np.array([[20], 
               [20]])

b1 = np.array([[-30]])

W2 = np.array([[-20], 
               [-20]])

b2 = np.array([[10]])

hidden_layer = Layer(W1, b1)
output_layer = Layer(W2, b2)

class Network():

   def __init__(self, hidden, output):
      self.hidden = hidden
      self.output = output

   def activate(self, X):
      z = self.hidden.activate(X)

      return self.output.activate(z)

xor_gate = Network(hidden_layer, output_layer)

xor_output = xor_gate.activate(X)
np.round(xor_output)

Error

ValueError                                Traceback (most recent call last)
<ipython-input-83-84793a680685> in <module>
     40 xor_gate = Network(hidden_layer, output_layer)
     41 
---> 42 xor_output = xor_gate.activate(X)
     43 np.round(xor_output)

<ipython-input-83-84793a680685> in activate(self, X)
     36     z = self.hidden.activate(X)
     37 
---> 38     return self.output.activate(z)
     39 
     40 xor_gate = Network(hidden_layer, output_layer)

<ipython-input-83-84793a680685> in activate(self, X)
     11 
     12   def activate(self, X):
---> 13     z = np.dot(X, self.W) + self.b
     14     return sigmoid(z)
     15 

<__array_function__ internals> in dot(*args, **kwargs)

ValueError: shapes (4,1) and (2,1) not aligned: 1 (dim 1) != 2 (dim 0)

Answer 1

You are trying to calculate dot product between two matrices with shapes (4,1) and (2,1) which is not possible. Dot product can only be calculated if shape of matrices are following: (a, n), (n, b) which yields a matrix of shape (a, b). You should initialize your weights to be of shape (1, 2)