错误尺寸的XOR神经网络python

Question

我正在尝试在python中建立一个具有隐藏层的XOR神经网络，但是我遇到了尺寸问题，由于数学看起来很简单，所以我不知道为什么我得到了错误的尺寸对我正确。

尺寸问题从反向传播部分开始，已注释。错误具体是

  File "nn.py", line 52, in <module>
    d_a1_d_W1 = inp * deriv_sigmoid(z1) 
  File "/usr/local/lib/python3.7/site-packages/numpy/matrixlib/defmatrix.py", line 220, in __mul__
    return N.dot(self, asmatrix(other))
ValueError: shapes (1,2) and (3,1) not aligned: 2 (dim 1) != 3 (dim 0)

另外，为什么这里的sigmoid_derivative函数仅在我强制转换为numpy数组时才起作用？

代码：

import numpy as np

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def deriv_sigmoid(x):

  fx = np.array(sigmoid(x)) # gives dimensions issues unless I cast to array
  return fx * (1 - fx)

hiddenNeurons = 3
outputNeurons = 1
inputNeurons = 2

X = np.array( [ [0, 1]  ])
elem = np.matrix(X[0])
elem_row, elem_col = elem.shape


y = np.matrix([1])

W1 = np.random.rand(hiddenNeurons, elem_col)
b1 = np.random.rand(hiddenNeurons, 1)
W2 = np.random.rand(outputNeurons, hiddenNeurons)
b2 = np.random.rand(outputNeurons, 1)
lr = .01



for inp, ytrue in zip(X, y):
    inp = np.matrix(inp)

    # feedforward
    z1 = W1 * inp.T + b1 # get weight matrix1 * inputs + bias1
    a1 = sigmoid(z1) # get activation of hidden layer

    z2 = W2 * a1 + b2 # get weight matrix2 * activated hidden + bias 2
    a2 = sigmoid(z2) # get activated output 
    ypred = a2 # and call it ypred (y prediction)

    # backprop
    d_L_d_ypred = -2 * (ytrue - ypred) # derivative of mean squared error loss

    d_ypred_d_W2 = a1 * deriv_sigmoid(z2) # deriviative of y prediction with respect to weight matrix 2
    d_ypred_d_b2 = deriv_sigmoid(z2) # deriviative of y prediction with respect to bias 2

    d_ypred_d_a1 = W2 * deriv_sigmoid(z2) # deriviative of y prediction with respect to hidden activation

    d_a1_d_W1 = inp * deriv_sigmoid(z1) # dimensions issue starts here ––––––––––––––––––––––––––––––––

    d_a1_d_b1 = deriv_sigmoid(b1) 

    W1 -= lr * d_L_d_ypred * d_ypred_d_a1 * d_a1_d_W1
    b1 -= lr * d_L_d_ypred * d_ypred_d_a1 * d_a1_d_b1
    W2 -= lr * d_L_d_ypred * d_ypred_d_W2
    b2 -= lr * d_L_d_ypred * d_ypred_d_b2

Answer 1

我从未尝试过使用神经网络。所以我不完全了解您要做什么。