異或神經網絡 python

Question

我是個菜鳥，這是我嘗試做的 ML 中的第一件事。 我只想運行代碼。 我知道前饋是正確的，我的錯誤應該是正確的，但我得到的結果不正確。

請幫忙

import numpy as np
inputs = np.array([
    [[0],[0]],
    [[1],[0]],
    [[0],[1]],
    [[1],[1]]
])

expected_output = np.array([
    [[0]],
    [[1]],
    [[1]],
    [[0]]
])

epochs = 1000
lr = 0.01

hidden_weights = np.array([
    [0.2, 0.3],
    [0.4, 0.5]
])
hidden_bias = np.array([[0.3], [0.6]])

output_weights = np.array([[0.6, 0.7]])
output_bias = np.array([[0.5]])

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

def sigmoid_derivative(z):
    return np.multiply(sigmoid(z), sigmoid(1.0-z))

for _ in range(epochs):
    for index, input in enumerate(inputs):
        hidden_layer_activation = np.dot(hidden_weights, input)
        hidden_layer_activation += hidden_bias
        hidden_layer_output = sigmoid(hidden_layer_activation)

        output_layer_activation = np.dot(output_weights, hidden_layer_output)
        output_layer_activation += output_bias
        predicted_output = sigmoid(output_layer_activation)

        #Backpropagation
        output_errors = expected_output[index] - predicted_output
        hidden_errors = output_weights.T.dot(output_errors)

        d_predicted_output = output_errors * sigmoid_derivative(predicted_output)
        d_hidden_layer = hidden_errors * sigmoid_derivative(hidden_layer_output)

        # I am almost certain the problem is in the next 2 linees
        output_weights += d_predicted_output.dot(hidden_layer_output.T) * lr
        hidden_weights += d_hidden_layer.dot(input.T) * lr

        output_bias += np.sum(d_predicted_output,axis=0,keepdims=True) * lr
        hidden_bias += np.sum(d_hidden_layer,axis=0,keepdims=True) * lr

# NOW THE TESTING,I pass 2 input neurons. One with value 0 and value 1
test = np.array([
    [[0], [1]]
])

hidden_layer_activation = np.dot(hidden_weights, test[0])
hidden_layer_activation += hidden_bias
hidden_layer_output = sigmoid(hidden_layer_activation)

output_layer_activation = np.dot(output_weights, hidden_layer_output)
output_layer_activation += output_bias
predicted_output = sigmoid(output_layer_activation)

print(predicted_output) # I usually get somewhere around [[0.5]], and the ideal answer should be [[1]] since it is a XOR gate

結果：輸入 0 和 1 的 [[0.5]]

需要：[[1]] 用於輸入 0 和 1

這就是所有代碼......提前謝謝你我猜問題出在我更新權重和偏差的地方。 我正在做前向傳播的路徑，我得到了正確的結果。

Answer 1

問題必須是在反向傳播步驟中轉置和取點積。

我在 XOR 上的代碼：

import numpy as np

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

def sigmoid_derivative(z):
    return np.multiply(sigmoid(z), sigmoid(1.0-z))

def init_w(epsilon):

    # Input nodes
    theta1=2*np.random.random([2,3])*epsilon - epsilon

    # Output nodes
    theta2=2*np.random.random([1,3])*epsilon - epsilon

    theta1,theta2=np.mat(theta1),np.mat(theta2)

    return theta1,theta2

def fit(X, Y, theta1,theta2, predict=False, x=None):
    grad1,grad2=np.mat(np.zeros(np.shape(theta1))),np.mat(np.zeros(np.shape(theta2)))

    for i in range(len(X)):
        x = x if predict else X[i]
        y = Y[0,i]
        # forward propagate
        a = x

        a1=np.mat(np.append(1, a)).T
        z2=theta1*a1
        a2=sigmoid(z2)
        a2=np.mat(np.append(1, a2)).T
        z3=theta2*a2
        a3=sigmoid(z3)

        if predict: return a3

        # back propagate

        delta3 = a3 - y.T
        grad2 += delta3 * a2.T
        delta2 = np.multiply(theta2.T*delta3, sigmoid_derivative(a2))
        grad1 += (delta2[1:] * a1.T)

    return grad1,grad2


def predict(x):
    return fit(X, Y, theta1,theta2, True, x)


X = np.mat([[0,0],
            [0,1],
            [1,0],
            [1,1]])

Y = np.mat([0,1,1,0])

epochs = 10000
alpha = 0.85
epsilon = 1

theta1,theta2 = init_w(epsilon)

for i in range(epochs):
    g1,g2 = fit(X, Y, theta1,theta2)

    theta1 -= alpha * g1
    theta2 -= alpha * g2



for i in range(len(X)):
    x = X[i]
    guess = predict(x)
    print(x, ":", guess)

---

Output：

[[0 0]] : [[ 0.00233143]]
[[0 1]] : [[ 0.99775431]]
[[1 0]] : [[ 0.9977526]]
[[1 1]] : [[ 0.00233134]]

編輯：

您的數組格式太復雜，所以我建議您在每個步驟之后寫下形狀，以便您輕松調試。

更新：

import numpy as np 
#np.random.seed(0)

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

def sigmoid_derivative(x):
    return x * (1 - x)

#Input datasets
inputs = np.array([[0,0],[0,1],[1,0],[1,1]])
expected_output = np.array([[0],[1],[1],[0]])

epochs = 10000
lr = 0.1
inputLayerNeurons, hiddenLayerNeurons, outputLayerNeurons = 2,2,1

#Random weights and bias initialization
#hidden_weights = np.random.uniform(size=(inputLayerNeurons,hiddenLayerNeurons))
#hidden_bias =np.random.uniform(size=(1,hiddenLayerNeurons))
#output_weights = np.random.uniform(size=(hiddenLayerNeurons,outputLayerNeurons))
#output_bias = np.random.uniform(size=(1,outputLayerNeurons))

hidden_weights = np.array([
    [0.2, 0.3],
    [0.4, 0.5]
])
hidden_bias = np.array([[0.3, 0.6]])
output_weights = np.array([[0.6], [0.7]])
output_bias = np.array([[0.5]])


print("Initial hidden weights: ",end='')
print(*hidden_weights)
print("Initial hidden biases: ",end='')
print(*hidden_bias)
print("Initial output weights: ",end='')
print(*output_weights)
print("Initial output biases: ",end='')
print(*output_bias)


#Training algorithm
for _ in range(epochs):
    #Forward Propagation
    hidden_layer_activation = np.dot(inputs,hidden_weights)
    hidden_layer_activation += hidden_bias
    hidden_layer_output = sigmoid(hidden_layer_activation)

    output_layer_activation = np.dot(hidden_layer_output,output_weights)
    output_layer_activation += output_bias
    predicted_output = sigmoid(output_layer_activation)

    #Backpropagation
    error = expected_output - predicted_output
    d_predicted_output = error * sigmoid_derivative(predicted_output)

    error_hidden_layer = d_predicted_output.dot(output_weights.T)
    d_hidden_layer = error_hidden_layer * sigmoid_derivative(hidden_layer_output)

    #Updating Weights and Biases
    output_weights += hidden_layer_output.T.dot(d_predicted_output) * lr
    output_bias += np.sum(d_predicted_output,axis=0,keepdims=True) * lr
    hidden_weights += inputs.T.dot(d_hidden_layer) * lr
    hidden_bias += np.sum(d_hidden_layer,axis=0,keepdims=True) * lr

print("Final hidden weights: ",end='')
print(*hidden_weights)
print("Final hidden bias: ",end='')
print(*hidden_bias)
print("Final output weights: ",end='')
print(*output_weights)
print("Final output bias: ",end='')
print(*output_bias)

print("\nOutput from neural network after 10,000 epochs: ",end='')
print(*predicted_output)

test = np.array([
    [0, 1]
])


hidden_layer_activation = np.dot(test, hidden_weights)
hidden_layer_activation += hidden_bias
hidden_layer_output = sigmoid(hidden_layer_activation)

output_layer_activation = np.dot( hidden_layer_output, output_weights)
output_layer_activation += output_bias
predicted_output = sigmoid(output_layer_activation)

print(predicted_output)

---

Final hidden weights: [3.59882402 5.68799788] [3.60260363 5.70714658]
Final hidden bias: [-5.50709978 -2.3415549 ]
Final output weights: [-7.85976304] [7.26409199]
Final output bias: [-3.26766959]

Output from neural network after 10,000 epochs: [0.06525552] [0.93906737] [0.93899963] [0.06635071]
[[0.93907536]]

---

結果如下：

[[0.93907536]]