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BP???Numpy??????

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BP??????????????????????????????????????????????????????????????????????????BP?????????????????????????

?????BP????????????????????????????????????PyTorch?TensorFlow??????????????????????????????????????????????????????????????Numpy????BP?????????????????

???????????Numpy???BP????????????????????????????????????????????

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????4?????????????????784??????128????1??64????2??10??????????????784?128?128?64?64?10?10?1???????????????

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• ????784????
• ???1?128????
• ???2?64????
• ????10????

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• W1?784?128?
• W2?128?64?
• W3?64?10?
• W4?10?1?

???????Sigmoid???????????

Sigmoid(x) = 1/(1 + e^(-x))

Sigmoid'(x) = Sigmoid(x) * (1 - Sigmoid(x))

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1. ?????

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def initialize_weights(shape):
    np.random.seed(42)
    return np.random.randn(*shape)

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2. ????

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def forward_propagation(inputs, weights, biases):
    activation = sigmoid(np.dot(inputs, weights) + biases)
    return activation, weights, biases

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3. ????

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def backward_propagation(outputs, targets, weights, biases):
    loss = np.mean(np.sum((outputs - targets) ** 2))
    delta = (outputs - targets) * sigmoid_derivative(outputs - targets)
    gradients = np.dot(weights.T, delta) + biases.T
    return loss, gradients

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4. ????

?????????

def update_parameters(weights, biases, gradients, learning_rate):
    weights -= gradients[0] * learning_rate
    biases -= gradients[1] * learning_rate
    return weights, biases

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• ????0.1
• epoch??1000
• ?????10

???????????????????????????????????????

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??????????????????BP???????????????????????????????????????????Numpy????????????????

????BP????????????????PaperWeekly??????????????????

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