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BP??????????????????????????????????????????????????????????????????????????BP?????????????????????????
?????BP????????????????????????????????????PyTorch?TensorFlow??????????????????????????????????????????????????????????????Numpy????BP?????????????????
???????????Numpy???BP????????????????????????????????????????????
????4?????????????????784??????128????1??64????2??10??????????????784?128?128?64?64?10?10?1???????????????
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???????Sigmoid???????????
Sigmoid(x) = 1/(1 + e^(-x))
Sigmoid'(x) = Sigmoid(x) * (1 - Sigmoid(x))
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data ??????MNIST??????????mnist.pkl.gzmnist_loader.py?????MNIST???BP_Numpy.py?BP??????????????????????
def initialize_weights(shape): np.random.seed(42) return np.random.randn(*shape)
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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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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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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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0.1100010???????????????????????????????????????
??????????????????BP???????????????????????????????????????????Numpy????????????????
????BP????????????????PaperWeekly??????????????????
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