这是我的代码：
import numpy as np
import random
class Network:
#layers, biases, weights
def __init__(self, size):
self.nr_layers = len(size)
self.size = size
self.bias = [np.random.rand(y, 1) for y in size[1:]]
self.weights = [np.random.randn(x, y) for x, y in zip(size[1:], size[:-1])]
def feedfoward(self, a):
#a is activation of last layer(or input)
for b,w in zip(self.bias, self.weights):
a = sigmoid(np.dot(w, a) + b)
return(a)
def SGD(self, training_data, test_data, nr_epoch, mini_batch_size, learning_rate):
test_data = list(test_data)
training_data = list(training_data)
n_test_data = len(test_data)
n_training_data = len(training_data)
#build mini batches
for i in range(nr_epoch):
random.shuffle(training_data)
mini_batches = [training_data[j:j + mini_batch_size]
for j in range(0,n_training_data,mini_batch_size)]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch, learning_rate)
print("Epoch {} : {} / {}".format(i, self.evaluate(test_data), n_test_data))
def update_mini_batch(self, mini_batch, learning_rate):
bias_gradient = [np.zeros(b.shape) for b in self.bias]
weights_gradient = [np.zeros(w.shape) for w in self.weights]
#summing up gradients for weights and biases(calculate each gradient with backprop)
for x, y in mini_batch:
delta_b, delta_w = self.backprop(x, y)
bias_gradient = [b + db for b, db in zip(bias_gradient, delta_b)]
weights_gradient = [w + db for w, db in zip(weights_gradient, delta_w)]
#now we update original weights and biases with gradient descent formula
self.bias = [b - (learning_rate/len(mini_batch)) * change
for b, change in zip(self.bias, bias_gradient)]
self.weights = [w - (learning_rate/len(mini_batch)) * change
for w, change in zip(self.weights, weights_gradient)]
def backprop(self, x, y):
bias_gradient = [np.zeros(bias.shape) for bias in self.bias]
weights_gradient = [np.zeros(weights.shape) for weights in self.weights]
activation = x
activations = [x]
#zs are weighted inputs
zs = []
#FEEDFOWARD
for b, w in zip(self.bias, self.weights):
z = np.dot(w, activation) + b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
#BACKWARD PASS
#first last layer(backprop formula #1), then we assign BP3 and BP4
delta = self.last_layer_cost(activations[-1], y) * sigmoid_derivative(zs[-1])
bias_gradient = delta
weights_gradient = np.dot(delta, activations[-2].transpose())
#now we apply BP formula #2 to all others(l-2) layers, then we assign BP3 and BP4
#first layer in this loop is last layer before output(a^L)
for l in range(2, self.nr_layers):
delta = np.dot(self.weights[-l + 1].transpose(), delta) * sigmoid_derivative(zs[-l])
bias_gradient = delta
weights_gradient = np.dot(delta, activations[-l - 1].transpose())
return weights_gradient, weights_gradient
def last_layer_cost(self, last_layer_activation, y):
return(last_layer_activation - y)
def evaluation(self, test_data):
test_result = [(np.argmax(self.feedfoward(x), y)) for x, y in test_data]
return sum(int(x==y) for x, y in test_result)
def sigmoid(z):
return 1.0/(1.0 + np.exp(-z))
def sigmoid_derivative(z):
return sigmoid(z)*(1-sigmoid(z))
import pickle
import gzip
# Next part is copied from solutions
import numpy as np
def load_data():
"""Return the MNIST data as a tuple containing the training data,
the validation data, and the test data.
The ``training_data`` is returned as a tuple with two entries.
The first entry contains the actual training images. This is a
numpy ndarray with 50,000 entries. Each entry is, in turn, a
numpy ndarray with 784 values, representing the 28 * 28 = 784
pixels in a single MNIST image.
The second entry in the ``training_data`` tuple is a numpy ndarray
containing 50,000 entries. Those entries are just the digit
values (0...9) for the corresponding images contained in the first
entry of the tuple.
The ``validation_data`` and ``test_data`` are similar, except
each contains only 10,000 images.
This is a nice data format, but for use in neural networks it's
helpful to modify the format of the ``training_data`` a little.
That's done in the wrapper function ``load_data_wrapper()``, see
below.
"""
f = gzip.open('mnist.pkl.gz', 'rb')
training_data, validation_data, test_data = pickle.load(f, encoding="latin1")
f.close()
return (training_data, validation_data, test_data)
def load_data_wrapper():
"""Return a tuple containing ``(training_data, validation_data,
test_data)``. Based on ``load_data``, but the format is more
convenient for use in our implementation of neural networks.
In particular, ``training_data`` is a list containing 50,000
2-tuples ``(x, y)``. ``x`` is a 784-dimensional numpy.ndarray
containing the input image. ``y`` is a 10-dimensional
numpy.ndarray representing the unit vector corresponding to the
correct digit for ``x``.
``validation_data`` and ``test_data`` are lists containing 10,000
2-tuples ``(x, y)``. In each case, ``x`` is a 784-dimensional
numpy.ndarry containing the input image, and ``y`` is the
corresponding classification, i.e., the digit values (integers)
corresponding to ``x``.
Obviously, this means we're using slightly different formats for
the training data and the validation / test data. These formats
turn out to be the most convenient for use in our neural network
code."""
tr_d, va_d, te_d = load_data()
training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]
training_results = [vectorized_result(y) for y in tr_d[1]]
training_data = zip(training_inputs, training_results)
validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]
validation_data = zip(validation_inputs, va_d[1])
test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]
test_data = zip(test_inputs, te_d[1])
return (training_data, validation_data, test_data)
def vectorized_result(j):
"""Return a 10-dimensional unit vector with a 1.0 in the jth
position and zeroes elsewhere. This is used to convert a digit
(0...9) into a corresponding desired output from the neural
network."""
e = np.zeros((10, 1))
e[j] = 1.0
return e
################################################################################
training_data, validation_data, test_data = load_data_wrapper()
net = Network([784, 30, 10])
net.SGD(training_data, test_data, 30, 10, 3.0)
这是解决方案..从解决方案复制的部分位于文件mnist_loader.py中。
这是我的错误：
Traceback (most recent call last): File "C:/Users/PycharmProjects/MachineLearning/ex.py", line 157, in <module>
net.SGD(training_data, test_data, 30, 10, 3.0)
File "C:/Users/PycharmProjects/MachineLearning/ex.py", line 29, in SGD
self.update_mini_batch(mini_batch, learning_rate)
File "C:/Users/PycharmProjects/MachineLearning/ex.py", line 39, in update_mini_batch
weights_gradient = [w + db for w, db in zip(weights_gradient, delta_w)]
File "C:/Users/PycharmProjects/MachineLearning/ex.py", line 39, in <listcomp>
weights_gradient = [w + db for w, db in zip(weights_gradient, delta_w)]
ValueError: operands could not be broadcast together with shapes (10,30) (784,)
我是 DL 的初学者，对 python 和 numpy 的了解超过 2-3 个月，但我知道什么是广播......但是我无法修复此错误，所以任何人都可以看看这个并建议我如何解决它吗？ 最让我困惑的是，这条线与解决方案相同(我尝试过(。
哦，还有简短的术语评论： nabla_b，nabla_w bias_gradient，在我的版本中weights_gradient
我认为在self.backprop中，第一个返回的变量应该是bias_gradient，而不是weights_gradient。
只是一个小提示：我认为将批量大小更改为不同于 10 的大小可能有助于区分错误中的 10 是您的批量大小还是输出层大小。我曾经听说，2的幂在计算上是有效的，但我不确定:)