我已经实现了一个简单的神经网络。它与“sigmoid+cross-entropy”、“sigmoid+quadratic-cost”和“tanh+quadratic-cost”很好地协同工作，但与“tanh+cross-entropy”没有协同工作（不比随机猜测好）。有谁能帮我弄清楚原因吗？只需查看FullConnectedLayer的代码：
class FullConnectedLayer(BaseLayer):
"""
FullConnectedLayer
~~~~~~~~~~~~~~~~~~~~
Data members:
sizes ---- <type list> sizes of the network
n_layers ---- <type int> number of sublayers
activation ---- <type Activation> activation function for neurons
weights ---- <type list> to store weights
biases ---- <type list> to store biases
neurons ---- <type list> to store states (outputs) of neurons
zs ---- <type list> to store weighted inputs to neurons
grad_w ---- <type list> to store gradient of Cost w.r.t weights
grad_b ---- <type list> to store gradient of Cost w.r.t biases
---------------------
Methods:
__init__(self, sizes, activation = Sigmoid())
size(self)
model(self)
feedforward(self, a)
backprop(self, C_p)
update(self, eta, lmbda, batch_size, n)
"""
def __init__(self, sizes, activation = Sigmoid(), normal_initialization = False):
"""
The list ''sizes'' contains the number of neurons in repective layers
of the network. For example, sizes = [2, 3, 2] represents 3 layers, with
the first layer having 2 neurons, the second 3 neurons, and the third 2
neurons.
Note that the input layer may be passed by other layer of another type
when connected after the layer, and we don't set biases for this layer.
Also note that the output layer my be passed to other layer if connected
before the layer, in this case, just assign the outputs to its inputs.
For examle, Layer1([3, 2, 4])->Layer2([4, 6, 3])->Layer3([3, 2]). Just
assign the output of Layer1 to the input Layer2, it will be safe.
"""
BaseLayer.__init__(self, sizes, activation)
if normal_initialization:
self.weights = [np.random.randn(j, i)
for i, j in zip(sizes[:-1], sizes[1:])]
else:
self.weights = [np.random.randn(j, i) / np.sqrt(i)
for i, j in zip(sizes[:-1], sizes[1:])]
self.biases = [np.random.randn(j, 1) for j in sizes[1:]]
self.grad_w = [np.zeros(w.shape) for w in self.weights]
self.grad_b = [np.zeros(b.shape) for b in self.biases]
def feedforward(self, a):
"""
Return output of the network if ''a'' is input.
"""
self.neurons = [a] # to store activations (outputs) of all layers
self.zs = []
for w, b in zip(self.weights, self.biases):
z = np.dot(w, self.neurons[-1]) + b
self.zs.append(z)
self.neurons.append(self.activation.func(z))
return self.neurons[-1]
def backprop(self, Cp_a):
"""
Backpropagate the delta error.
------------------------------
Return a tuple whose first component is a list of the gradients of
weights and biases, whose second component is the backpropagated delta.
Cp_a, dC/da: derivative of cost function w.r.t a, output of neurons.
"""
# The last layer
delta = Cp_a * self.activation.prime(self.zs[-1])
self.grad_b[-1] += delta
self.grad_w[-1] += np.dot(delta, self.neurons[-2].transpose())
for l in range(2, self.n_layers):
sp = self.activation.prime(self.zs[-l]) # a.prime(z)
delta = np.dot(self.weights[-l + 1].transpose(), delta) * sp
self.grad_b[-l] += delta
self.grad_w[-l] += np.dot(delta, self.neurons[-l - 1].transpose())
Cp_a_out = np.dot(self.weights[0].transpose(), delta)
return Cp_a_out
def update(self, eta, lmbda, batch_size, n):
"""
Update the network's weights and biases by applying gradient descent
algorithm.
''eta'' is the learning rate
''lmbda'' is the regularization parameter
''n'' is the total size of the training data set
"""
self.weights = [(1 - eta * (lmbda/n)) * w - (eta/batch_size) * delta_w\
for w, delta_w in zip(self.weights, self.grad_w)]
self.biases = [ b - (eta / batch_size) * delta_b\
for b, delta_b in zip(self.biases, self.grad_b)]
# Clear ''grad_w'' and ''grad_b'' so that they are not added to the
# next update pass
for dw, db in zip(self.grad_w, self.grad_b):
dw.fill(0)
db.fill(0)
下面是tanh函数的代码：
class Tanh(Activation):
@staticmethod
def func(z):
""" The functionality. """
return (np.exp(z) - np.exp(-z)) / (np.exp(z) + np.exp(-z))
@staticmethod
def prime(z):
""" The derivative. """
return 1. - Tanh.func(z) ** 2
下面是交叉熵类的代码：
class CrossEntropyCost(Cost):
@staticmethod
def func(a, y):
"""
Return the cost associated with an output ''a'' and desired output
''y''.
Note that np.nan_to_num is used to ensure numerical stability. In
particular, if both ''a'' and ''y'' have a 1.0 in the same slot,
then the expression (1-y) * np.log(1-a) returns nan. The np.nan_to_num
ensures that that is converted to the correct value(0.0).
"""
for ai in a:
if ai < 0:
print("in CrossEntropyCost.func(a, y)... require a_i > 0, a_i belong to a.")
exit(1)
return np.sum(np.nan_to_num(-y * np.log(a) - (1-y) * np.log(1-a)))
@staticmethod
def Cp_a(a, y):
"""
Cp_a, dC/da: the derivative of C w.r.t a
''a'' is the output of neurons
''y'' is the expected output of neurons
"""
#return (a - y) # delta
return (a - y) / (a * (1 - a))
编辑：
似乎问题在于
tanh的范围是-1到+1，这对于交叉熵是非法的。但如果我只需要一个tanh激活和一个交叉熵代价，我应该如何处理它？ 最佳答案
看起来您在输出层中使用了tanh，其中tanh的范围是-1, +1，预期的输出在0, +1的范围内。这对于在Sigmoid范围内产生输出的0, +1来说并不重要。