调试神经网络的前馈传播

Question

我正在实现一个神经网络的正向传播。

这是我的train方法：

def train(self, x, y):
for layer in self.layers:
prediction = layer.forward_prop(x.T)  # column vector

这就是forward_prop方法：

def forward_prop(self, x):
if self.is_input:
self.out = x
else:
# bug here: x has to be updated according to previous layer's output!
w_sum = np.dot(self.weight, x) + self.bias
self.out = self.activation(w_sum)
return self.out

有一个错误，因为第2层试图将self.weight和x相乘，而不是前一层的输出：

ValueError: shapes (4,4) and (2,1) not aligned: 4 (dim 1) != 2 (dim 0)

这就是我想要的：

• 第0层(输入层(：返回z^(0) = x
• 第1层(第一个隐藏层(：返回z^(1) = sig(W^(1) @ z^(0) + b^(1))
• 第二层(第二个隐藏层(：返回z^(2) = sig(W^(2) @ z^(1) + b^(2))
• 第3层(输出(：返回z^(3) = sig(W^(3) @ z^(2) + b^(3))
• 第i层：返回z^(i) = sig(W^(i) @ z^(i-1) + b^(i))

如何存储上一层的输出？

这是我可复制的例子：

import numpy as np
def sigmoid(x):
return 1 / (1 + np.exp(-x))
class NeuralNetwork:
def __init__(self):
self.layers = []
def add_layer(self, layer):
self.layers.append(layer)
def create(self):
for i, layer in enumerate(self.layers):
if i == 0:
layer.is_input = True
else:
layer.init_parameters(self.layers[i - 1].neurons)
def summary(self):
for i, layer in enumerate(self.layers):
print("Layer", i)
print("neurons:", layer.neurons)
print("is_input:", layer.is_input)
print("act:", layer.activation)
print("weight:", np.shape(layer.weight))
print(layer.weight)
print("bias:", np.shape(layer.bias))
print(layer.bias)
print("")
def train(self, x, y):
for layer in self.layers:
prediction = layer.forward_prop(x.T)  # column vector

class Layer:
def __init__(self, neurons, is_input=False, activation=None):
self.out = None
self.weight = None
self.bias = None
self.neurons = neurons
self.is_input = is_input
self.activation = activation
def init_parameters(self, prev_layer_neurons):
self.weight = np.asmatrix(np.random.normal(0, 0.5, (self.neurons, prev_layer_neurons)))
self.bias = np.asmatrix(np.random.normal(0, 0.5, self.neurons)).T  # column vector
if self.activation is None:
self.activation = sigmoid
def forward_prop(self, x):
if self.is_input:
self.out = x
else:
w_sum = np.dot(self.weight, x) + self.bias  # Bug
self.out = self.activation(w_sum)
return self.out

if __name__ == '__main__':
net = NeuralNetwork() 
d = 2  # input dimension 
c = 1  # output
for m in (d, 4, 4, c):
layer = Layer(m) 
net.add_layer(layer)
net.create()
# net.summary()  # dbg
# Training set
X = np.asmatrix([
[0, 0],
[0, 1],
[1, 0],
[1, 1]
])
y = np.asarray([0, 0, 1, 0])
net.train(X[2], y[2])

Answer 1

我只是用这种方式解决了：

def train(self, x, y):
z = x.T
for layer in self.layers:
z = layer.forward_prop(z)