文章标题

总结：此教程通过简单的例子介绍递归神经网络，很简短的的python实现。

先给出代码:

import copy, numpy as np
np.random.seed(0)

# compute sigmoid nonlinearity
def sigmoid(x):
output = 1/(1+np.exp(-x))
return output

# convert output of sigmoid function to its derivative
def sigmoid_output_to_derivative(output):
return output*(1-output)

# training dataset generation
int2binary = {}
binary_dim = 8

largest_number = pow(2,binary_dim)
binary = np.unpackbits(
np.array([range(largest_number)],dtype=np.uint8).T,axis=1)
for i in range(largest_number):
int2binary[i] = binary[i]

# input variables
alpha = 0.1
input_dim = 2
hidden_dim = 16
output_dim = 1

# initialize neural network weights
synapse_0 = 2*np.random.random((input_dim,hidden_dim)) - 1
synapse_1 = 2*np.random.random((hidden_dim,output_dim)) - 1
synapse_h = 2*np.random.random((hidden_dim,hidden_dim)) - 1

synapse_0_update = np.zeros_like(synapse_0)
synapse_1_update = np.zeros_like(synapse_1)
synapse_h_update = np.zeros_like(synapse_h)

# training logic
for j in range(10000):

# generate a simple addition problem (a + b = c)
a_int = np.random.randint(largest_number/2) # int version
a = int2binary[a_int] # binary encoding

b_int = np.random.randint(largest_number/2) # int version
b = int2binary[b_int] # binary encoding

# true answer
c_int = a_int + b_int
c = int2binary[c_int]

# where we'll store our best guess (binary encoded)
d = np.zeros_like(c)

overallError = 0

layer_2_deltas = list()
layer_1_values = list()
layer_1_values.append(np.zeros(hidden_dim))

# moving along the positions in the binary encoding
for position in range(binary_dim):

# generate input and output
X = np.array([[a[binary_dim - position - 1],b[binary_dim - position - 1]]])
y = np.array([[c[binary_dim - position - 1]]]).T

# hidden layer (input ~+ prev_hidden)
layer_1 = sigmoid(np.dot(X,synapse_0) + np.dot(layer_1_values[-1],synapse_h))

# output layer (new binary representation)
layer_2 = sigmoid(np.dot(layer_1,synapse_1))

# did we miss?... if so, by how much?
layer_2_error = y - layer_2
layer_2_deltas.append((layer_2_error)*sigmoid_output_to_derivative(layer_2))
overallError += np.abs(layer_2_error[0])

# decode estimate so we can print it out
d[binary_dim - position - 1] = np.round(layer_2[0][0])

# store hidden layer so we can use it in the next timestep
layer_1_values.append(copy.deepcopy(layer_1))

future_layer_1_delta = np.zeros(hidden_dim)

for position in range(binary_dim):

X = np.array([[a[position],b[position]]])
layer_1 = layer_1_values[-position-1]
prev_layer_1 = layer_1_values[-position-2]

# error at output layer
layer_2_delta = layer_2_deltas[-position-1]
# error at hidden layer
layer_1_delta = (future_layer_1_delta.dot(synapse_h.T) + layer_2_delta.dot(synapse_1.T)) * sigmoid_output_to_derivative(layer_1)

# let's update all our weights so we can try again
synapse_1_update += np.atleast_2d(layer_1).T.dot(layer_2_delta)
synapse_h_update += np.atleast_2d(prev_layer_1).T.dot(layer_1_delta)
synapse_0_u
4000
pdate += X.T.dot(layer_1_delta)

future_layer_1_delta = layer_1_delta

synapse_0 += synapse_0_update * alpha
synapse_1 += synapse_1_update * alpha
synapse_h += synapse_h_update * alpha

synapse_0_update *= 0
synapse_1_update *= 0
synapse_h_update *= 0

# print out progress
if(j % 1000 == 0):
print "Error:" + str(overallError)
print "Pred:" + str(d)
print "True:" + str(c)
out = 0
for index,x in enumerate(reversed(d)):
out += x*pow(2,index)
print str(a_int) + " + " + str(b_int) + " = " + str(out)
print "------------"

按顺序背字母表我们都可以，但是如果要求倒着被字母表呢？是不是很困难。有个非常明显的逻辑在里面，我们学习字母表或者歌词并不像储存硬盘那样。我们更擅长从一个字母接着另一个字母的记忆，我们是按照序列（sequence）学习它。就像某种条件记忆，当有前面的记忆时候才会有下一时刻的记忆。

像关联列表那样存储记忆会非常有效。如果建模成一个短的条件记忆，一些过程/问题/表达/搜索会非常有效。

如果你的数据是一个序列，那么记忆就非常重要。（意味着需要记忆某些东西！）

神经网络有隐藏层。通常，隐层只基于你的输入，常见的神经网络信息流像这样：

input -> hidden -> output

这个很直白。特定的输入产生特定的隐层，特定的隐层产生特定的输出层。就像一个封闭的系统。记忆能够改变这个。记忆意味着隐层是你当前时刻的输入与前一时刻隐层的结合：

(input + prev_hidden) -> hidden -> output

Why the hidden layer? Well, we could technically do this.

为什么是隐层呢？从技术上我们可以这样做：

(input + prev_input) -> hidden -> output

但是，这样我们就丢失了东西。我建议你坐下并且思考这两种信息之间的区别。给一些这是如何运作的小提示。这里我们有递归网络从前层隐层获取信息的4次迭代。

(input + empty_hidden) -> hidden -> output

(input + prev_hidden) -> hidden -> output

(input + prev_hidden) -> hidden -> output

(input + prev_hidden) -> hidden -> output

However, we’d be missing out. I encourage you to sit and consider the difference between these two information flows. For a lit1tle helpful hint, consider how this plays out. Here, we have 4 timesteps of a recurrent neural network pulling information from the previous hidden layer.