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 npnp.random.seed(0)# compute sigmoid nonlinearitydef sigmoid(x):    output = 1/(1+np.exp(-x))    return output# convert output of sigmoid function to its derivativedef sigmoid_output_to_derivative(output):    return output*(1-output)# training dataset generationint2binary = {}binary_dim = 8largest_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 variablesalpha = 0.1input_dim = 2hidden_dim = 16output_dim = 1# initialize neural network weightssynapse_0 = 2*np.random.random((input_dim,hidden_dim)) - 1synapse_1 = 2*np.random.random((hidden_dim,output_dim)) - 1synapse_h = 2*np.random.random((hidden_dim,hidden_dim)) - 1synapse_0_update = np.zeros_like(synapse_0)synapse_1_update = np.zeros_like(synapse_1)synapse_h_update = np.zeros_like(synapse_h)# training logicfor 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_update += 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.