BP算法是神经网络的基础，也是最重要的部分。由于误差反向传播的过程中，可能会出现梯度消失或者爆炸，所以需要调整损失函数。在LSTM中，通过sigmoid来实现三个门来解决记忆问题，用tensorflow实现的过程中，需要进行梯度修剪操作，以防止梯度爆炸。RNN的BPTT算法同样存在着这样的问题，所以步数超过5步以后，记忆效果大大下降。LSTM的效果能够支持到30多步数，太长了也不行。如果要求更长的记忆，或者考虑更多的上下文，可以把多个句子的LSTM输出组合起来作为另一个LSTM的输入。下面上传用Python实现的普通DNN的BP算法，激活为sigmoid.
字迹有些潦草，凑合用吧，习惯了手动绘图，个人习惯。后面的代码实现思路是最重要的：每个层有多个节点，层与层之间单向链接（前馈网络），因此数据结构可以设计为单向链表。实现的过程属于典型的递归，递归调用到最后一层后把每一层的back_weights反馈给上一层，直到推导结束。上传代码(未经过优化的代码)：
测试代码：
import numpy as np
import NeuralNetWork as nw if __name__ == '__main__':
print("test neural network") data = np.array([[1, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 1]]) np.set_printoptions(precision=3, suppress=True) for i in range(10):
network = nw.NeuralNetWork([8, 20, 8])
# 让输入数据与输出数据相等
network.fit(data, data, learning_rate=0.1, epochs=150) print("\n\n", i, "result")
for item in data:
print(item, network.predict(item))
#NeuralNetWork.py
# encoding: utf-8
#NeuralNetWork.py
import numpy as np; def logistic(inX):
return 1 / (1+np.exp(-inX)) def logistic_derivative(x):
return logistic(x) * (1 - logistic(x)) class Neuron:
'''
构建神经元单元，每个单元都有如下属性：1.input;2.output;3.back_weight;4.deltas_item;5.weights.
每个神经元单元更新自己的weights,多个神经元构成layer,形成weights矩阵
'''
def __init__(self,len_input):
#输入的初始参数，随机取很小的值(<0.1)
self.weights = np.random.random(len_input) * 0.1
#当前实例的输入
self.input = np.ones(len_input)
#对下一层的输出值
self.output = 1.0
#误差项
self.deltas_item = 0.0
# 上一次权重增加的量，记录起来方便后面扩展时可考虑增加冲量
self.last_weight_add = 0 def calculate_output(self,x):
#计算输出值
self.input = x;
self.output = logistic(np.dot(self.weights,self.input))
return self.output def get_back_weight(self):
#获取反馈差值
return self.weights * self.deltas_item def update_weight(self,target = 0,back_weight = 0,learning_rate=0.1,layer="OUTPUT"):
#更新权重
if layer == "OUTPUT":
self.deltas_item = (target - self.output) * logistic_derivative(self.input)
elif layer == "HIDDEN":
self.deltas_item = back_weight * logistic_derivative(self.input) delta_weight = self.input * self.deltas_item * learning_rate + 0.9 * self.last_weight_add #添加冲量
self.weights += delta_weight
self.last_weight_add = delta_weight class NetLayer:
'''
网络层封装，管理当前网络层的神经元列表
''' def __init__(self,len_node,in_count):
'''
:param len_node: 当前层的神经元数
:param in_count: 当前层的输入数
'''
# 当前层的神经元列表
self.neurons = [Neuron(in_count) for _ in range(len_node)];
# 记录下一层的引用，方便递归操作
self.next_layer = None def calculate_output(self,inX):
output = np.array([node.calculate_output(inX) for node in self.neurons])
if self.next_layer is not None:
return self.next_layer.calculate_output(output)
return output def get_back_weight(self):
return sum([node.get_back_weight() for node in self.neurons]) def update_weight(self,learning_rate,target):
layer = "OUTPUT"
back_weight = np.zeros(len(self.neurons))
if self.next_layer is not None:
back_weight = self.next_layer.update_weight(learning_rate,target)
layer = "HIDDEN"
for i,node in enumerate(self.neurons):
target_item = 0 if len(target) <= i else target[i]
node.update_weight(target = target_item,back_weight = back_weight[i],learning_rate=learning_rate,layer=layer)
return self.get_back_weight() class NeuralNetWork:
def __init__(self, layers):
self.layers = []
self.construct_network(layers)
pass def construct_network(self, layers):
last_layer = None
for i, layer in enumerate(layers):
if i == 0:
continue
cur_layer = NetLayer(layer, layers[i - 1])
self.layers.append(cur_layer)
if last_layer is not None:
last_layer.next_layer = cur_layer
last_layer = cur_layer def fit(self, x_train, y_train, learning_rate=0.1, epochs=100000, shuffle=False):
'''''
训练网络, 默认按顺序来训练
方法 1：按训练数据顺序来训练
方法 2: 随机选择测试
:param x_train: 输入数据
:param y_train: 输出数据
:param learning_rate: 学习率
:param epochs:权重更新次数
:param shuffle:随机取数据训练
'''
indices = np.arange(len(x_train))
for _ in range(epochs):
if shuffle:
np.random.shuffle(indices)
for i in indices:
self.layers[0].calculate_output(x_train[i])
self.layers[0].update_weight(learning_rate, y_train[i])
pass def predict(self, x):
return self.layers[0].calculate_output(x)