RNN(Recurrent Neural Network)的几个难点
1. vanish of gradient
RNN的error相对于某个时间点t的梯度为:
\(\frac{\partial E_t}{\partial W}=\sum_{k=1}^{t}\frac{\partial E_t}{\partial y_t}\frac{\partial y_t}{\partial h_i}\frac{\partial h_t}{\partial h_k}\frac{\partial h_k}{\partial W}\) (公式1),
其中\(h\)是hidden node的输出,\(y_t\)是网络在t时刻的output,\(W\)是hidden nodes 到hidden nodes的weight,而\(\frac{\partial h_t}{\partial h_k}\)是导数在时间段[k,t]上的链式展开,这段时间可能很长,会造成vanish或者explosion gradiant。将\(\frac{\partial h_t}{\partial h_k}\)沿时间展开:\(\frac{\partial h_t}{\partial h_k}=\prod_{j=k+1}^{t}\frac{\partial h_j}{\partial h_{j-1}}=\prod_{j=k+1}^{t}W^T \times diag [\frac{\partial\sigma(h_{j-1})}{\partial h_{j-1}}]\)。上式中的diag矩阵是个什么鬼?我来举个例子,你就明白了。假设现在要求解\(\frac{\partial h_5}{\partial h_4}\),回忆向前传播时\(h_5\)是怎么得到的:\(h_5=W\sigma(h_4)+W^{hx}x_4\),则\(\frac{\partial h_5}{\partial h_4}=W\frac{\partial \sigma(h_4)}{\partial h_4}\),注意到\(\sigma(h_4)\)和\(h_4\)都是向量(维度为D),所以\(\frac{\partial \sigma(h_4)}{\partial h_4}\)是Jacobian矩阵也即:\(\frac{\partial \sigma(h_4)}{\partial h_4}=\) \(\begin{bmatrix} \frac{\partial\sigma_1(h_{41})}{\partial h_{41}}&\cdots&\frac{\partial\sigma_1(h_{41})}{\partial h_{4D}} \\ \vdots&\cdots&\vdots \\ \frac{\partial\sigma_D(h_{4D})}{\partial h_{41}}&\cdots&\frac{\partial\sigma_D(h_{4D})}{\partial h_{4D}}\end{bmatrix}\),明显的,非对角线上的值都是0。这是因为sigmoid logistic function \(\sigma\)是element-wise的操作。
后面推导vanish或者explosion gradiant的过程就很简单了,我就不写了,请参考http://cs224d.stanford.edu/lecture_notes/LectureNotes4.pdf 中的公式(14)往后部分。
2. weight shared (tied) 时, the gradient of tied weight = sum of gradient of individual weights
举个例子你就明白了:假设有向前传播\(y=F[W_1f(W_2x)]\), 且weights \(W_1\) \(W_2\) tied, 现在要求gradient \(\frac{\partial y}{\partial W}\)
办法一:
先求gradient \(\frac{\partial F[]}{\partial W_2} = F'[]f() \)
再求gradient \(\frac{\partial F[]}{\partial W_1} = F'[] (W_2f'()x) \)
将上两式相加后得,\(F'[]f()+F'[] (W_2f'()x)=F'[](f()+W_2f'()x)\)
假设weights \(W_1\) \(W_2\) tied,则上式=\(F'[](f()+Wf'()x) = \frac{\partial y}{\partial W} \)
办法二:
现在我们换个办法,在假设weights \(W_1\) \(W_2\) tied的基础上,直接求gradient
\(\frac{\partial y}{\partial W} = F'[]( \frac{\partial Wf()}{\partial W} + W \frac{\partial f()}{\partial W} ) = F'[](f()+Wf'()x) \)
可见,两种方法的结果是一样的。所以,当权重共享时,关于权重的梯度=两个不同权重梯度的和。
3. LSTM & Gated Recurrent units 是如何避免vanish的?
To understand this, you will have to go through some math. The most accessible article wrt recurrent gradient problems IMHO is Pascanu's ICML2013 paper [1].
A summary: vanishing/exploding gradient comes from the repeated application of the recurrent weight matrix [2]. That the spectral radius of the recurrent weight matrix is bigger than 1 makes exploding gradients possible (it is a necessary condition), while a spectral radius smaller than 1 makes it vanish, which is a sufficient condition.
Now, if gradients vanish, that does not mean that all gradients vanish. Only some of them, gradient information local in time will still be present. That means, you might still have a non-zero gradient--but it will not contain long term information. That's because some gradient g + 0 is still g. (上文中公式1,因为是相加,所以有些为0,也不会引起全部为0)
If gradients explode, all of them do. That is because some gradient g + infinity is infinity.(上文中公式1,因为是相加,所以有些为无限大,会引起全部为无限大)
That is the reason why LSTM does not protect you from exploding gradients, since LSTM also uses a recurrent weight matrix(h(t) = o(t) ◦ tanh(c(t))?), not only internal state-to-state connections( c(t) = f (t) ◦ ˜c(t−1) +i(t) ◦ ˜c(t) h(t)). Successful LSTM applications typically use gradient clipping.
LSTM overcomes the vanishing gradient problem, though. That is because if you look at the derivative of the internal state at T to the internal state at T-1, there is no repeated weight application. The derivative actually is the value of the forget gate. And to avoid that this becomes zero, we need to initialise it properly in the beginning.
That makes it clear why the states can act as "a wormhole through time", because they can bridge long time lags and then (if the time is right) "re inject" it into the other parts of the net by opening the output gate.
[1] Pascanu, Razvan, Tomas Mikolov, and Yoshua Bengio. "On the difficulty of training recurrent neural networks." arXiv preprint arXiv:1211.5063 (2012).
[2] It might "vanish" also due to saturating nonlinearities, but that is sth that can also happen in shallow nets and can be overcome with more careful weight initialisations.
ref: Recursive Deep Learning for Natural Language Processing and Computer Vision.pdf
CS224D-3-note bp.pdf
未完待续。。。
RNN(Recurrent Neural Network)的几个难点的更多相关文章
- Recurrent Neural Network系列2--利用Python,Theano实现RNN
作者:zhbzz2007 出处:http://www.cnblogs.com/zhbzz2007 欢迎转载,也请保留这段声明.谢谢! 本文翻译自 RECURRENT NEURAL NETWORKS T ...
- Recurrent Neural Network系列3--理解RNN的BPTT算法和梯度消失
作者:zhbzz2007 出处:http://www.cnblogs.com/zhbzz2007 欢迎转载,也请保留这段声明.谢谢! 这是RNN教程的第三部分. 在前面的教程中,我们从头实现了一个循环 ...
- 循环神经网络(Recurrent Neural Network,RNN)
为什么使用序列模型(sequence model)?标准的全连接神经网络(fully connected neural network)处理序列会有两个问题:1)全连接神经网络输入层和输出层长度固定, ...
- Recurrent neural network (RNN) - Pytorch版
import torch import torch.nn as nn import torchvision import torchvision.transforms as transforms # ...
- 4.5 RNN循环神经网络(recurrent neural network)
自己开发了一个股票智能分析软件,功能很强大,需要的点击下面的链接获取: https://www.cnblogs.com/bclshuai/p/11380657.html 1.1 RNN循环神经网络 ...
- Recurrent Neural Network系列1--RNN(循环神经网络)概述
作者:zhbzz2007 出处:http://www.cnblogs.com/zhbzz2007 欢迎转载,也请保留这段声明.谢谢! 本文翻译自 RECURRENT NEURAL NETWORKS T ...
- Recurrent Neural Network(循环神经网络)
Reference: Alex Graves的[Supervised Sequence Labelling with RecurrentNeural Networks] Alex是RNN最著名变种 ...
- 循环神经网络(RNN, Recurrent Neural Networks)介绍(转载)
循环神经网络(RNN, Recurrent Neural Networks)介绍 这篇文章很多内容是参考:http://www.wildml.com/2015/09/recurrent-neur ...
- Recurrent Neural Network系列4--利用Python,Theano实现GRU或LSTM
yi作者:zhbzz2007 出处:http://www.cnblogs.com/zhbzz2007 欢迎转载,也请保留这段声明.谢谢! 本文翻译自 RECURRENT NEURAL NETWORK ...
- Recurrent Neural Network[Content]
下面的RNN,LSTM,GRU模型图来自这里 简单的综述 1. RNN 图1.1 标准RNN模型的结构 2. BiRNN 3. LSTM 图3.1 LSTM模型的结构 4. Clockwork RNN ...
随机推荐
- 1、libgdx简介
Libgdx 是一个跨平台和可视化的的开发框架.它当前支持Windows,Linux,Mac OS X,Android,IOS和HTML5作为目标平台. Libgdx允许你一次编写代码不经修改部署到多 ...
- 供应商信息全SQL
SELECT hou.name, pv.vendor_name 供应商, pv.party_id, pvs.vendor_site_id, pvs.terms_id, pv.vendor_name_a ...
- struts2 easyui实现datagrid的crud
最近两天因为项目需要,接触了easyui,要用它的datagrid实现crud.第一次做,花了一天时间才完成所有功能,昨天做另外一个模块,同样的功能只用了两个小时. 现在把第一次做datagrid时遇 ...
- Android官方技术文档翻译——开发工具的构建概述
本文译自Android官方技术文档<Build Overview>,原文地址:http://tools.android.com/build. 因为<Android Lint Chec ...
- 【编程练习】kmp算法代码
代码来自: http://blog.csdn.net/v_JULY_v #include "StdAfx.h" #include <iostream> using na ...
- 用C语言将一个数开根号后再取倒数的方法
在上学的时候,曾经看过有人写过这样的算法,就是将一个数开根号后再取倒数的算法,我本人也觉得十分巧妙,于是就将它积累了下来,让我们来看看是怎么回事: #include <stdio.h> # ...
- android studio比较长用的几款插件
不懂安装studio插件,看参考博文:android stuido插件安装:http://blog.csdn.net/liang5630/article/details/46372447 1.Butt ...
- android EventBus详解(一)
EventBus 是一款针对Android优化的发布/订阅事件总线.主要功能是替代Intent, Handler, BroadCast 在 Fragment,Activity,Service,线程之间 ...
- SharePoint2010搜索的简单设置
1. 开启搜索服务,管理中心 – 应用程序管理 – 服务应用程序 – 管理服务器上的服务 2. 点击进去,启动"SharePoint Foundation搜索"."S ...
- Github上的原文XMPP环境搭建步骤,英语能力差不多的可以看看
Getting started using XMPPFramework on iOS Here is a post on StackOverflow describing how to install ...