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<p>这是一篇译文,<a href="https://colah.github.io/posts/2015-08-Understanding-LSTMs/">原文地址</a>.如果英文可以,建议直接看英文.</p>
<h1 id="循环神经网络-Recurrent-Neural-Networks"><a href="#循环神经网络-Recurrent-Neural-Networks" class="headerlink" title="循环神经网络(Recurrent Neural Networks)"></a>循环神经网络(Recurrent Neural Networks)</h1><p>在我们思考时,我们不会从头开始,肯定会在思考时加入之前的知识.就如同当你在阅读当前的博客时,你读的每个单词都是基于前面的单词.你不会扔掉所有的东西,然后在从头开始.你的想法有持久性.<br>传统的神经网络不能使用之前信息.假设你使用传统神经网络来将一部电影中的正在发生的事件分类,怎么使用当前事件之前的信息是很困难的.<br>循环神经网络解决了这个问题,在其中有循环,允许信息能够保持.<br><img src="/Understanding-LSTM-Networks/RNN-rolled.png" class="" title="Recurrent Neural Networks have loops."><br>这个图看起来有点奇怪,我们可以将其展开,如下图所示<br><img src="/Understanding-LSTM-Networks/RNN-unrolled.png" class="" title="An unrolled recurrent neural network"><br>从图中可以看出,RNN使用了前一时刻的状态来预测当前的状态<br>RNN在很多领域都取得了成功,比如:语音识别,自然语言处理,翻译,图像字幕等等.这里Andrej Karpathy的<a href="http://karpathy.github.io/2015/05/21/rnn-effectiveness/">blog</a>,里面列举了RNN一些应用.<br>本文主要介绍LSTM模型,LSTM模型是RNN的一种变种,在很多领域的表现都要比一般的RNN模型更好</p>
<h1 id="长期依赖存在的问题-The-Problem-of-Long-Term-Dependencies"><a href="#长期依赖存在的问题-The-Problem-of-Long-Term-Dependencies" class="headerlink" title="长期依赖存在的问题(The Problem of Long-Term Dependencies)"></a>长期依赖存在的问题(The Problem of Long-Term Dependencies)</h1><p>加入我们要基于之前的单词预测下一个单词,如”the clouds are in the <em>sky</em>“,我们要预测最后一个单词sky.在这个例子中,我们不需要更多的上下文,很明显最后一个单词是sky.RNN针对这种情况有很好的表现.<br><img src="/Understanding-LSTM-Networks/RNN-shorttermdepdencies.png" class=""><br>但是在有些情况下,我们需要更多的上下文.例如,我们要预测”I grew up in France… I speak fluent <em>French</em>.”中的最后一个单词French.从最近的信息,比如speak fluent等,可以推测最后一个单词是一种语言.但是如果要知道具体的语言,我们需要更多的上下文.预测点和其对应的相关信息之间的差距很大是由很大可能的.<br>但是,不幸的是随着差距增加,RNN不可能学会如何连接这种信息<br><img src="/Understanding-LSTM-Networks/RNN-longtermdependencies.png" class=""><br>从图中可以看出$h_{t+1}$不能很好地利用$X_0$和$X_1$的信息.理论上,RNN能够学习到长期依赖,但是在实践中,要想在RNN中使用这些长期依赖很困难.幸运的是LSTM模型解决了这个问题.</p>
<h1 id="LSTM网络-LSTM-Networks"><a href="#LSTM网络-LSTM-Networks" class="headerlink" title="LSTM网络(LSTM Networks)"></a>LSTM网络(LSTM Networks)</h1><p>LSTM全称Long Short Term Memory,长短期记忆网络.LSTM的设计就是为了避免长依赖问题,记忆长周期的信息是LSTM的默认行为.<br>所有的递归神经网络都具有重复模块的链式结构.在标准的RNN中,重复模块是一个非常简单的结构,例如单层tanh<br><img src="/Understanding-LSTM-Networks/LSTM3-SimpleRNN.png" class="" title="The repeating module in a standard RNN contains a single layer."><br>LSTM也有这种链式结构,但是重复的模块有一个不同的结构,在其中一个模块中,包含一个四层的神经网络,并且这四层以一种特别方式进行交互.<br><img src="/Understanding-LSTM-Networks/LSTM3-chain.png" class="" title="The repeating module in an LSTM contains four interacting layers."><br>图中的示例如下<br><img src="/Understanding-LSTM-Networks/LSTM2-notation.png" class=""><br>接下来我会详细介绍其中涉及的内容.</p>
<h1 id="LSTMs中的核心思想-The-Core-Idea-Behind-LSTMs"><a href="#LSTMs中的核心思想-The-Core-Idea-Behind-LSTMs" class="headerlink" title="LSTMs中的核心思想(The Core Idea Behind LSTMs)"></a>LSTMs中的核心思想(The Core Idea Behind LSTMs)</h1><p>LSTMs中的核心是单元状态,在图中就是最上面的那条水平线.单元状态就像是一条输送带.单元状态沿着整个链流动,对其只有一些线性作用,信息的流动很容易.<br><img src="/Understanding-LSTM-Networks/LSTM3-C-line.png" class=""><br>LSTM能够移除或者添加信息到单元状态,并且由成为门的结构来控制.门可以选择性的让信息通过或不通过,它是由sigmoid神经网络层和点积操作组成.<br><img src="/Understanding-LSTM-Networks/LSTM3-gate.png" class=""><br>sigmoid层的输出范围0-1,描述了可以通过多少的信息.输出为0意味着什么都不通过,输出为1意味着都能通过.从LSTM的结构中,我们可以看到LSTM的一个重复模块包括三个这样的门.</p>
<h1 id="一步一步认识LSTM"><a href="#一步一步认识LSTM" class="headerlink" title="一步一步认识LSTM"></a>一步一步认识LSTM</h1><p>LSTM的第一步就是决定从单元状态中丢弃哪些信息.这个决定是由一个称为”遗忘门(forget gate layer)”单层sigmoid层组成.它接收$h<em>{t-1}$和$x_t$作为输入,输出0到1之间的数字.对于前一个单元状态$C</em>{t-1}$,当遗忘门的输出为1时,表示完全保留$C<em>{t-1}$;当遗忘门的输出为0时,表示完全舍弃$C</em>{t-1}$.<br>我们在回到之前根据之前的内容来预测下一个单词这个问题.在这样的问题中,单元状态可能包括当前对象的性别,所以可以使用正确的代词.但是当遇到一个新的对象时,我们就想要忘记老对象的性别.<br><img src="/Understanding-LSTM-Networks/LSTM3-focus-f.png" class=""></p>
<blockquote>
<p>图中的$W<em>f \cdot [h</em>{t-1},x<em>t]$,大家看起来有些不清楚.个人认为比较合适的写法如下<br>$\sigma(W_fx_t + U_r h</em>{t-1} + b_f)$.大家可以参考下<a href="http://blog.echen.me/2017/05/30/exploring-lstms/">英文博客</a>,<a href="https://www.jiqizhixin.com/articles/2017-07-24-2">中文博客</a></p>
</blockquote>
<p>接下来这一步就是决定新信息中的哪些部分需要保存在单元状态中.这包括两个部分,第一部分是sigmoid层(input gate layer),决定更新的值.第二部分是一个tanh层,用来创建一个新的候选值.在下一步中,我们将会把这两个结合起来用来给单元状态做更新.在语言模型的例子中,这一步就代表我们将新对象的性别加入单元状态中,用来代替我们需要忘记的老对象性别.<br><img src="/Understanding-LSTM-Networks/LSTM3-focus-i.png" class=""><br>现在要把旧的单元状态$C_{t-1}$更新为$C_t$.上一步已经决定了更新的内容.我们把旧的单元状态乘以$f_t$,表示我们需要忘记的内容.然后将结果加上$i_t*\tilde{C_t}$,这表示将候选值进行缩放或者延伸.在语言模型的例子中,这表示我们从旧对象的性别中去除信息,然后加上新的信息.<br><img src="/Understanding-LSTM-Networks/LSTM3-focus-C.png" class=""><br>最终,我们需要决定输出的内容.输出内容基于单元状态,但是需要一些处理.首先,我们使用一个sigmoid层来决定单元状态的哪部分需要输出.然后,我们将单元状态经过tanh(将值限定在-1到1之间),在乘以sigmoid gate的输出.所以我们仅仅输出了我们决定的.<br>对于语言模型例子,因为网络之前看到了主语,所以接下来它可能想要输出的信息是关于动词的.例如,网络会根据主语的单数或复数来决定接下来动词的形式.<br><img src="/Understanding-LSTM-Networks/LSTM3-focus-o.png" class=""></p>
<h1 id="长短期记忆模型的其他形式-Variants-on-Long-Short-Term-Memory"><a href="#长短期记忆模型的其他形式-Variants-on-Long-Short-Term-Memory" class="headerlink" title="长短期记忆模型的其他形式(Variants on Long Short Term Memory)"></a>长短期记忆模型的其他形式(Variants on Long Short Term Memory)</h1><p>上面提到的是LSTM的一般形式.但是还有好多LSTM的一些变形,虽然变化不大.其中一个流行的LSTM变形是由<a href="ftp://ftp.idsia.ch/pub/juergen/TimeCount-IJCNN2000.pdf">Gers & Schmidhuber (2000)</a>提出.此模型添加了”peephole connections”,这意味着让门看到了单元状态.<br><img src="/Understanding-LSTM-Networks/LSTM3-var-peepholes.png" class=""><br>从图中可以看到模型对于所有的gate都添加了peepholes,但是有很多文章只添加了一些peepholes,而另一些则没有.</p>
<p>LSTM另一种变形是将input gate和forget gate进行耦合.这种网络不会单独的决定哪些内容需要忘记,哪些新的信息需要添加,而是一起做这些决定.当我们将要输入内容时,我们仅仅忘记;当我们忘记旧的内容时,我们仅仅输入一些新的值.模型的结构如下<br><img src="/Understanding-LSTM-Networks/LSTM3-var-tied.png" class=""></p>
<p>一种引入注意的LSTM变形是GRU(Gated Recurrent Unit),它将forget gate和input gate结合为一个单独的”update gate”.它同样融合了单元状态和隐藏状态以及一些其他的改变.GRU模型要比标准的LSTM模型简单,并且越来越流行.<br><img src="/Understanding-LSTM-Networks/LSTM3-var-GRU.png" class=""><br>这里仅仅列举了一些LSTM变形,还有很多其他的LSTM变形.比如Depth Gated RNNs by <a href="http://arxiv.org/pdf/1508.03790v2.pdf">Yao, et al. (2015)</a>.同时在解决长期依赖问题上,也有跟LSTM完全不同的方法,比如Clockwork RNNs by <a href="http://arxiv.org/pdf/1402.3511v1.pdf">Koutnik, et al. (2014)</a>.<br><a href="http://arxiv.org/pdf/1503.04069.pdf">Greff, et al. (2015)</a>对这些变形做了一个对比.<a href="http://jmlr.org/proceedings/papers/v37/jozefowicz15.pdf">Jozefowicz, et al. (2015)</a>测试很多的RNN结构,发现在一些特定的任务上比LSTM模型表现的更好的模型.</p>
<h1 id="参考"><a href="#参考" class="headerlink" title="参考"></a>参考</h1><p><a href="https://colah.github.io/posts/2015-08-Understanding-LSTMs/">colah博客</a><br><a href="http://blog.echen.me/2017/05/30/exploring-lstms/">echen博客</a></p>
<blockquote>
<p>echen博客中公式介绍的较为详细</p>
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