index_cn.html 46.9 KB
Newer Older
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34


<!DOCTYPE html>
<!--[if IE 8]><html class="no-js lt-ie9" lang="en" > <![endif]-->
<!--[if gt IE 8]><!--> <html class="no-js" lang="en" > <!--<![endif]-->
<head>
  <meta charset="utf-8">
  
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  
  <title>文本生成教程 &mdash; PaddlePaddle  文档</title>
  

  
  

  

  
  
    

  

  
  
    <link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
  

  
  
        <link rel="index" title="索引"
              href="../../genindex.html"/>
        <link rel="search" title="搜索" href="../../search.html"/>
35
    <link rel="top" title="PaddlePaddle  文档" href="../../index.html"/> 
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

  <link rel="stylesheet" href="https://cdn.jsdelivr.net/perfect-scrollbar/0.6.14/css/perfect-scrollbar.min.css" type="text/css" />
  <link rel="stylesheet" href="../../_static/css/override.css" type="text/css" />
  <script>
  var _hmt = _hmt || [];
  (function() {
    var hm = document.createElement("script");
    hm.src = "//hm.baidu.com/hm.js?b9a314ab40d04d805655aab1deee08ba";
    var s = document.getElementsByTagName("script")[0]; 
    s.parentNode.insertBefore(hm, s);
  })();
  </script>

  

  
  <script src="../../_static/js/modernizr.min.js"></script>

</head>

<body class="wy-body-for-nav" role="document">

  
  <header class="site-header">
    <div class="site-logo">
      <a href="/"><img src="../../_static/images/PP_w.png"></a>
    </div>
    <div class="site-nav-links">
      <div class="site-menu">
65
        <a class="fork-on-github" href="https://github.com/PaddlePaddle/Paddle" target="_blank"><i class="fa fa-github"></i>Fork me on Github</a>
66 67 68 69 70 71 72 73 74 75 76 77
        <div class="language-switcher dropdown">
          <a type="button" data-toggle="dropdown">
            <span>English</span>
            <i class="fa fa-angle-up"></i>
            <i class="fa fa-angle-down"></i>
          </a>
          <ul class="dropdown-menu">
            <li><a href="/doc_cn">中文</a></li>
            <li><a href="/doc">English</a></li>
          </ul>
        </div>
        <ul class="site-page-links">
78
          <li><a href="/">Home</a></li>
79 80 81 82
        </ul>
      </div>
      <div class="doc-module">
        
83
        <ul>
84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107
<li class="toctree-l1"><a class="reference internal" href="../../getstarted/index_cn.html">新手入门</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../howto/index_cn.html">进阶指南</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../api/index_cn.html">API</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../faq/index_cn.html">FAQ</a></li>
</ul>

        
<div role="search">
  <form id="rtd-search-form" class="wy-form" action="../../search.html" method="get">
    <input type="text" name="q" placeholder="Search docs" />
    <input type="hidden" name="check_keywords" value="yes" />
    <input type="hidden" name="area" value="default" />
  </form>
</div>        
      </div>
    </div>
  </header>
  
  <div class="main-content-wrap">

    
    <nav class="doc-menu-vertical" role="navigation">
        
          
108
          <ul>
109 110
<li class="toctree-l1"><a class="reference internal" href="../../getstarted/index_cn.html">新手入门</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../getstarted/build_and_install/index_cn.html">安装与编译</a><ul>
111
<li class="toctree-l3"><a class="reference internal" href="../../getstarted/build_and_install/docker_install_cn.html">PaddlePaddle的Docker容器使用方式</a></li>
112 113 114 115
<li class="toctree-l3"><a class="reference internal" href="../../getstarted/build_and_install/ubuntu_install_cn.html">Ubuntu部署PaddlePaddle</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../getstarted/build_and_install/cmake/build_from_source_cn.html">PaddlePaddle的编译选项</a></li>
</ul>
</li>
116
<li class="toctree-l2"><a class="reference internal" href="../../getstarted/concepts/use_concepts_cn.html">基本使用概念</a></li>
117 118 119 120 121 122 123 124 125 126 127 128 129
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../../howto/index_cn.html">进阶指南</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../../howto/usage/cmd_parameter/index_cn.html">设置命令行参数</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../howto/usage/cmd_parameter/use_case_cn.html">使用案例</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../howto/usage/cmd_parameter/arguments_cn.html">参数概述</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../howto/usage/cmd_parameter/detail_introduction_cn.html">细节描述</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../howto/usage/cluster/cluster_train_cn.html">运行分布式训练</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../howto/usage/k8s/k8s_basis_cn.html">Kubernetes 简介</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../howto/usage/k8s/k8s_cn.html">Kubernetes单机训练</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../howto/usage/k8s/k8s_distributed_cn.html">Kubernetes分布式训练</a></li>
130
<li class="toctree-l2"><a class="reference internal" href="../../howto/dev/build_cn.html">编译PaddlePaddle和运行单元测试</a></li>
131 132 133
<li class="toctree-l2"><a class="reference internal" href="../../howto/dev/write_docs_cn.html">如何贡献/修改文档</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../howto/dev/contribute_to_paddle_cn.html">如何贡献代码</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../howto/deep_model/rnn/index_cn.html">RNN相关模型</a><ul>
134
<li class="toctree-l3"><a class="reference internal" href="../../howto/deep_model/rnn/rnn_config_cn.html">RNN配置</a></li>
135 136 137 138 139 140 141 142
<li class="toctree-l3"><a class="reference internal" href="../../howto/deep_model/rnn/recurrent_group_cn.html">Recurrent Group教程</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../howto/deep_model/rnn/hierarchical_layer_cn.html">支持双层序列作为输入的Layer</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../howto/deep_model/rnn/hrnn_rnn_api_compare_cn.html">单双层RNN API对比介绍</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../howto/optimization/gpu_profiling_cn.html">GPU性能分析与调优</a></li>
</ul>
</li>
143
<li class="toctree-l1"><a class="reference internal" href="../../api/index_cn.html">API</a><ul>
144 145 146
<li class="toctree-l2"><a class="reference internal" href="../../api/v2/model_configs.html">模型配置</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../../api/v2/config/activation.html">Activation</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/v2/config/layer.html">Layers</a></li>
147
<li class="toctree-l3"><a class="reference internal" href="../../api/v2/config/evaluators.html">Evaluators</a></li>
148 149 150 151 152 153 154 155
<li class="toctree-l3"><a class="reference internal" href="../../api/v2/config/optimizer.html">Optimizer</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/v2/config/pooling.html">Pooling</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/v2/config/networks.html">Networks</a></li>
<li class="toctree-l3"><a class="reference internal" href="../../api/v2/config/attr.html">Parameter Attribute</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../../api/v2/data.html">数据访问</a></li>
<li class="toctree-l2"><a class="reference internal" href="../../api/v2/run_logic.html">训练与应用</a></li>
156 157
</ul>
</li>
158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582
<li class="toctree-l1"><a class="reference internal" href="../../faq/index_cn.html">FAQ</a></li>
</ul>

        
    </nav>
    
    <section class="doc-content-wrap">

      

 







<div role="navigation" aria-label="breadcrumbs navigation">
  <ul class="wy-breadcrumbs">
      
    <li>文本生成教程</li>
  </ul>
</div>
      
      <div class="wy-nav-content" id="doc-content">
        <div class="rst-content">
          <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
           <div itemprop="articleBody">
            
  <div class="section" id="">
<span id="id1"></span><h1>文本生成教程<a class="headerlink" href="#" title="永久链接至标题"></a></h1>
<p>在语言生成领域中,“序列到序列”(sequence to sequence)的方法已被证明是一种强大的模型。它可以被应用于进行机器翻译(machine translation)、query改写(query rewriting)、图像描述(image captioning)等等。</p>
<p>本篇教程将会指导你通过训练一个“序列到序列”的神经网络机器翻译(NMT)模型来将法语翻译成英语。</p>
<p>我们遵循 <a class="reference external" href="http://arxiv.org/abs/1409.0473">Neural Machine Translation by Jointly Learning to Align and Translate</a> 这篇文章,其中详细说明了模型架构,以及在WMT-14数据集上得到良好表现的训练过程。本篇教程在PaddlePaddle中重现了这一良好的训练结果。</p>
<p>我们感谢&#64;caoying的pull request,其中定义了模型架构和solver配置。</p>
<div class="section" id="">
<span id="id2"></span><h2>数据准备<a class="headerlink" href="#" title="永久链接至标题"></a></h2>
<div class="section" id="">
<span id="id3"></span><h3>下载与解压缩<a class="headerlink" href="#" title="永久链接至标题"></a></h3>
<p>从该链接 <a class="reference external" href="http://www-lium.univ-lemans.fr/~schwenk/cslm_joint_paper/">http://www-lium.univ-lemans.fr/~schwenk/cslm_joint_paper/</a> 下载WMT-14数据集,然后解压,并将Develop和Test数据分别放入不同的文件夹。</p>
<ul class="simple">
<li><strong>Train data</strong>: <a class="reference external" href="http://www-lium.univ-lemans.fr/~schwenk/cslm_joint_paper/data/bitexts.tgz">bitexts (选择过后的)</a></li>
<li><strong>Develop and Test data</strong>: <a class="reference external" href="http://www-lium.univ-lemans.fr/~schwenk/cslm_joint_paper/data/dev+test.tgz">dev 与 test 数据</a></li>
</ul>
<p>在Linux下,只需要简单地运行以下命令。否则你需要自己下载、解压、拆分到不同文件夹、并且分别重命名文件后缀。</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span><span class="nb">cd</span> demo/seqToseq/data
./wmt14_data.sh
</pre></div>
</div>
<p>我们会发现数据集 <code class="docutils literal"><span class="pre">wmt14</span></code> 中包含如下表所示的3个文件夹。</p>
<table border="2" cellspacing="0" cellpadding="6" rules="all" frame="border">
<colgroup>
<col  class="left" />
<col  class="left" />
<col  class="left" />
<col  class="left" />
</colgroup><thead>
<tr>
<th scope="col" class="left">folder name</th>
<th scope="col" class="left">French-English parallel corpora file</th>
<th scope="col" class="left">number of total file</th>
<th scope="col" class="left">size</th>
</tr>
</thead><tbody>
<tr>
<td class="left">train_data</td>
<td class="left">ccb2_pc30.src, ccb2_pc30.trg, etc</td>
<td class="left">12</td>
<td class="left">3.55G</td>
</tr><tr>
<td class="left">test_data</td>
<td class="left">ntst1213.src, ntst1213.trg</td>
<td class="left">2</td>
<td class="left">1636k</td>
</tr><tr>
<td class="left">gen_data</td>
<td class="left">ntst14.src, ntst14.trg</td>
<td class="left">2</td>
<td class="left">864k</td>
</tr>
</tbody>
</table>
<br/><ul class="simple">
<li>每个文件夹都包含法语到英语的平行语料库</li>
<li><strong>XXX.src</strong> 是原始法语文件;<strong>XXX.trg</strong> 是目标英语文件</li>
<li><strong>XXX.src</strong><strong>XXX.trg</strong> 的行数应该一致</li>
<li>每行都是一个法语或者英语的句子</li>
<li><strong>XXX.src</strong><strong>XXX.trg</strong> 中任意第i行的句子之间都有着一一对应的关系</li>
</ul>
</div>
<div class="section" id="">
<span id="id4"></span><h3>用户自定义数据集<a class="headerlink" href="#" title="永久链接至标题"></a></h3>
<p>如果你想进行诸如语义转述(Paraphrasing)等其他“序列到序列”的任务,你只需要按照如下方式组织数据,并将它们放在<code class="docutils literal"><span class="pre">demo/seqToseq/data</span></code>目录下:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">dataset</span>
  <span class="n">train</span>
    <span class="n">file1</span><span class="o">.</span><span class="n">src</span> <span class="n">file1</span><span class="o">.</span><span class="n">trg</span>
    <span class="n">file2</span><span class="o">.</span><span class="n">src</span> <span class="n">file2</span><span class="o">.</span><span class="n">trg</span>
    <span class="o">......</span>
  <span class="n">test</span>
    <span class="n">file1</span><span class="o">.</span><span class="n">src</span> <span class="n">file1</span><span class="o">.</span><span class="n">trg</span>
    <span class="n">file2</span><span class="o">.</span><span class="n">src</span> <span class="n">file2</span><span class="o">.</span><span class="n">trg</span>
    <span class="o">......</span>
  <span class="n">gen</span>
    <span class="n">file1</span><span class="o">.</span><span class="n">src</span> <span class="n">file1</span><span class="o">.</span><span class="n">trg</span>
    <span class="n">file2</span><span class="o">.</span><span class="n">src</span> <span class="n">file2</span><span class="o">.</span><span class="n">trg</span>
    <span class="o">......</span>
</pre></div>
</div>
<ul class="simple">
<li>一级目录:数据集文件夹名称</li>
<li>二级目录:train、test和gen这三个文件夹是固定的</li>
<li>三级目录:源语言到目标语言的平行语料库文件<ul>
<li><strong>XXX.src</strong> 是源语言的文件,<strong>XXX.trg</strong> 时目标语言的文件</li>
<li>文件中的每行都必须是一个句子</li>
<li><strong>XXX.src</strong><strong>XXX.trg</strong> 中任意第i行的句子之间都必须有着一一对应的关系</li>
</ul>
</li>
</ul>
</div>
</div>
<div class="section" id="">
<span id="id5"></span><h2>数据预处理<a class="headerlink" href="#" title="永久链接至标题"></a></h2>
<div class="section" id="">
<span id="id6"></span><h3>预处理工作流程<a class="headerlink" href="#" title="永久链接至标题"></a></h3>
<ul class="simple">
<li>将每个源语言到目标语言的平行语料库文件合并为一个文件:<ul>
<li>合并每个 <strong>XXX.src</strong><strong>XXX.trg</strong> 文件为 <strong>XXX</strong></li>
<li><strong>XXX</strong> 中的第i行 = <strong>XXX.src</strong> 中的第i行 + &#8216;\t&#8217; + <strong>XXX.trg</strong>中的第i行</li>
</ul>
</li>
<li>创建训练数据的“源字典”和“目标字典”,每个字典都有DICTSIZE个单词,包括:<ul>
<li>词频最高的(DICTSIZE - 3)个单词</li>
<li>3个特殊符号</li>
<li><code class="docutils literal"><span class="pre">&lt;s&gt;</span></code>:序列的开始</li>
<li><code class="docutils literal"><span class="pre">&lt;e&gt;</span></code>:序列的结束</li>
<li><code class="docutils literal"><span class="pre">&lt;unk&gt;</span></code>:未包含在字典中的单词</li>
</ul>
</li>
</ul>
</div>
<div class="section" id="">
<span id="id7"></span><h3>预处理命令和结果<a class="headerlink" href="#" title="永久链接至标题"></a></h3>
<p>对数据集进行预处理的基本命令是:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="n">cd</span> <span class="n">demo</span><span class="o">/</span><span class="n">seqToseq</span><span class="o">/</span>
<span class="n">python</span> <span class="n">preprocess</span><span class="o">.</span><span class="n">py</span> <span class="o">-</span><span class="n">i</span> <span class="n">INPUT</span> <span class="p">[</span><span class="o">-</span><span class="n">d</span> <span class="n">DICTSIZE</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="n">m</span><span class="p">]</span>
</pre></div>
</div>
<ul class="simple">
<li><code class="docutils literal"><span class="pre">-i</span> <span class="pre">INPUT</span></code>:输入的原始数据集路径</li>
<li><code class="docutils literal"><span class="pre">-d</span> <span class="pre">DICTSIZE</span></code>:指定的字典单词数,如果没有设置,字典会包含输入数据集中的所有单词</li>
<li><code class="docutils literal"><span class="pre">-m</span> <span class="pre">--mergeDict</span></code>:合并 “源字典”和“目标字典”,使得两个字典有相同的上下文</li>
</ul>
<p>你将会看到如下消息:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">concat</span> <span class="n">parallel</span> <span class="n">corpora</span> <span class="k">for</span> <span class="n">dataset</span>
<span class="n">build</span> <span class="n">source</span> <span class="n">dictionary</span> <span class="k">for</span> <span class="n">train</span> <span class="n">data</span>
<span class="n">build</span> <span class="n">target</span> <span class="n">dictionary</span> <span class="k">for</span> <span class="n">train</span> <span class="n">data</span>
<span class="n">dictionary</span> <span class="n">size</span> <span class="ow">is</span> <span class="n">XXX</span>
</pre></div>
</div>
<p>然后你只需要运行以下命令:</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="n">python</span> <span class="n">preprocess</span><span class="o">.</span><span class="n">py</span> <span class="o">-</span><span class="n">i</span> <span class="n">data</span><span class="o">/</span><span class="n">wmt14</span> <span class="o">-</span><span class="n">d</span> <span class="mi">30000</span>
</pre></div>
</div>
<p>这将花费数分钟的时间,并且将预处理好的数据集存放在<code class="docutils literal"><span class="pre">demo/seqToseq/data/pre-wmt14</span></code>目录下。目录结构如下:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">train</span> <span class="n">test</span> <span class="n">gen</span> <span class="n">train</span><span class="o">.</span><span class="n">list</span> <span class="n">test</span><span class="o">.</span><span class="n">list</span> <span class="n">gen</span><span class="o">.</span><span class="n">list</span> <span class="n">src</span><span class="o">.</span><span class="n">dict</span> <span class="n">trg</span><span class="o">.</span><span class="n">dict</span><span class="c1"># Text generation Tutorial #</span>
</pre></div>
</div>
<ul class="simple">
<li><strong>train, test, gen</strong>:分别包含了法语到英语的平行语料库的训练数据、测试数据和生成数据。文件夹中的每个文件的每一行包含两部分,首先是法语序列,然后是对应的英语序列。</li>
<li><strong>train.list, test.list, gen.list</strong>:分别为train,test,gen文件夹中的文件列表</li>
<li><strong>src.dict, trg.dict</strong>:源(法语)/目标(英语)字典,每个字典包含总共30000个单词:29997个最高频单词和3个特殊符号</li>
</ul>
</div>
</div>
<div class="section" id="">
<span id="id8"></span><h2>模型训练<a class="headerlink" href="#" title="永久链接至标题"></a></h2>
<div class="section" id="">
<span id="id9"></span><h3>简介<a class="headerlink" href="#" title="永久链接至标题"></a></h3>
<p>神经网络机器翻译(NMT)旨在建立一个可以被协同调至最优翻译效果的单神经元网络。近期提出的NMT模型通常都属于编解码模型(encoder–decoder models)的一种。编解码模型将一个源语句编码为一个定长的向量,然后解码器通过这个向量生成一个目标语句。</p>
<p>在这个任务中,我们使用了一个编解码模型的扩展,它同时学习排列(align)与翻译。每当模型在翻译过程中生成了一个单词,它就会在源语句中搜索出最相关信息的位置的集合。解码器根据上下文向量预测出一个目标单词,这个向量与源中搜索出的位置和所有之前生成的目标单词有关。如想了解更多详细的解释,可以参考 <a class="reference external" href="http://arxiv.org/abs/1409.0473">Neural Machine Translation by Jointly Learning to Align and Translate</a></p>
<p>这个模型对于编解码模型来说,最不同的特色是它并没有将输入语句编码为一个单独的定长向量。相反,它将输入语句编码为向量的序列,其中每个向量对应输入语句中的一个元素。然后在解码被翻译的语句时,会自适应地从这些向量中选择一个子集出来。这使得NMT模型得以解放出来,不必再将任意长度源语句中的所有信息压缩至一个定长的向量中。该模型在长语句翻译的场景下效果提升更加明显,在任意长度语句翻译的场景下都可以观察到其效果的提升。
<center><img alt="" src="../../_images/encoder-decoder-attention-model1.png" /></center>
<center>Figure 1. Encoder-Decoder-Attention-Model</center></p>
</div>
<div class="section" id="paddlepaddle">
<span id="paddlepaddle"></span><h3>使用PaddlePaddle训练模型<a class="headerlink" href="#paddlepaddle" title="永久链接至标题"></a></h3>
<p>我们在训练之前需要常见一个模型配置文件,这里是一个例子<code class="docutils literal"><span class="pre">demo/seqToseq/translation/train.conf</span></code>。前三行import了定义network,job_mode和attention_mode的python函数。</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">seqToseq_net</span> <span class="kn">import</span> <span class="o">*</span>
<span class="n">is_generating</span> <span class="o">=</span> <span class="bp">False</span>

<span class="c1">### Data Definiation</span>
<span class="n">train_conf</span> <span class="o">=</span> <span class="n">seq_to_seq_data</span><span class="p">(</span><span class="n">data_dir</span> <span class="o">=</span> <span class="s2">&quot;./data/pre-wmt14&quot;</span><span class="p">,</span>
                             <span class="n">is_generating</span> <span class="o">=</span> <span class="n">is_generating</span><span class="p">)</span>

<span class="c1">### Algorithm Configuration</span>
<span class="n">settings</span><span class="p">(</span>
    <span class="n">learning_method</span> <span class="o">=</span> <span class="n">AdamOptimizer</span><span class="p">(),</span>
    <span class="n">batch_size</span> <span class="o">=</span> <span class="mi">50</span><span class="p">,</span>
    <span class="n">learning_rate</span> <span class="o">=</span> <span class="mf">5e-4</span><span class="p">)</span>

<span class="c1">### Network Architecture</span>
<span class="n">gru_encoder_decoder</span><span class="p">(</span><span class="n">train_conf</span><span class="p">,</span> <span class="n">is_generating</span><span class="p">)</span>
</pre></div>
</div>
<ol class="simple">
<li><strong>Data Definiation</strong>:在示例中我们定义了一个序列到序列的训练和测试数据。它返回train_conf作为配置,其输入参数如下:</li>
</ol>
<ul class="simple">
<li>data_dir:训练数据和测试数据的目录</li>
<li>is_generating:这个配置是否用来生成,这里设置为False</li>
</ul>
<ol class="simple">
<li><strong>Algorithm Configuration</strong>:在示例中我们使用SGD训练算法(默认),和ADAM学习方法,指定batch_size为50,learning_rate为5e-4</li>
<li><strong>Network Architecture</strong>:在示例中我们使用attention版本的GRU编解码网络。它包括了一个双向的GRU作为编码器和解码器,它模拟了解码翻译过程中在源语句中的搜索。</li>
</ol>
</div>
<div class="section" id="">
<span id="id10"></span><h3>训练模型的命令与结果<a class="headerlink" href="#" title="永久链接至标题"></a></h3>
<p>写完模型配置之后,我们可以通过以下命令来训练模型:</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span><span class="nb">cd</span> demo/seqToseq/translation
./train.sh
</pre></div>
</div>
<p><code class="docutils literal"><span class="pre">train.sh</span></code> 的内容如下所示:</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span>paddle train <span class="se">\</span>
--config<span class="o">=</span><span class="s1">&#39;translation/train.conf&#39;</span> <span class="se">\</span>
--save_dir<span class="o">=</span><span class="s1">&#39;translation/model&#39;</span> <span class="se">\</span>
--use_gpu<span class="o">=</span><span class="nb">false</span> <span class="se">\</span>
--num_passes<span class="o">=</span><span class="m">16</span> <span class="se">\</span>
--show_parameter_stats_period<span class="o">=</span><span class="m">100</span> <span class="se">\</span>
--trainer_count<span class="o">=</span><span class="m">4</span> <span class="se">\</span>
--log_period<span class="o">=</span><span class="m">10</span> <span class="se">\</span>
--dot_period<span class="o">=</span><span class="m">5</span> <span class="se">\</span>
<span class="m">2</span>&gt;<span class="p">&amp;</span><span class="m">1</span> <span class="p">|</span> tee <span class="s1">&#39;translation/train.log&#39;</span>
</pre></div>
</div>
<ul class="simple">
<li>config: 设置神经网络的配置文件</li>
<li>save_dir: 设置保存模型的输出路径</li>
<li>use_gpu: 是否使用GPU训练,这里设置为使用CPU</li>
<li>num_passes: 设置passes的数量。paddle中的一条pass表示训练数据集中所有的样本一次</li>
<li>show_parameter_stats_period: 这里每隔100个batch显示一次参数统计信息</li>
<li>trainer_count: 设置CPU线程数或者GPU设备数</li>
<li>log_period: 这里每隔10个batch打印一次日志</li>
<li>dot_period: 这里每个5个batch打印一个点&#8221;.&#8221;</li>
</ul>
<p>训练的损失函数默认每隔10个batch打印一次,你将会看到如下消息:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">I0719</span> <span class="mi">19</span><span class="p">:</span><span class="mi">16</span><span class="p">:</span><span class="mf">45.952062</span> <span class="mi">15563</span> <span class="n">TrainerInternal</span><span class="o">.</span><span class="n">cpp</span><span class="p">:</span><span class="mi">160</span><span class="p">]</span>  <span class="n">Batch</span><span class="o">=</span><span class="mi">10</span> <span class="n">samples</span><span class="o">=</span><span class="mi">500</span> <span class="n">AvgCost</span><span class="o">=</span><span class="mf">198.475</span> <span class="n">CurrentCost</span><span class="o">=</span><span class="mf">198.475</span> <span class="n">Eval</span><span class="p">:</span> <span class="n">classification_error_evaluator</span><span class="o">=</span><span class="mf">0.737155</span>  <span class="n">CurrentEval</span><span class="p">:</span> <span class="n">classification_error_evaluator</span><span class="o">=</span><span class="mf">0.737155</span>
<span class="n">I0719</span> <span class="mi">19</span><span class="p">:</span><span class="mi">17</span><span class="p">:</span><span class="mf">56.707319</span> <span class="mi">15563</span> <span class="n">TrainerInternal</span><span class="o">.</span><span class="n">cpp</span><span class="p">:</span><span class="mi">160</span><span class="p">]</span>  <span class="n">Batch</span><span class="o">=</span><span class="mi">20</span> <span class="n">samples</span><span class="o">=</span><span class="mi">1000</span> <span class="n">AvgCost</span><span class="o">=</span><span class="mf">157.479</span> <span class="n">CurrentCost</span><span class="o">=</span><span class="mf">116.483</span> <span class="n">Eval</span><span class="p">:</span> <span class="n">classification_error_evaluator</span><span class="o">=</span><span class="mf">0.698392</span>  <span class="n">CurrentEval</span><span class="p">:</span> <span class="n">classification_error_evaluator</span><span class="o">=</span><span class="mf">0.659065</span>
<span class="o">.....</span>
</pre></div>
</div>
<ul class="simple">
<li>AvgCost:从第0个batch到当前batch的平均cost</li>
<li>CurrentCost::当前batch的cost</li>
<li>classification_error_evaluator(Eval):从第0个评估到当前评估中,每个单词的预测错误率</li>
<li>classification_error_evaluator(CurrentEval):当前评估中,每个单词的预测错误率</li>
</ul>
<p>当classification_error_evaluator的值低于0.35时,模型就训练成功了。</p>
</div>
</div>
<div class="section" id="">
<span id="id11"></span><h2>文本生成<a class="headerlink" href="#" title="永久链接至标题"></a></h2>
<div class="section" id="">
<span id="id12"></span><h3>简介<a class="headerlink" href="#" title="永久链接至标题"></a></h3>
<p>一般而言,NMT模型受制于源语句的编码,并且通过给出当前目标单词来预测下一个目标单词。在训练过程中,当前单词在相比之下总是被当作真值(ground truth)。在生成过程中,当前单词是解码器最后一步的输出,这来自于PaddlePaddle的内存中。</p>
<p>而且,我们使用集束搜索(Beam Search)来生成序列。集束搜索使用广度优先搜索来构建搜索树。对于树的每一层,生成当前层的所有后继状态,并将它们按照启发代价(heuristic cost)升序排列。但是这种方法在每层只保存预设数量的最优状态(这个数量称为beam size)。</p>
</div>
<div class="section" id="">
<span id="id13"></span><h3>预训练的模型<a class="headerlink" href="#" title="永久链接至标题"></a></h3>
<p>我们在拥有50个节点的集群中训练模型,每个节点有两个6核CPU。我们在5天里训练了16个pass,其中每条pass花费了7个小时。model_dir中有16个子目录,每个里面都包含202MB的全部的模型参数。然后我们发现pass-00012的模型有着最高的BLEU值27.77(参考文献<a class="reference external" href="http://www.aclweb.org/anthology/P02-1040.pdf">BLEU: a Method for Automatic Evaluation of Machine Translation</a>)。要下载解压这个模型,只需在linux下运行如下命令:</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span><span class="nb">cd</span> demo/seqToseq/data
./wmt14_model.sh
</pre></div>
</div>
</div>
<div class="section" id="paddlepaddle">
<span id="id14"></span><h3>使用PaddlePaddle生成模型<a class="headerlink" href="#paddlepaddle" title="永久链接至标题"></a></h3>
<p>在翻译法语句子之前,我们需要创建模型配置文件。这里是一个例子<code class="docutils literal"><span class="pre">demo/seqToseq/translation/gen.conf</span></code>。前三行import了定义network,job_mode和attention_mode的python函数。</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">seqToseq_net</span> <span class="kn">import</span> <span class="o">*</span>
<span class="n">is_generating</span> <span class="o">=</span> <span class="bp">True</span>

<span class="c1">################## Data Definiation #####################</span>
<span class="n">gen_conf</span> <span class="o">=</span> <span class="n">seq_to_seq_data</span><span class="p">(</span><span class="n">data_dir</span> <span class="o">=</span> <span class="s2">&quot;./data/pre-wmt14&quot;</span><span class="p">,</span>
                           <span class="n">is_generating</span> <span class="o">=</span> <span class="n">is_generating</span><span class="p">,</span>
                           <span class="n">gen_result</span> <span class="o">=</span> <span class="s2">&quot;./translation/gen_result&quot;</span><span class="p">)</span>

<span class="c1">############## Algorithm Configuration ##################</span>
<span class="n">settings</span><span class="p">(</span>
  <span class="n">learning_method</span> <span class="o">=</span> <span class="n">AdamOptimizer</span><span class="p">(),</span>
  <span class="n">batch_size</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
  <span class="n">learning_rate</span> <span class="o">=</span> <span class="mi">0</span><span class="p">)</span>

<span class="c1">################# Network configure #####################</span>
<span class="n">gru_encoder_decoder</span><span class="p">(</span><span class="n">gen_conf</span><span class="p">,</span> <span class="n">is_generating</span><span class="p">)</span>
</pre></div>
</div>
<ol class="simple">
<li><strong>Data Definiation</strong>:在示例中我们定义了一个序列到序列的生成数据。它返回gen_conf作为配置,其输入参数如下:</li>
</ol>
<ul class="simple">
<li>data_dir:生成数据的目录
&nbsp;- is_generating:这个配置是否用来生成,这里设置为True
&nbsp;- gen_result:保存生成结果的文件</li>
</ul>
<ol class="simple">
<li><strong>Algorithm Configuration</strong>:在生成过程中我们使用SGD训练算法,并指定batch_size为1(每次生成1个序列),learning_rate为0</li>
<li><strong>Network Architecture</strong>:本质上与训练模型一样</li>
</ol>
</div>
<div class="section" id="">
<span id="id15"></span><h3>生成模型的命令与结果<a class="headerlink" href="#" title="永久链接至标题"></a></h3>
<p>写完模型配置之后,我们可以通过以下命令来进行从法语到英语的文本翻译:</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span><span class="nb">cd</span> demo/seqToseq/translation
./gen.sh
</pre></div>
</div>
<p><code class="docutils literal"><span class="pre">gen.sh</span></code> 的内容如下所示。与训练模型不同的是,这里有一些不同的参数需要指定:</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span>paddle train <span class="se">\</span>
--job<span class="o">=</span><span class="nb">test</span> <span class="se">\</span>
--config<span class="o">=</span><span class="s1">&#39;translation/gen.conf&#39;</span> <span class="se">\</span>
--save_dir<span class="o">=</span><span class="s1">&#39;data/wmt14_model&#39;</span> <span class="se">\</span>
--use_gpu<span class="o">=</span><span class="nb">true</span> <span class="se">\</span>
--num_passes<span class="o">=</span><span class="m">13</span> <span class="se">\</span>
--test_pass<span class="o">=</span><span class="m">12</span> <span class="se">\</span>
--trainer_count<span class="o">=</span><span class="m">1</span> <span class="se">\</span>
<span class="m">2</span>&gt;<span class="p">&amp;</span><span class="m">1</span> <span class="p">|</span> tee <span class="s1">&#39;translation/gen.log&#39;</span>
</pre></div>
</div>
<ul class="simple">
<li>job:设置任务的模式为测试</li>
<li>save_dir:存储模型的路径</li>
<li>num_passes and test_pass:从test_pass到(num_passes - 1)加载模型参数,这里只加载 <code class="docutils literal"><span class="pre">data/wmt14_model/pass-00012</span></code></li>
</ul>
<p>你将会看到这样的消息:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">I0706</span> <span class="mi">14</span><span class="p">:</span><span class="mi">48</span><span class="p">:</span><span class="mf">31.178915</span> <span class="mi">31441</span> <span class="n">GradientMachine</span><span class="o">.</span><span class="n">cpp</span><span class="p">:</span><span class="mi">143</span><span class="p">]</span> <span class="n">Loading</span> <span class="n">parameters</span> <span class="kn">from</span> <span class="nn">data</span><span class="o">/</span><span class="n">wmt14_model</span><span class="o">/</span><span class="k">pass</span><span class="o">-</span><span class="mi">00012</span>
<span class="n">I0706</span> <span class="mi">14</span><span class="p">:</span><span class="mi">48</span><span class="p">:</span><span class="mf">40.012039</span> <span class="mi">31441</span> <span class="n">Tester</span><span class="o">.</span><span class="n">cpp</span><span class="p">:</span><span class="mi">125</span><span class="p">]</span>  <span class="n">Batch</span><span class="o">=</span><span class="mi">100</span> <span class="n">samples</span><span class="o">=</span><span class="mi">100</span> <span class="n">AvgCost</span><span class="o">=</span><span class="mi">0</span>
<span class="n">I0706</span> <span class="mi">14</span><span class="p">:</span><span class="mi">48</span><span class="p">:</span><span class="mf">48.898632</span> <span class="mi">31441</span> <span class="n">Tester</span><span class="o">.</span><span class="n">cpp</span><span class="p">:</span><span class="mi">125</span><span class="p">]</span>  <span class="n">Batch</span><span class="o">=</span><span class="mi">200</span> <span class="n">samples</span><span class="o">=</span><span class="mi">200</span> <span class="n">AvgCost</span><span class="o">=</span><span class="mi">0</span>
<span class="o">...</span>
</pre></div>
</div>
<p>然后在<code class="docutils literal"><span class="pre">demo/seqToseq/translation/gen_result</span></code>中的生成结果如下所示:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="mi">0</span>
<span class="mi">0</span>       <span class="o">-</span><span class="mf">11.1314</span>         <span class="n">The</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="n">about</span> <span class="n">the</span> <span class="n">width</span> <span class="n">of</span> <span class="n">the</span> <span class="n">seats</span> <span class="k">while</span> <span class="n">large</span> <span class="n">controls</span> <span class="n">are</span> <span class="n">at</span> <span class="n">stake</span> <span class="o">&lt;</span><span class="n">e</span><span class="o">&gt;</span>
<span class="mi">1</span>       <span class="o">-</span><span class="mf">11.1519</span>         <span class="n">The</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="n">on</span> <span class="n">the</span> <span class="n">width</span> <span class="n">of</span> <span class="n">the</span> <span class="n">seats</span> <span class="k">while</span> <span class="n">large</span> <span class="n">controls</span> <span class="n">are</span> <span class="n">at</span> <span class="n">stake</span> <span class="o">&lt;</span><span class="n">e</span><span class="o">&gt;</span>
<span class="mi">2</span>       <span class="o">-</span><span class="mf">11.5988</span>         <span class="n">The</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="n">about</span> <span class="n">the</span> <span class="n">width</span> <span class="n">of</span> <span class="n">the</span> <span class="n">seats</span> <span class="k">while</span> <span class="n">large</span> <span class="n">controls</span> <span class="n">are</span> <span class="n">at</span> <span class="n">stake</span> <span class="o">.</span> <span class="o">&lt;</span><span class="n">e</span><span class="o">&gt;</span>

<span class="mi">1</span>
<span class="mi">0</span>       <span class="o">-</span><span class="mf">24.4149</span>         <span class="n">The</span> <span class="n">dispute</span> <span class="ow">is</span> <span class="n">between</span> <span class="n">the</span> <span class="n">major</span> <span class="n">aircraft</span> <span class="n">manufacturers</span> <span class="n">about</span> <span class="n">the</span> <span class="n">width</span> <span class="n">of</span> <span class="n">the</span> <span class="n">tourist</span> <span class="n">seats</span> <span class="n">on</span> <span class="n">the</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="n">flights</span> <span class="p">,</span> <span class="n">paving</span> <span class="n">the</span> <span class="n">way</span> <span class="k">for</span> <span class="n">a</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="n">confrontation</span> <span class="n">during</span> <span class="n">the</span> <span class="n">month</span> <span class="n">of</span> <span class="n">the</span> <span class="n">Dubai</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="o">.</span> <span class="o">&lt;</span><span class="n">e</span><span class="o">&gt;</span>
<span class="mi">1</span>       <span class="o">-</span><span class="mf">26.9524</span>         <span class="n">The</span> <span class="n">dispute</span> <span class="ow">is</span> <span class="n">between</span> <span class="n">the</span> <span class="n">major</span> <span class="n">aircraft</span> <span class="n">manufacturers</span> <span class="n">about</span> <span class="n">the</span> <span class="n">width</span> <span class="n">of</span> <span class="n">the</span> <span class="n">tourist</span> <span class="n">seats</span> <span class="n">on</span> <span class="n">the</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="n">flights</span> <span class="p">,</span> <span class="n">paving</span> <span class="n">the</span> <span class="n">way</span> <span class="k">for</span> <span class="n">a</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="n">confrontation</span> <span class="n">during</span> <span class="n">the</span> <span class="n">month</span> <span class="n">of</span> <span class="n">Dubai</span> <span class="o">&amp;</span><span class="n">apos</span><span class="p">;</span> <span class="n">s</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="o">.</span> <span class="o">&lt;</span><span class="n">e</span><span class="o">&gt;</span>
<span class="mi">2</span>       <span class="o">-</span><span class="mf">27.9574</span>         <span class="n">The</span> <span class="n">dispute</span> <span class="ow">is</span> <span class="n">between</span> <span class="n">the</span> <span class="n">major</span> <span class="n">aircraft</span> <span class="n">manufacturers</span> <span class="n">about</span> <span class="n">the</span> <span class="n">width</span> <span class="n">of</span> <span class="n">the</span> <span class="n">tourist</span> <span class="n">seats</span> <span class="n">on</span> <span class="n">the</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="n">flights</span> <span class="p">,</span> <span class="n">paving</span> <span class="n">the</span> <span class="n">way</span> <span class="k">for</span> <span class="n">a</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="n">confrontation</span> <span class="n">during</span> <span class="n">the</span> <span class="n">month</span> <span class="n">of</span> <span class="n">Dubai</span> <span class="o">&amp;</span><span class="n">apos</span><span class="p">;</span> <span class="n">s</span> <span class="n">Dubai</span> <span class="o">&lt;</span><span class="n">unk</span><span class="o">&gt;</span> <span class="o">.</span> <span class="o">&lt;</span><span class="n">e</span><span class="o">&gt;</span>
<span class="o">...</span>
</pre></div>
</div>
<ul class="simple">
<li>这是集束搜索的结果,其中beam size是3</li>
<li>第一行的“0”和第6行的“1”表示生成数据的序列id</li>
<li>其他六行列出了集束搜索的结果<ul>
<li>第二列是集束搜索的得分(从大到小)</li>
<li>第三列是生成的英语序列</li>
</ul>
</li>
<li>有两个特殊标识:<ul>
<li><code class="docutils literal"><span class="pre">&lt;e&gt;</span></code>:序列的结尾</li>
<li><code class="docutils literal"><span class="pre">&lt;unk&gt;</span></code>:不包含在字典中的单词</li>
</ul>
</li>
</ul>
</div>
<div class="section" id="bleu">
<span id="bleu"></span><h3>BLEU评估<a class="headerlink" href="#bleu" title="永久链接至标题"></a></h3>
<p>对机器翻译的人工评估工作很广泛但也很昂贵。一篇论文 <a class="reference external" href="http://www.aclweb.org/anthology/P02-1040.pdf">BLEU: a Method for Automatic Evaluation of Machine Translation</a> 展示了一种方法,当需要快速或者频繁的评估时,使用自动的替补来替代经验丰富的人工评判。<a class="reference external" href="http://www.statmt.org/moses/">Moses</a> 是一个统计学的机器翻译系统,我们使用其中的 <a class="reference external" href="https://github.com/moses-smt/mosesdecoder/blob/master/scripts/generic/multi-bleu.perl">multi-bleu.perl</a> 来做BLEU评估。运行以下命令来下载这个脚本:</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span><span class="nb">cd</span> demo/seqToseq/translation
./moses_bleu.sh
</pre></div>
</div>
<p>由于标准的翻译结果已经下载到这里<code class="docutils literal"><span class="pre">data/wmt14/gen/ntst14.trg</span></code>,我们可以运行以下命令来做BLEU评估。</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span><span class="nb">cd</span> demo/seqToseq/translation
./eval_bleu.sh FILE BEAMSIZE
</pre></div>
</div>
<ul class="simple">
<li>FILE:生成的结果文件</li>
<li>BEAMSIZE:集束搜索中的扩展广度</li>
</ul>
</div>
</div>
</div>


           </div>
          </div>
          <footer>
  

  <hr/>

  <div role="contentinfo">
    <p>
        &copy; Copyright 2016, PaddlePaddle developers.

    </p>
  </div>
  Built with <a href="http://sphinx-doc.org/">Sphinx</a> using a <a href="https://github.com/snide/sphinx_rtd_theme">theme</a> provided by <a href="https://readthedocs.org">Read the Docs</a>. 

</footer>

        </div>
      </div>

    </section>

  </div>
  


  

    <script type="text/javascript">
        var DOCUMENTATION_OPTIONS = {
            URL_ROOT:'../../',
            VERSION:'',
            COLLAPSE_INDEX:false,
            FILE_SUFFIX:'.html',
583 584
            HAS_SOURCE:  true,
            SOURCELINK_SUFFIX: ".txt",
585 586 587 588 589 590
        };
    </script>
      <script type="text/javascript" src="../../_static/jquery.js"></script>
      <script type="text/javascript" src="../../_static/underscore.js"></script>
      <script type="text/javascript" src="../../_static/doctools.js"></script>
      <script type="text/javascript" src="../../_static/translations.js"></script>
591
      <script type="text/javascript" src="https://cdn.bootcss.com/mathjax/2.7.0/MathJax.js"></script>
592 593 594 595 596 597 598 599 600 601 602 603 604
       
  

  
  
    <script type="text/javascript" src="../../_static/js/theme.js"></script>
  
  
  <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha384-Tc5IQib027qvyjSMfHjOMaLkfuWVxZxUPnCJA7l2mCWNIpG9mGCD8wGNIcPD7Txa" crossorigin="anonymous"></script>
  <script src="https://cdn.jsdelivr.net/perfect-scrollbar/0.6.14/js/perfect-scrollbar.jquery.min.js"></script>
  <script src="../../_static/js/paddle_doc_init.js"></script> 

</body>
605
</html>