Skip to content

P
Paddle

PaddlePaddle / Paddle
大约 1 年 前同步成功

通知 2298
Star 20931
Fork 5422
P
Paddle
切换分支/标签
查找文件 普通视图历史永久链接Permalink
auto_gradient_check.html 25.4 KB
Newer Older
T
Deploy to GitHub Pages: 1ff47b284c565d030b198705d5f18b4bd4ce53e5  
Travis CI 已提交
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 35 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 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 


<!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>Auto Gradient Checker Design &mdash; PaddlePaddle  documentation</title>
  

  
  

  

  
  
    

  

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

  
  
        <link rel="index" title="Index"
              href="../genindex.html"/>
        <link rel="search" title="Search" href="../search.html"/>
    <link rel="top" title="PaddlePaddle  documentation" href="../index.html"/> 

  <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">
        <a class="fork-on-github" href="https://github.com/PaddlePaddle/Paddle" target="_blank"><i class="fa fa-github"></i>Fork me on Github</a>
        <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">
          <li><a href="/">Home</a></li>
        </ul>
      </div>
      <div class="doc-module">
        
        <ul>
<li class="toctree-l1"><a class="reference internal" href="../getstarted/index_en.html">GET STARTED</a></li>
<li class="toctree-l1"><a class="reference internal" href="../howto/index_en.html">HOW TO</a></li>
<li class="toctree-l1"><a class="reference internal" href="../api/index_en.html">API</a></li>
<li class="toctree-l1"><a class="reference internal" href="../mobile/index_en.html">MOBILE</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">
        
          
          <ul>
<li class="toctree-l1"><a class="reference internal" href="../getstarted/index_en.html">GET STARTED</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../getstarted/build_and_install/index_en.html">Install and Build</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../getstarted/build_and_install/pip_install_en.html">Install Using pip</a></li>
<li class="toctree-l3"><a class="reference internal" href="../getstarted/build_and_install/docker_install_en.html">Run in Docker Containers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../howto/dev/build_en.html">Build using Docker</a></li>
<li class="toctree-l3"><a class="reference internal" href="../getstarted/build_and_install/build_from_source_en.html">Build from Sources</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../howto/index_en.html">HOW TO</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../howto/usage/cmd_parameter/index_en.html">Set Command-line Parameters</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../howto/usage/cmd_parameter/use_case_en.html">Use Case</a></li>
<li class="toctree-l3"><a class="reference internal" href="../howto/usage/cmd_parameter/arguments_en.html">Argument Outline</a></li>
<li class="toctree-l3"><a class="reference internal" href="../howto/usage/cmd_parameter/detail_introduction_en.html">Detail Description</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../howto/usage/cluster/cluster_train_en.html">PaddlePaddle Distributed Training</a></li>
<li class="toctree-l2"><a class="reference internal" href="../howto/usage/k8s/k8s_en.html">Paddle On Kubernetes</a></li>
<li class="toctree-l2"><a class="reference internal" href="../howto/usage/k8s/k8s_aws_en.html">Distributed PaddlePaddle Training on AWS with Kubernetes</a></li>
<li class="toctree-l2"><a class="reference internal" href="../howto/dev/new_layer_en.html">Write New Layers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../howto/dev/contribute_to_paddle_en.html">Contribute Code</a></li>
<li class="toctree-l2"><a class="reference internal" href="../howto/dev/write_docs_en.html">Contribute Documentation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../howto/deep_model/rnn/index_en.html">RNN Models</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../howto/deep_model/rnn/rnn_config_en.html">RNN Configuration</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../howto/optimization/gpu_profiling_en.html">Tune GPU Performance</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../api/index_en.html">API</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../api/v2/model_configs.html">Model Configuration</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>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/config/evaluators.html">Evaluators</a></li>
<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">Data Reader Interface and DataSets</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/data/data_reader.html">Data Reader Interface</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/data/image.html">Image Interface</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/data/dataset.html">Dataset</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="../api/v2/run_logic.html">Training and Inference</a></li>
<li class="toctree-l2"><a class="reference internal" href="../api/v2/fluid.html">Fluid</a><ul>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/fluid/layers.html">Layers</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/fluid/data_feeder.html">DataFeeder</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/fluid/executor.html">Executor</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/fluid/initializer.html">Initializer</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/fluid/evaluator.html">Evaluator</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/fluid/nets.html">Nets</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/fluid/optimizer.html">Optimizer</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/fluid/param_attr.html">ParamAttr</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/fluid/profiler.html">Profiler</a></li>
<li class="toctree-l3"><a class="reference internal" href="../api/v2/fluid/regularizer.html">Regularizer</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../mobile/index_en.html">MOBILE</a><ul>
<li class="toctree-l2"><a class="reference internal" href="../mobile/cross_compiling_for_android_en.html">Build PaddlePaddle for Android</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mobile/cross_compiling_for_raspberry_en.html">Build PaddlePaddle for Raspberry Pi</a></li>
</ul>
</li>
</ul>

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

      

 







<div role="navigation" aria-label="breadcrumbs navigation">
  <ul class="wy-breadcrumbs">
      
    <li>Auto Gradient Checker Design</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="auto-gradient-checker-design">
<span id="auto-gradient-checker-design"></span><h1>Auto Gradient Checker Design<a class="headerlink" href="#auto-gradient-checker-design" title="Permalink to this headline"></a></h1>
</div>
<div class="section" id="backgraound">
<span id="backgraound"></span><h1>Backgraound：<a class="headerlink" href="#backgraound" title="Permalink to this headline"></a></h1>
<ul class="simple">
<li>Generally, it is easy to check whether the forward computation of an Operator is correct or not. However, backpropagation is a notoriously difficult algorithm to debug and get right:<ol>
<li>you should get the right backpropagation formula according to the forward computation.</li>
<li>you should implement it right in CPP.</li>
<li>it&#8217;s difficult to prepare test data.</li>
</ol>
</li>
<li>Auto gradient checking gets a numerical gradient by forward Operator and use it as a reference of the backward Operator&#8217;s result. It has several advantages:<ol>
<li>numerical gradient checker only need forward operator.</li>
<li>user only need to prepare the input data for forward Operator.</li>
</ol>
</li>
</ul>
</div>
<div class="section" id="mathematical-theory">
<span id="mathematical-theory"></span><h1>Mathematical Theory<a class="headerlink" href="#mathematical-theory" title="Permalink to this headline"></a></h1>
<p>The following two document from Stanford has a detailed explanation of how to get numerical gradient and why it&#8217;s useful.</p>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference external" href="http://deeplearning.stanford.edu/wiki/index.php/Gradient_checking_and_advanced_optimization">Gradient checking and advanced optimization(en)</a></li>
<li class="toctree-l1"><a class="reference external" href="http://ufldl.stanford.edu/wiki/index.php/%E6%A2%AF%E5%BA%A6%E6%A3%80%E9%AA%8C%E4%B8%8E%E9%AB%98%E7%BA%A7%E4%BC%98%E5%8C%96">Gradient checking and advanced optimization(cn)</a></li>
</ul>
</div>
</div>
<div class="section" id="numeric-gradient-implementation">
<span id="numeric-gradient-implementation"></span><h1>Numeric Gradient Implementation<a class="headerlink" href="#numeric-gradient-implementation" title="Permalink to this headline"></a></h1>
<div class="section" id="python-interface">
<span id="python-interface"></span><h2>Python Interface<a class="headerlink" href="#python-interface" title="Permalink to this headline"></a></h2>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">get_numerical_gradient</span><span class="p">(</span><span class="n">op</span><span class="p">,</span>
                         <span class="n">input_values</span><span class="p">,</span>
                         <span class="n">output_name</span><span class="p">,</span>
                         <span class="n">input_to_check</span><span class="p">,</span>
                         <span class="n">delta</span><span class="o">=</span><span class="mf">0.005</span><span class="p">,</span>
                         <span class="n">local_scope</span><span class="o">=</span><span class="bp">None</span><span class="p">):</span>
    <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">    Get Numeric Gradient for an operator&#39;s input.</span>

<span class="sd">    :param op: C++ operator instance, could be an network</span>
<span class="sd">    :param input_values: The input variables. Should be an dictionary, whose key is</span>
<span class="sd">    variable name, and value is numpy array.</span>
<span class="sd">    :param output_name: The final output variable name.</span>
<span class="sd">    :param input_to_check: The input variable with respect to which to compute the gradient.</span>
<span class="sd">    :param delta: The perturbation value for numeric gradient method. The</span>
<span class="sd">    smaller delta is, the more accurate result will get. But if that delta is</span>
<span class="sd">     too small, it will suffer from numerical stability problem.</span>
<span class="sd">    :param local_scope: The local scope used for get_numeric_gradient.</span>
<span class="sd">    :return: The gradient array in numpy format.</span>
<span class="sd">    &quot;&quot;&quot;</span>
</pre></div>
</div>
</div>
<div class="section" id="explaination">
<span id="explaination"></span><h2>Explaination:<a class="headerlink" href="#explaination" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li>Why need <code class="docutils literal"><span class="pre">output_name</span></code><ul>
<li>An Operator may have multiple Output, one can get independent gradient from each Output. So caller should specify the name of the output variable.</li>
</ul>
</li>
<li>Why need <code class="docutils literal"><span class="pre">input_to_check</span></code><ul>
<li>One operator may have multiple inputs. Gradient Op can calculate the gradient of these inputs at the same time. But Numeric Gradient needs to calculate them one by one. So <code class="docutils literal"><span class="pre">get_numeric_gradient</span></code> is designed to calculate the gradient for one input. If you need to compute multiple inputs, you can call <code class="docutils literal"><span class="pre">get_numeric_gradient</span></code> multiple times.</li>
</ul>
</li>
</ul>
</div>
<div class="section" id="core-algorithm-implementation">
<span id="core-algorithm-implementation"></span><h2>Core Algorithm Implementation<a class="headerlink" href="#core-algorithm-implementation" title="Permalink to this headline"></a></h2>
<div class="highlight-python"><div class="highlight"><pre><span></span>    <span class="c1"># we only compute gradient of one element a time.</span>
    <span class="c1"># we use a for loop to compute the gradient of each element.</span>
    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="n">tensor_size</span><span class="p">):</span>
        <span class="c1"># get one input element by its index i.</span>
        <span class="n">origin</span> <span class="o">=</span> <span class="n">tensor_to_check</span><span class="o">.</span><span class="n">get_float_element</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>

        <span class="c1"># add delta to it, run op and then get the new value of the result tensor.</span>
        <span class="n">x_pos</span> <span class="o">=</span> <span class="n">origin</span> <span class="o">+</span> <span class="n">delta</span>
        <span class="n">tensor_to_check</span><span class="o">.</span><span class="n">set_float_element</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">x_pos</span><span class="p">)</span>
        <span class="n">y_pos</span> <span class="o">=</span> <span class="n">get_output</span><span class="p">()</span>

        <span class="c1"># plus delta to this element, run op and get the new value of the result tensor.</span>
        <span class="n">x_neg</span> <span class="o">=</span> <span class="n">origin</span> <span class="o">-</span> <span class="n">delta</span>
        <span class="n">tensor_to_check</span><span class="o">.</span><span class="n">set_float_element</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">x_neg</span><span class="p">)</span>
        <span class="n">y_neg</span> <span class="o">=</span> <span class="n">get_output</span><span class="p">()</span>

        <span class="c1"># restore old value</span>
        <span class="n">tensor_to_check</span><span class="o">.</span><span class="n">set_float_element</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">origin</span><span class="p">)</span>

        <span class="c1"># compute the gradient of this element and store it into a numpy array.</span>
        <span class="n">gradient_flat</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">y_pos</span> <span class="o">-</span> <span class="n">y_neg</span><span class="p">)</span> <span class="o">/</span> <span class="n">delta</span> <span class="o">/</span> <span class="mi">2</span>

    <span class="c1"># reshape the gradient result to the shape of the source tensor.</span>
    <span class="k">return</span> <span class="n">gradient_flat</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">tensor_to_check</span><span class="o">.</span><span class="n">get_dims</span><span class="p">())</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="auto-graident-checker-framework">
<span id="auto-graident-checker-framework"></span><h1>Auto Graident Checker Framework<a class="headerlink" href="#auto-graident-checker-framework" title="Permalink to this headline"></a></h1>
<p>Each Operator Kernel has three kinds of Gradient:</p>
<ol class="simple">
<li>Numerical gradient</li>
<li>CPU kernel gradient</li>
<li>GPU kernel gradient (if supported)</li>
</ol>
<p>The numerical gradient only relies on forward Operator. So we use the numerical gradient as the reference value. And the gradient checking is performed in the following three steps:</p>
<ol class="simple">
<li>calculate the numerical gradient</li>
<li>calculate CPU kernel gradient with the backward Operator and compare it with the numerical gradient</li>
<li>calculate GPU kernel gradient with the backward Operator and compare it with the numeric gradient (if supported)</li>
</ol>
<div class="section" id="python-interface">
<span id="id1"></span><h2>Python Interface<a class="headerlink" href="#python-interface" title="Permalink to this headline"></a></h2>
<div class="highlight-python"><div class="highlight"><pre><span></span>    <span class="k">def</span> <span class="nf">check_grad</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
                   <span class="n">forward_op</span><span class="p">,</span>
                   <span class="n">input_vars</span><span class="p">,</span>
                   <span class="n">inputs_to_check</span><span class="p">,</span>
                   <span class="n">output_name</span><span class="p">,</span>
                   <span class="n">no_grad_set</span><span class="o">=</span><span class="bp">None</span><span class="p">,</span>
                   <span class="n">only_cpu</span><span class="o">=</span><span class="bp">False</span><span class="p">,</span>
                   <span class="n">max_relative_error</span><span class="o">=</span><span class="mf">0.005</span><span class="p">):</span>
        <span class="sd">&quot;&quot;&quot;</span>
<span class="sd">        :param forward_op: used to create backward_op</span>
<span class="sd">        :param input_vars: numpy value of input variable. The following</span>
<span class="sd">            computation will use these variables.</span>
<span class="sd">        :param inputs_to_check: the input variable with respect to which to compute the gradient.</span>
<span class="sd">        :param output_name: The final output variable name.</span>
<span class="sd">        :param max_relative_error: The relative tolerance parameter.</span>
<span class="sd">        :param no_grad_set: used when create backward ops</span>
<span class="sd">        :param only_cpu: only compute and check gradient on cpu kernel.</span>
<span class="sd">        :return:</span>
<span class="sd">        &quot;&quot;&quot;</span>
</pre></div>
</div>
</div>
<div class="section" id="how-to-check-if-two-numpy-array-is-close-enough">
<span id="how-to-check-if-two-numpy-array-is-close-enough"></span><h2>How to check if two numpy array is close enough?<a class="headerlink" href="#how-to-check-if-two-numpy-array-is-close-enough" title="Permalink to this headline"></a></h2>
<p>if <code class="docutils literal"><span class="pre">abs_numerical_grad</span></code> is nearly zero, then use abs error for numerical_grad</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="n">numerical_grad</span> <span class="o">=</span> <span class="o">...</span>
<span class="n">operator_grad</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">scope</span><span class="o">.</span><span class="n">find_var</span><span class="p">(</span><span class="n">grad_var_name</span><span class="p">(</span><span class="n">name</span><span class="p">))</span><span class="o">.</span><span class="n">get_tensor</span><span class="p">())</span>

<span class="n">abs_numerical_grad</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">numerical_grad</span><span class="p">)</span>
<span class="c1"># if abs_numerical_grad is nearly zero, then use abs error for numeric_grad, not relative</span>
<span class="c1"># error.</span>
<span class="n">abs_numerical_grad</span><span class="p">[</span><span class="n">abs_numerical_grad</span> <span class="o">&lt;</span> <span class="mf">1e-3</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>

<span class="n">diff_mat</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">abs_numerical_grad</span> <span class="o">-</span> <span class="n">operator_grad</span><span class="p">)</span> <span class="o">/</span> <span class="n">abs_numerical_grad</span>
<span class="n">max_diff</span> <span class="o">=</span> <span class="n">numpy</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">diff_mat</span><span class="p">)</span>
</pre></div>
</div>
<div class="section" id="notes">
<span id="notes"></span><h3>Notes：<a class="headerlink" href="#notes" title="Permalink to this headline"></a></h3>
<p>The Input data for auto gradient checker should be reasonable to avoid numerical  stability problem.</p>
</div>
<div class="section" id="refs">
<span id="refs"></span><h3>Refs:<a class="headerlink" href="#refs" title="Permalink to this headline"></a></h3>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference external" href="http://deeplearning.stanford.edu/wiki/index.php/Gradient_checking_and_advanced_optimization">Gradient checking and advanced optimization(en)</a></li>
<li class="toctree-l1"><a class="reference external" href="http://ufldl.stanford.edu/wiki/index.php/%E6%A2%AF%E5%BA%A6%E6%A3%80%E9%AA%8C%E4%B8%8E%E9%AB%98%E7%BA%A7%E4%BC%98%E5%8C%96">Gradient checking and advanced optimization(cn)</a></li>
</ul>
</div>
</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',
            HAS_SOURCE:  true,
            SOURCELINK_SUFFIX: ".txt",
        };
    </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="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
       
  

  
  
    <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>
</html>