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实验报告.html
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<!doctype html>
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</style><title>实验报告</title>
</head>
<body class='typora-export os-windows'><div class='typora-export-content'>
<div id='write' class=''><h1 id='实验报告基于全连接网络的手写数字体识别'><span>实验报告：基于全连接网络的手写数字体识别</span></h1><ul><li><p><span>作者：王佳旭</span></p></li><li><p><span>学号：2021213444</span></p></li><li><p><span>班级：2021219111</span></p></li><li><p><span>学院：人工智能学院</span></p></li></ul><h2 id='文件夹说明'><span>文件夹说明</span></h2><figure><table><thead><tr><th><span>文件名</span></th><th><span>内容及作用</span></th></tr></thead><tbody><tr><td><span>mnist.pkl.gz</span></td><td><span>手写数字的数据集</span></td></tr><tr><td><span>network.py</span></td><td><span>实现识别手写数字的主要代码</span></td></tr><tr><td><span>execute.py</span></td><td><span>运行一个神经网网络的脚本</span></td></tr><tr><td><span>figure.py</span></td><td><span>执行小规模训练的绘图代码</span></td></tr><tr><td><span>mnist_loader.py</span></td><td><span>解压加载mnist数据集的脚本</span></td></tr><tr><td><span>result.json</span></td><td><span>用于存储的运行后的cost和accuracy</span></td></tr><tr><td><span>model.json</span></td><td><span>保存训练后的模型参数</span></td></tr><tr><td><span>requirements.txt</span></td><td><span>项目依赖的第三方库</span></td></tr></tbody></table></figure><p> </p><h2 id='代码实现的主要功能'><span>代码实现的主要功能</span></h2><h3 id='神经网络'><span>神经网络</span></h3><ol start='' ><li><p><span>指定神经网络层数以及每层神经网络使用的神经元数量</span></p></li><li><p><span>每层神经网络的所使用的的激活函数</span></p></li></ol><p> </p><h3 id='损失函数'><span>损失函数：</span></h3><ol start='' ><li><p><span>交叉熵损失函数 CrossEntropyCost</span></p></li><li><p><span>均方误差损失函数 QuadraticCost</span></p></li></ol><p> </p><h3 id='参数初始化'><span>参数初始化：</span></h3><ol start='' ><li><p><span>普通参数初始化 large_weight_initializer</span></p></li><li><p><span>小参数初始化 default_weight_initializer</span></p></li></ol><p> </p><h3 id='激活函数'><span>激活函数：</span></h3><ol start='' ><li><p><span>sigmoid激活函数及其偏导数</span></p></li><li><p><span>softmax激活函数及其偏导数</span></p></li></ol><p> </p><h3 id='正则化正则化被整合入参数更新部分）'><span>正则化：（正则化被整合入参数更新部分）</span></h3><ol start='' ><li><p><span>L2正则化</span></p></li><li><p><span>L1正则化</span></p></li></ol><p> </p><h3 id='数据集分割'><span>数据集分割：</span></h3><ol start='' ><li><p><span>test_data：50000</span></p></li><li><p><span>validation_data: 10000</span></p></li><li><p><span>test_data: 10000</span></p></li></ol><blockquote><p><span>使用的数据集由参考书作者提供，作者已经将数据集分为三个部分，且对输入x做了归一化处理</span></p><p><span>在excute.py中将evaluation_data = test_data,改为evaludation_data = validation_data就是使用验证集来进行测试</span>
<span>同时也可以用来实现对学习率 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.319ex" height="1.597ex" role="img" focusable="false" viewBox="0 -694 583 706" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.027ex;"><defs><path id="MJX-17-TEX-I-1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D706" xlink:href="#MJX-17-TEX-I-1D706"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\lambda</script><span> 和正则化参数 </span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.124ex" height="1.489ex" role="img" focusable="false" viewBox="0 -442 497 658" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.489ex;"><defs><path id="MJX-24-TEX-I-1D702" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q156 442 175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336V326Q503 302 439 53Q381 -182 377 -189Q364 -216 332 -216Q319 -216 310 -208T299 -186Q299 -177 358 57L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D702" xlink:href="#MJX-24-TEX-I-1D702"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>η</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\eta</script><span> 等超参数进行调整</span></p></blockquote><p> </p><h3 id='参数更新方式通过调整minibatch的大小即可实现三种算法）'><span>参数更新方式：（通过调整mini_batch的大小即可实现三种算法）</span></h3><ol start='' ><li><p><span>普通梯度下降算法</span></p></li><li><p><span>小批量随机梯度下降算法</span></p></li><li><p><span>随机梯度下降</span></p></li></ol><p> </p><h3 id='绘图'><span>绘图：</span></h3><p><span>使用figure.py绘制模型在训练集和测试集的准确率和损失函数随着epoch迭代的图像。</span></p><p><span>为了保证绘图速度较快，在运行figure.py之后，需要选择训练的样本数量，通常建议1000，这样可以保证训练的速度，快速出图，但是准确率也会下降。</span></p><p><span>当然，也可以通过导入模型参数，直接对模型进行测试。这需要对figure中的部分代码进行调整。</span></p><blockquote><p><span>figure中的cost已经对除以了绘图所用的数据，所以较小</span></p><p><span>损失函数的图像绘制通常会重叠，因为损失函数量级较大，且图像精度较低</span></p></blockquote><p> </p><h3 id='模型参数保存与加载'><span>模型参数保存与加载：</span></h3><p><span>由save 和 load通过对json文件的操作实现模型参数的存储和加载，同样可以使用test_model单独对模型进行测试</span></p><p> </p><blockquote><p><span>以上所有功能，可以通过在execute.py中指定参数，或者在network.py选择性注释掉部分代码实现</span><strong><span>参数更新方式</span></strong><span>等可选功能的切换</span></p></blockquote><p> </p><p> </p><h2 id='运行实例'><span>运行实例</span></h2><h4 id='executepy--关键代码执行后'><span>execute.py 关键代码执行后</span></h4><p><span>（784 * 30 * 10的神经网络，每层分别采用sigmoid, sigmoid, softmax激活函数，使用交叉熵损失函数）</span></p><p><span>（30个epoch，小批量数据集分为10个， 学习率0.5， 正则化参数5.0）</span></p><pre class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" spellcheck="false" lang="python"><div class="CodeMirror cm-s-inner cm-s-null-scroll CodeMirror-wrap" lang="python"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 9.52282px; left: 35.9921px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 28px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>4</div></div></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation"><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -27.996px; width: 28px;"></div><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -27.996px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 19px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable">net</span> <span class="cm-operator">=</span> <span class="cm-variable">network</span>.<span class="cm-property">Network</span>([<span class="cm-number">784</span>, <span class="cm-number">30</span>, <span class="cm-number">10</span>], [<span class="cm-string">'sigmoid'</span>, <span class="cm-string">'sigmoid'</span>, <span class="cm-string">'softmax'</span>], <span class="cm-variable">cost</span><span class="cm-operator">=</span><span class="cm-variable">network</span>.<span class="cm-property">CrossEntropyCost</span>)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -27.996px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 19px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable">net</span>.<span class="cm-property">large_weight_initializer</span>() <span class="cm-comment"># 比较不好初始化方法，注释掉的话会默认选择方差为1，均值为0，初始权值的正态分布初始化</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -27.996px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 19px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable">net</span>.<span class="cm-property">SGD</span>(<span class="cm-variable">training_data</span>, <span class="cm-number">30</span>, <span class="cm-number">10</span>, <span class="cm-number">0.5</span>, <span class="cm-number">5.0</span>, <span class="cm-variable">evaluation_data</span><span class="cm-operator">=</span><span class="cm-variable">test_data</span>, <span class="cm-variable">monitor_evaluation_accuracy</span><span class="cm-operator">=</span><span class="cm-keyword">True</span>) <span class="cm-comment"># 小批量梯度下降法，包含迭代测试结果的输出</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -27.996px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 19px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span class="cm-variable">net</span>.<span class="cm-property">save</span>(<span class="cm-string">'model.json'</span>) <span class="cm-comment"># 保存模型</span></span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 115px;"></div><div class="CodeMirror-gutters" style="height: 115px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 27px;"></div></div></div></div></pre><p> </p><p><span>输出</span></p><pre class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" spellcheck="false" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner cm-s-null-scroll CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 9.31702px; left: 43.9881px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 36px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre><span>xxxxxxxxxx</span></pre><div class="CodeMirror-linenumber CodeMirror-gutter-elt"><div>28</div></div></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation" style=""><div class="CodeMirror-activeline" style="position: relative;"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -35.9921px; width: 36px;"></div><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 27px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">PS C:\Users\85927\Desktop\手写数字识别代码> & D:/anaconda/envs/limu_deepl/python.exe c:/Users/85927/Desktop/手写数字识别代码/execute.py</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">开始训练，请等待...</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Epoch 0 训练完成</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集准确率: 0.9144</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Epoch 1 训练完成</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 27px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集准确率: 0.9282</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">…………（省略部分）</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Epoch 27 训练完成</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集准确率: 0.9644</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">18</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">19</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 27px;">20</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">21</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Epoch 28 训练完成</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">22</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集准确率: 0.9477</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">23</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">24</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">25</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">26</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Epoch 29 训练完成</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">27</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集准确率: 0.9608</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 27px;">28</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 668px;"></div><div class="CodeMirror-gutters" style="height: 668px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 35px;"></div></div></div></div></pre><p><span>（模型参数已经保存进入model.json 中）</span></p><h4 id='figurepy在默认参数下执行测试样例后'><span>figure.py在默认参数下执行测试样例后</span></h4><p><span>终端</span></p><pre class="md-fences md-end-block md-fences-with-lineno ty-contain-cm modeLoaded" spellcheck="false" lang="" style="break-inside: unset;"><div class="CodeMirror cm-s-inner cm-s-null-scroll CodeMirror-wrap" lang=""><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 9.31696px; left: 43.9881px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" tabindex="0" style="position: absolute; bottom: -1em; padding: 0px; width: 1000px; height: 1em; outline: none;"></textarea></div><div class="CodeMirror-scrollbar-filler" cm-not-content="true"></div><div class="CodeMirror-gutter-filler" cm-not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1"><div class="CodeMirror-sizer" style="margin-left: 36px; margin-bottom: 0px; border-right-width: 0px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines" role="presentation"><div role="presentation" style="position: relative; outline: none;"><div class="CodeMirror-measure"></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-code" role="presentation" style=""><div style="position: relative;" class="CodeMirror-activeline"><div class="CodeMirror-activeline-background CodeMirror-linebackground"></div><div class="CodeMirror-gutter-background CodeMirror-activeline-gutter" style="left: -35.9921px; width: 36px;"></div><div class="CodeMirror-gutter-wrapper CodeMirror-activeline-gutter" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 27px;">1</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">PS C:\Users\85927\Desktop\手写数字识别代码> & D:/anaconda/envs/limu_deepl/python.exe c:/Users/85927/Desktop/手写数字识别代码/figure.py</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">2</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">输入保存结果的文件名称(建议result.json): result.json</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">3</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">输入想要运行的epoch数: 20 </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">4</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">输入训练集的采用的数据规模(建议1000): 1000 </span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">5</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">输入正则化参数,lambda(建议5.0): 5.0</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">6</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">7</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Epoch 0 训练完成</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">8</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">训练集损失: 1.9727215009866323</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">9</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">训练集准确率: 649 / 1000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 27px;">10</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集损失: 2.276804397074614</span></pre></div><div class="" style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">11</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集准确率: 5575 / 10000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">12</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">13</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">14</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">15</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Epoch 1 训练完成</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">16</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">训练集损失: 1.3040527620294522</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">17</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">训练集准确率: 807 / 1000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">18</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集损失: 1.671468298844578</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">19</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集准确率: 6975 / 10000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 27px;">20</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">21</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">22</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">…………（中间省略）</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">23</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">24</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">25</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Epoch 18 训练完成</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">26</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">训练集损失: 0.20076835410959984</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">27</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">训练集准确率: 990 / 1000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">28</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集损失: 1.2169281585694622</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">29</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集准确率: 8143 / 10000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 27px;">30</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">31</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;"><span cm-text="" cm-zwsp="">
</span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">32</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">33</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">Epoch 19 训练完成</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">34</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">训练集损失: 0.19770628582780783</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">35</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">训练集准确率: 991 / 1000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">36</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集损失: 1.2136953746150674</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 27px;">37</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">测试集准确率: 8168 / 10000</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -35.9921px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt CodeMirror-linenumber-show" style="left: 0px; width: 27px;">38</div></div><pre class=" CodeMirror-line " role="presentation"><span role="presentation" style="padding-right: 0.1px;">****************************************</span></pre></div></div></div></div></div></div><div style="position: absolute; height: 0px; width: 1px; border-bottom: 0px solid transparent; top: 899px;"></div><div class="CodeMirror-gutters" style="height: 899px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 35px;"></div></div></div></div></pre><center class="half">
<img src="./assets/Figure_1.png" width="450"/>
<img src="./assets/Figure_2.png" width="450"/>
</center><p> </p><h2 id='实验内容'><span>实验内容</span></h2><p><span>A1: 基于全链接网络的手写数字体识别 (15 points)</span></p><p><span>• 本题目考察如何设计并实现一个简单的图像分类器。设置本题目的目的如下：</span></p><p> </p><ul><li><p><span>理解基本的图像识别流程及数据驱动的方法（训练、预测等阶段）</span></p></li><li><p><span>答：见代码，已完成</span></p></li></ul><p> </p><ul><li><p><span>理解训练集/验证集/测试集的数据划分，以及如何使用验证数据调整模型的超参数</span></p></li><li><p><span>答：见代码以及上述对validation_data的作用描述</span></p></li></ul><p> </p><ul><li><p><span>实现一个</span><strong><span>全连接神经网络</span></strong><span>分类器</span></p></li><li><p><span>答：见代码，已实现</span></p><p> </p></li><li><p><span>理解不同的分类器之间的区别，以及使用不同的更新方法优化神经网络</span></p></li><li><p><span>答：在神经网络中，常用的分类器包括 softmax 分类器和二元分类器。Softmax 分类器适用于多类别分类问题，它会将神经网络的输出转化为概率分布，使用sigmoid作为输出层的神经元同样可行，但是效果不如softmax。</span></p><p><span>常用的优化算法包括梯度下降法、随机梯度下降法（SGD）、小批量梯度下降法等。随机梯度下降的优点是计算效率高。缺点是，收敛性相对不稳定由于每次迭代只考虑一个样本，可能会引入一些随机性，使得收敛过程相对不稳定。可能会陷入局部最优解，而不是全局最优解。而小批量梯度下降算法在保留了一定随机性的同时，可以保证参数更新是向着全局最优的方向进行，同时，还可以减轻计算设备的开销。</span></p><p><span>学习率是梯度下降算法中一个重要的超参数，它控制了参数更新的步幅。合适的学习率能够加速收敛，但过大的学习率可能会导致震荡甚至发散。正则化方法如 L1 正则化和 L2 正则化可以用于防止过拟合，它们通过对参数进行惩罚来降低模型的复杂度。而正则化参数lambda则是对正则化的一种约束。</span></p><p> </p></li></ul><p> </p><p><strong><span>• 附加题：</span></strong><span> </span></p><p><span> 尝试使用不同的损失函数和正则化方法，观察并分析其对实验结果的影响 </span></p><p><span>答：</span></p><h4 id='两种损失函数的对比\nλ\n--50\nη\n--05）'><span>两种损失函数的对比（</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.319ex" height="1.597ex" role="img" focusable="false" viewBox="0 -694 583 706" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.027ex;"><defs><path id="MJX-17-TEX-I-1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D706" xlink:href="#MJX-17-TEX-I-1D706"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\lambda</script><span> = 5.0，</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.124ex" height="1.489ex" role="img" focusable="false" viewBox="0 -442 497 658" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.489ex;"><defs><path id="MJX-24-TEX-I-1D702" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q156 442 175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336V326Q503 302 439 53Q381 -182 377 -189Q364 -216 332 -216Q319 -216 310 -208T299 -186Q299 -177 358 57L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D702" xlink:href="#MJX-24-TEX-I-1D702"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>η</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\eta</script><span> = 0.5）</span></h4><p><strong><span>1.</span></strong><span>采用784 * 30 * 10的神经网络，每层分别采用sigmoid, sigmoid, softmax激活函数，</span><strong><span>使用交叉熵损失函数，L2正则化</span></strong></p><p><span>结果如下</span></p><center class="half">
<img src="./assets/Figure_3.png" width="450"/>
<img src="./assets/Figure_4.png" width="450"/>
</center><p> </p><p> </p><p><strong><span>2.</span></strong><span>网络同上，</span><strong><span>使用均方误差损失函数，L2正则化</span></strong></p><p><span>结果如下</span></p><center class="half">
<img src="./assets/Figure_5.png" width="450"/>
<img src="./assets/Figure_6.png" width="450"/>
</center><p><span>通过对比上面面两种不同损失函数的对模型训练效果的对比，发现交叉熵损失函数，cost下降更快，模型准确率更高，且训练速度更快。这样的效果是基于sigmoid和交叉熵损失函数在数学原理上的相适性更好。但是通过图像也可以看出，交叉熵函数的不稳定行大于均方误差函数。</span></p><p> </p><h4 id='不同正则化方式的对比\nλ\n--50\nη\n--05）'><span>不同正则化方式的对比（</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.319ex" height="1.597ex" role="img" focusable="false" viewBox="0 -694 583 706" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.027ex;"><defs><path id="MJX-17-TEX-I-1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D706" xlink:href="#MJX-17-TEX-I-1D706"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\lambda</script><span> = 5.0，</span><mjx-container class="MathJax" jax="SVG" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="1.124ex" height="1.489ex" role="img" focusable="false" viewBox="0 -442 497 658" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.489ex;"><defs><path id="MJX-24-TEX-I-1D702" d="M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q156 442 175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336V326Q503 302 439 53Q381 -182 377 -189Q364 -216 332 -216Q319 -216 310 -208T299 -186Q299 -177 358 57L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D702" xlink:href="#MJX-24-TEX-I-1D702"></use></g></g></g></svg><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>η</mi></math></mjx-assistive-mml></mjx-container><script type="math/tex">\eta</script><span> = 0.5）</span></h4><p><strong><span>1.</span></strong><span>采用784 * 30 * 10的神经网络，每层分别采用sigmoid, sigmoid, softmax激活函数，</span><strong><span>使用交叉熵损失函数，L2正则化</span></strong></p><p><span>结果如下</span></p><center class="half">
<img src="./assets/Figure_3.png" width="450"/>
<img src="./assets/Figure_4.png" width="450"/>
</center><p> </p><p><strong><span>2.</span></strong><span>采用784 * 30 * 10的神经网络，每层分别采用sigmoid, sigmoid, softmax激活函数，</span><strong><span>使用交叉熵损失函数，L1正则化</span></strong></p><p><span>结果如下</span></p><center class="half">
<img src="./assets/Figure_7.png" width="450"/>
<img src="./assets/Figure_8.png" width="450"/>
</center><p><strong><span>3.</span></strong><span>采用784 * 30 * 10的神经网络，每层分别采用sigmoid, sigmoid, softmax激活函数，</span><strong><span>使用交叉熵损失函数，无正则化</span></strong></p><p><span>结果如下</span></p><center class="half">
<img src="./assets/Figure_9.png" width="450"/>
<img src="./assets/Figure_10.png" width="450"/>
</center><p><strong><span>对比上列三个实验结果，发现，添加了正则化项的模型，过拟合程度显著降低，且准确率有所提高。</span></strong></p><p> </p><p> </p><p><span> 尝试使用不同的优化算法，观察并分析其对训练过程和实验结果的影响 (如batch GD, online GD, mini-batch GD, SGD, 或其它的优化算法，如Momentum, Adsgrad, Adam, Admax) (+5 points)</span></p><p><strong><span>1.</span></strong><span> 784 * 30 * 10神经网络（激活函数同上），</span><strong><span>使用交叉熵损失函数，L2正则化，小批量随机梯度下降（batch_size = 10), epoch = 30</span></strong></p><p><span>结果如下</span></p><center class="half">
<img src="./assets/Figure_11.png" width="450"/>
<img src="./assets/Figure_12.png" width="450"/>
</center><p><strong><span>2.</span></strong><span>网络同上，</span><strong><span>使用交叉熵损失函数，L2正则化，普通梯度下降（batch_size = 50000)，epoch = 100(补偿性增大)</span></strong></p><p><span>结果如下</span></p><center class="half">
<img src="./assets/Figure_13.png" width="450"/>
<img src="./assets/Figure_14.png" width="450"/>
</center><p> </p><p><strong><span>3.</span></strong><span> 网络同上，</span><strong><span>使用交叉熵损失函数，L2正则化，随机梯度下降（batch_size = 1 ), epoch = 30</span></strong></p><p><span>结果如下</span></p><center class="half">
<img src="./assets/Figure_17.png" width="450"/>
<img src="./assets/Figure_18.png" width="450"/>
</center><p><span>根据上述实验结果，发现普通梯度下降算法虽然可以正常更新参数，逐步提高模型准确率，但是每个epoch只更新参数一次，速度非常慢。随机梯度下降，因为每个样例都会导致参数更新，所以随机性会更强，不易控制朝着最优解的方向下降。小批量随机梯度下降法，batch = 10,每个epoch更新5000次参数，在保证了训练速度的同时，提高了模型的稳定性，并且训练效果优于其余两种方法。</span></p><p> </p><p> </p><h2 id='参考文章书籍代码'><span>参考文章、书籍、代码</span></h2><ol start='' ><li><p><a href='https://www.cnblogs.com/jsfantasy/p/12177275.html'><span>神经网络之反向传播算法（BP）公式推导（超详细 jsfantasy - 博客园 </span></a></p></li><li><p><a href='http://neuralnetworksanddeeplearning.com/index.html'><span>Neural networks and deep learning</span></a></p></li><li><p><a href='https://github.com/mnielsen/neural-networks-and-deep-learning'><span>mnielsen/neural-networks-and-deep-learning</span></a></p></li></ol><p> </p><h2 id='辅助工具'><span>辅助工具</span></h2><ol start='' ><li><p><span>Github copilot ：VScode插件，辅助编写代码</span></p></li><li><p><span>gpt_academic ：通过API部署的本地自用GPT项目，解释上述书籍和仓库中较为难以理解的代码</span></p></li></ol><p> </p><h2 id='声明'><span>声明</span></h2><p><strong><span>所有代码均为本人逐行实现，代码机制、公式以及涉及到的数学原理，均理解透彻</span></strong></p></div></div>
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