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<a href="https://lampze.github.io">lampze's Blog</a>
<span id="post-date" style="float: right">2021-08-21 六 00:00</span>
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<div id="content" class="content">
<header>
<h1 class="title">正则化对 GAN 输出结果的影响</h1>
</header>
<div id="outline-container-orgcb0898b" class="outline-2">
<h2 id="orgcb0898b">前言</h2>
<div class="outline-text-2" id="text-orgcb0898b">
<p>
在我尝试使用正则化解决 <code>GAN</code> 模式崩溃的问题时,我发现了一个有意思的现象。我给模型添加了 <code>L2</code> 正则项后,生成的图片比以往要模糊许多,所以我决定测试一下,模糊是不是由 <code>L2</code> 导致的。<br>
</p>
</div>
</div>
<div id="outline-container-orgaabc24f" class="outline-2">
<h2 id="orgaabc24f">测试</h2>
<div class="outline-text-2" id="text-orgaabc24f">
<p>
本模型除了 <code>L1</code> 、 <code>L2</code> 、 <code>Dropout</code> 还使用了其他的优化方法, <code>LayerNorm</code> 、 <code>GELU</code> 、 <code>Adam</code> 。每种模型的训练次数相同,没有给图片加标签,让模式崩溃的效果更明显些。<br>
</p>
</div>
<div id="outline-container-orgf4725a3" class="outline-3">
<h3 id="orgf4725a3">基础代码</h3>
<div class="outline-text-3" id="text-orgf4725a3">
<p>
后面的测试都是基于这份代码之上修改,只放了关键的模型定义与训练代码。<br>
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="font-weight: bold;">class</span> <span style="font-weight: bold;">Discriminator</span>(nn.Module):
<span style="font-weight: bold;">def</span> <span style="font-weight: bold;">__init__</span>(<span style="font-weight: bold;">self</span>):
<span style="font-weight: bold;">super</span>().__init__()
<span style="font-weight: bold;">self</span>.<span style="color: #383a42;">model</span> = nn.Sequential(
nn.Flatten(),
nn.Linear(<span style="color: #8a3b3c; font-weight: bold;">28</span> * <span style="color: #8a3b3c; font-weight: bold;">28</span>, <span style="color: #8a3b3c; font-weight: bold;">200</span>),
nn.GELU(),
nn.LayerNorm(<span style="color: #8a3b3c; font-weight: bold;">200</span>),
nn.Linear(<span style="color: #8a3b3c; font-weight: bold;">200</span>, <span style="color: #8a3b3c; font-weight: bold;">1</span>),
nn.Sigmoid(),
)
<span style="font-weight: bold;">self</span>.<span style="color: #383a42;">loss_function</span> = nn.BCELoss()
<span style="font-weight: bold;">self</span>.<span style="color: #383a42;">optimiser</span> = torch.optim.Adam(
<span style="font-weight: bold;">self</span>.parameters(), lr=<span style="color: #8a3b3c; font-weight: bold;">0.0001</span>
)
<span style="font-weight: bold;">self</span>.progress = []
<span style="font-weight: bold;">pass</span>
<span style="font-weight: bold;">def</span> <span style="font-weight: bold;">forward</span>(<span style="font-weight: bold;">self</span>, inputs):
<span style="font-weight: bold;">return</span> <span style="font-weight: bold;">self</span>.model(inputs).reshape(<span style="color: #8a3b3c; font-weight: bold;">1</span>)
<span style="font-weight: bold;">def</span> <span style="font-weight: bold;">train</span>(<span style="font-weight: bold;">self</span>, inputs, targets):
outputs = <span style="font-weight: bold;">self</span>.forward(inputs)
loss = <span style="font-weight: bold;">self</span>.loss_function(outputs, targets)
<span style="font-weight: bold;">self</span>.optimiser.zero_grad()
loss.backward()
<span style="font-weight: bold;">self</span>.optimiser.step()
<span style="font-weight: bold;">pass</span>
<span style="font-weight: bold;">class</span> <span style="font-weight: bold;">Generator</span>(nn.Module):
<span style="font-weight: bold;">def</span> <span style="font-weight: bold;">__init__</span>(<span style="font-weight: bold;">self</span>):
<span style="font-weight: bold;">super</span>().__init__()
<span style="font-weight: bold;">self</span>.model = nn.Sequential(
nn.Linear(<span style="color: #8a3b3c; font-weight: bold;">200</span>, <span style="color: #8a3b3c; font-weight: bold;">400</span>),
nn.GELU(),
nn.LayerNorm(<span style="color: #8a3b3c; font-weight: bold;">400</span>),
nn.Linear(<span style="color: #8a3b3c; font-weight: bold;">400</span>, <span style="color: #8a3b3c; font-weight: bold;">28</span> * <span style="color: #8a3b3c; font-weight: bold;">28</span>),
nn.Sigmoid(),
)
<span style="font-weight: bold;">self</span>.optimiser = torch.optim.Adam(
<span style="font-weight: bold;">self</span>.parameters(), lr=<span style="color: #8a3b3c; font-weight: bold;">0.0001</span>
)
<span style="font-weight: bold;">self</span>.progress = []
<span style="font-weight: bold;">pass</span>
<span style="font-weight: bold;">def</span> <span style="font-weight: bold;">forward</span>(<span style="font-weight: bold;">self</span>, inputs):
<span style="font-weight: bold;">return</span> <span style="font-weight: bold;">self</span>.model(inputs)
<span style="font-weight: bold;">def</span> <span style="font-weight: bold;">train</span>(<span style="font-weight: bold;">self</span>, D, inputs, targets):
g_output = <span style="font-weight: bold;">self</span>.forward(inputs)
d_output = D.forward(g_output.reshape(<span style="color: #8a3b3c; font-weight: bold;">1</span>, <span style="color: #8a3b3c; font-weight: bold;">28</span>, <span style="color: #8a3b3c; font-weight: bold;">28</span>))
loss = D.loss_function(d_output, targets)
<span style="font-weight: bold;">self</span>.optimiser.zero_grad()
loss.backward()
<span style="font-weight: bold;">self</span>.optimiser.step()
<span style="font-weight: bold;">pass</span>
D = Discriminator()
G = Generator()
<span style="font-weight: bold;">for</span> epoch <span style="font-weight: bold;">in</span> <span style="font-weight: bold;">range</span>(<span style="color: #8a3b3c; font-weight: bold;">4</span>):
<span style="font-weight: bold;">for</span> image_data_tensor, label <span style="font-weight: bold;">in</span> mnist_train:
D.train(image_data_tensor, torch.tensor([<span style="color: #8a3b3c; font-weight: bold;">1.0</span>]))
D.train(
G.forward(generate_random_seed(<span style="color: #8a3b3c; font-weight: bold;">200</span>)).detach().reshape(<span style="color: #8a3b3c; font-weight: bold;">1</span>, <span style="color: #8a3b3c; font-weight: bold;">28</span>, <span style="color: #8a3b3c; font-weight: bold;">28</span>),
torch.tensor([<span style="color: #8a3b3c; font-weight: bold;">0.0</span>]),
)
G.train(D, generate_random_seed(<span style="color: #8a3b3c; font-weight: bold;">200</span>), torch.tensor([<span style="color: #8a3b3c; font-weight: bold;">1.0</span>]))
<span style="font-weight: bold;">pass</span>
<span style="font-weight: bold;">pass</span>
</pre>
</div>
<p>
后面的测试只放修改位置的代码。<br>
</p>
</div>
<div id="outline-container-org476dc8d" class="outline-4">
<h4 id="org476dc8d">训练结果</h4>
<div class="outline-text-4" id="text-org476dc8d">
<figure id="orgaf957af">
<img src="./static/img/regularization_with_gan_output/normal.png" alt="normal.png"><br>
</figure>
</div>
</div>
<div id="outline-container-orgfd9449d" class="outline-4">
<h4 id="orgfd9449d">评价</h4>
<div class="outline-text-4" id="text-orgfd9449d">
<p>
有些许的模式崩溃现象,只有几种类型的数字,数字的颗粒感比较严重,不够平滑。<br>
</p>
</div>
</div>
</div>
<div id="outline-container-orgbe1d6fd" class="outline-3">
<h3 id="orgbe1d6fd">L1</h3>
<div class="outline-text-3" id="text-orgbe1d6fd">
<p>
更改训练函数即可<br>
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="font-weight: bold;">def</span> <span style="font-weight: bold;">train</span>(<span style="font-weight: bold;">self</span>, D, inputs, targets):
<span style="color: #383a42;">g_output</span> = <span style="font-weight: bold;">self</span>.forward(inputs)
<span style="color: #383a42;">d_output</span> = D.forward(g_output.reshape(<span style="color: #8a3b3c; font-weight: bold;">1</span>, <span style="color: #8a3b3c; font-weight: bold;">28</span>, <span style="color: #8a3b3c; font-weight: bold;">28</span>))
<span style="color: #383a42;">loss</span> = D.loss_function(d_output, targets)
<span style="color: #383a42;">l1_loss</span> = <span style="color: #8a3b3c; font-weight: bold;">0</span>
<span style="font-weight: bold;">for</span> param <span style="font-weight: bold;">in</span> <span style="font-weight: bold;">self</span>.parameters():
<span style="color: #383a42;">l1_loss</span> += torch.<span style="font-weight: bold;">sum</span>(torch.<span style="font-weight: bold;">abs</span>(param))
<span style="font-weight: bold;">pass</span>
<span style="color: #383a42;">loss</span> += <span style="color: #8a3b3c; font-weight: bold;">0.005</span> * l1_loss
<span style="font-weight: bold;">self</span>.optimiser.zero_grad()
loss.backward()
<span style="font-weight: bold;">self</span>.optimiser.step()
<span style="font-weight: bold;">pass</span>
</pre>
</div>
</div>
<div id="outline-container-org0ee3427" class="outline-4">
<h4 id="org0ee3427">训练结果</h4>
<div class="outline-text-4" id="text-org0ee3427">
<figure id="orgda7de16">
<img src="./static/img/regularization_with_gan_output/l1.png" alt="l1.png"><br>
</figure>
</div>
</div>
<div id="outline-container-org09291a8" class="outline-4">
<h4 id="org09291a8">评价</h4>
<div class="outline-text-4" id="text-org09291a8">
<p>
几乎没有可以识别的数字,可能是训练次数不够,但数字可以明显看出比较平滑,也就是那种模糊的效果。<br>
</p>
</div>
</div>
</div>
<div id="outline-container-org401c451" class="outline-3">
<h3 id="org401c451">L2</h3>
<div class="outline-text-3" id="text-org401c451">
<p>
<code>pytorch</code> 的优化器通过参数 <code>weight_decay</code> 可以实现 <code>L2</code> 正则。<br>
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="font-weight: bold;">self</span>.<span style="color: #383a42;">optimiser</span> = torch.optim.Adam(
<span style="font-weight: bold;">self</span>.parameters(), lr=<span style="color: #8a3b3c; font-weight: bold;">0.0001</span>, weight_decay=<span style="color: #8a3b3c; font-weight: bold;">0.005</span>
)
</pre>
</div>
</div>
<div id="outline-container-org4d2ccc8" class="outline-4">
<h4 id="org4d2ccc8">训练结果</h4>
<div class="outline-text-4" id="text-org4d2ccc8">
<figure id="org00f7cc7">
<img src="./static/img/regularization_with_gan_output/l2.png" alt="l2.png"><br>
</figure>
</div>
</div>
<div id="outline-container-org6275533" class="outline-4">
<h4 id="org6275533">评价</h4>
<div class="outline-text-4" id="text-org6275533">
<p>
相比 <code>L1</code> 数字周围更加干净,更加清晰一些,但模糊的效果还在,与 <code>L1</code> 的差异不排除随机误差的可能。<br>
</p>
</div>
</div>
</div>
<div id="outline-container-orgc8a7ec6" class="outline-3">
<h3 id="orgc8a7ec6">Dropout</h3>
<div class="outline-text-3" id="text-orgc8a7ec6">
<p>
这个添加一个 <code>Dropout</code> 层即可<br>
</p>
<div class="org-src-container">
<pre class="src src-python"><span style="font-weight: bold;">self</span>.<span style="color: #383a42;">model</span> = nn.Sequential(
nn.Linear(<span style="color: #8a3b3c; font-weight: bold;">200</span>, <span style="color: #8a3b3c; font-weight: bold;">400</span>),
nn.Dropout(<span style="color: #8a3b3c; font-weight: bold;">0.5</span>),
nn.GELU(),
nn.LayerNorm(<span style="color: #8a3b3c; font-weight: bold;">400</span>),
nn.Linear(<span style="color: #8a3b3c; font-weight: bold;">400</span>, <span style="color: #8a3b3c; font-weight: bold;">28</span> * <span style="color: #8a3b3c; font-weight: bold;">28</span>),
nn.Sigmoid(),
)
</pre>
</div>
</div>
<div id="outline-container-org3c0eb7b" class="outline-4">
<h4 id="org3c0eb7b">训练结果</h4>
<div class="outline-text-4" id="text-org3c0eb7b">
<figure id="org67078d9">
<img src="./static/img/regularization_with_gan_output/dropout.png" alt="dropout.png"><br>
</figure>
</div>
</div>
<div id="outline-container-org6a94aad" class="outline-4">
<h4 id="org6a94aad">评价</h4>
<div class="outline-text-4" id="text-org6a94aad">
<p>
没有了模糊效果,但数字都不成形,可能是训练次数不够。<br>
</p>
</div>
</div>
</div>
<div id="outline-container-orga0f0edb" class="outline-3">
<h3 id="orga0f0edb">Dropout + L2</h3>
<div class="outline-text-3" id="text-orga0f0edb">
</div>
<div id="outline-container-org0995401" class="outline-4">
<h4 id="org0995401">训练结果</h4>
<div class="outline-text-4" id="text-org0995401">
<figure id="org0057163">
<img src="./static/img/regularization_with_gan_output/dropout_l2.png" alt="dropout_l2.png"><br>
</figure>
</div>
</div>
<div id="outline-container-org538c2aa" class="outline-4">
<h4 id="org538c2aa">评价</h4>
<div class="outline-text-4" id="text-org538c2aa">
<p>
数字很平滑,但都不成型。<br>
</p>
</div>
</div>
</div>
</div>
<div id="outline-container-org69fd22e" class="outline-2">
<h2 id="org69fd22e">结论</h2>
<div class="outline-text-2" id="text-org69fd22e">
<p>
经过我不严谨的实验可以发现, <code>L1</code> 与 <code>L2</code> 正则化生成的图片确实会有模糊的效果,具体的原因可能是因为 <code>L1</code> 会让神经网络的参数矩阵更加稀疏, <code>L2</code> 不会让单个参数过大,也就不会因为一个神经元大范围改变结果,而尖锐的效果就是相邻的像素之间差别过大,故会产生模糊的效果。<br>
</p>
</div>
</div>
</div>
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<center id="modi-date">2021-12-09 四 17:18</center>
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