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向量
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机器学习
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计算语言学
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计算机视觉
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音频与语音
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多模态学习
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统计学
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</a>
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抽样
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推断
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<span class="md-ellipsis">
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概率论
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<span class="md-nav__icon md-icon"></span>
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概率论
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计数
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</span>
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</a>
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概率概念
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</a>
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分布
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</span>
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</a>
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<span class="md-ellipsis">
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贝叶斯
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</span>
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</a>
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</li>
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信息论
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</span>
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</a>
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<span class="md-ellipsis">
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机器学习
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</span>
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<span class="md-nav__icon md-icon"></span>
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</label>
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<span class="md-nav__icon md-icon"></span>
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机器学习
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经典机器学习
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</span>
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</a>
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梯度机器学习
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</span>
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</a>
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</li>
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<span class="md-ellipsis">
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深度学习
|
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</span>
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|
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|
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</a>
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</li>
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<a href="../../chapter%2006%3A%20machine%20learning/04.%20reinforcement%20learning/" class="md-nav__link">
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强化学习
|
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</span>
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|
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</a>
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</li>
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<a href="../../chapter%2006%3A%20machine%20learning/05.%20distributed%20deep%20learning/" class="md-nav__link">
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<span class="md-ellipsis">
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分布式深度学习
|
||
|
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|
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|
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</span>
|
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|
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|
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|
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</a>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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计算语言学
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</span>
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<span class="md-nav__icon md-icon"></span>
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<span class="md-nav__icon md-icon"></span>
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计算语言学
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语言学基础
|
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</span>
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</a>
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文本处理与经典 NLP
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</span>
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|
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</a>
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</li>
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嵌入与序列模型
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</span>
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</a>
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</li>
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<a href="../../chapter%2007%3A%20computational%20linguistics/04.%20transformers%20and%20language%20models/" class="md-nav__link">
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<span class="md-ellipsis">
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Transformer 与语言模型
|
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</span>
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|
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|
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|
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</a>
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</li>
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<span class="md-ellipsis">
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|
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高级文本生成
|
||
|
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|
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|
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</span>
|
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|
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|
||
|
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</a>
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|
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|
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<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
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计算机视觉
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</span>
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计算机视觉
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图像基础
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</span>
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</a>
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</li>
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卷积网络
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卷积网络
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音频与语音
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数字信号处理
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自动语音识别
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语音合成
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</span>
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</a>
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说话人与音频分析
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</span>
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</a>
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源分离与降噪
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</span>
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<span class="md-ellipsis">
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多模态学习
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</span>
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<span class="md-nav__icon md-icon"></span>
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<span class="md-nav__icon md-icon"></span>
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多模态学习
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
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多模态表征
|
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|
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</span>
|
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|
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|
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|
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</a>
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</li>
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视觉语言模型
|
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|
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|
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</span>
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|
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|
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|
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</a>
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</li>
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<span class="md-ellipsis">
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图像与视频 Token 化
|
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|
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|
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|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
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<span class="md-ellipsis">
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跨模态生成
|
||
|
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|
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|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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<a href="../../chapter%2010%3A%20multimodal%20learning/05.%20unified%20multimodal%20architectures/" class="md-nav__link">
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|
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<span class="md-ellipsis">
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|
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|
||
统一多模态架构
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
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</a>
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</ul>
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</nav>
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|
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|
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||
|
||
|
||
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<li class="md-nav__item md-nav__item--nested">
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<span class="md-ellipsis">
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|
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自主系统
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</span>
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<span class="md-nav__icon md-icon"></span>
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</label>
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<span class="md-nav__icon md-icon"></span>
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自主系统
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感知
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</span>
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</a>
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机器人学习
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</span>
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|
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|
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</a>
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</li>
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<span class="md-ellipsis">
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视觉-语言-动作模型
|
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|
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|
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|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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<a href="../../chapter%2011%3A%20autonomous%20systems/04.%20self-driving/" class="md-nav__link">
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<span class="md-ellipsis">
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自动驾驶
|
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|
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|
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</span>
|
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|
||
|
||
|
||
</a>
|
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</li>
|
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<li class="md-nav__item">
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<a href="../../chapter%2011%3A%20autonomous%20systems/05.%20space%20and%20extreme%20robotics/" class="md-nav__link">
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|
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|
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<span class="md-ellipsis">
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|
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|
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太空与极端机器人
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
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</a>
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</ul>
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</nav>
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||
|
||
|
||
|
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<li class="md-nav__item md-nav__item--nested">
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<span class="md-ellipsis">
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|
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图神经网络
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|
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</span>
|
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<span class="md-nav__icon md-icon"></span>
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</label>
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<span class="md-nav__icon md-icon"></span>
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图神经网络
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
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几何深度学习
|
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|
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|
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||
|
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硬件基础
|
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|
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|
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</a>
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ARM 与 NEON
|
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x86 与 AVX
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Triton、TPU 与 Pallas
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边缘推理
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ML 系统设计
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应用 AI
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前沿 AI
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<h1 id="_1">卷积网络<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
|
||
<p><em>卷积神经网络直接从像素数据中学习空间特征层级，用梯度优化的滤波器取代人工设计的滤波器。本文涵盖卷积机制、池化、步长、空洞卷积、感受野，以及定义了图像分类的标志性架构（LeNet、AlexNet、VGG、ResNet、Inception、EfficientNet）。</em></p>
|
||
<ul>
|
||
<li>
|
||
<p>在文件 01 中，我们手工设计了用于边缘检测、模糊和角点检测的滤波器。一个自然而然的问题是：我们能否从数据中学习最优的滤波器？这正是卷积神经网络（CNN）所做的。</p>
|
||
</li>
|
||
<li>
|
||
<p>CNN 不是手动选择滤波器权重，而是通过梯度下降（第 06 章）学习它们，发现对当前任务直接有用的特征。</p>
|
||
</li>
|
||
<li>
|
||
<p>在第 06 章中，我们介绍了卷积操作、CNN 基础以及滤波器学习的思想。在这里，我们深入探讨使 CNN 在十多年来成为计算机视觉主导范式的架构创新。</p>
|
||
</li>
|
||
<li>
|
||
<p>回顾核心的<strong>卷积操作</strong>：一个大小为 <span class="arithmatex">\(k \times k\)</span> 的滤波器 <span class="arithmatex">\(K\)</span> 在输入特征图上滑动，在每个位置计算点积（第 06 章）。输出大小由三个超参数控制：</p>
|
||
<ul>
|
||
<li><strong>步长</strong>：滤波器在位置之间移动的像素数。步长 1 意味着滤波器每次移动一个像素。步长 2 意味着每次移动两个像素，空间维度减半。步长卷积是下采样时池化的一种替代方案。</li>
|
||
<li><strong>填充</strong>：在输入边界周围添加零。"Same"填充（<span class="arithmatex">\(p = \lfloor k/2 \rfloor\)</span>）保持空间维度不变。"Valid"填充（<span class="arithmatex">\(p = 0\)</span>）会减小空间维度。</li>
|
||
<li><strong>空洞卷积</strong>：在滤波器元素之间插入间隙。一个 3x3 的滤波器以空洞率 2 工作，仅用 9 个参数就覆盖了 5x5 的感受野。空洞卷积扩大了感受野而不增加计算量。</li>
|
||
</ul>
|
||
</li>
|
||
<li>
|
||
<p>卷积后的输出空间大小：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\text{out} = \left\lfloor \frac{\text{in} - k + 2p}{s} \right\rfloor + 1\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>其中 <span class="arithmatex">\(\text{in}\)</span> 是输入大小，<span class="arithmatex">\(k\)</span> 是卷积核大小，<span class="arithmatex">\(p\)</span> 是填充，<span class="arithmatex">\(s\)</span> 是步长。该公式独立地适用于高度和宽度。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>感受野</strong>是指能够影响某个神经元值的原始输入区域。</p>
|
||
<ul>
|
||
<li>早期层的感受野较小（它们看到的是边缘等局部模式）。</li>
|
||
<li>更深层的感受野较大（它们看到的是物体部件等更大的结构）。</li>
|
||
</ul>
|
||
</li>
|
||
<li>
|
||
<p>感受野随着每一层增长：大致每层卷积增加 <span class="arithmatex">\(k - 1\)</span> 个像素（加入步长或空洞卷积时增长更多）。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="感受野逐层增长：第 1 层神经元看到 3x3 的补丁，第 2 层神经元看到 5x5 的补丁，第 3 层神经元看到原始输入中 7x7 的补丁" src="../../images/receptive_field.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>池化</strong>层在保留最重要信息的同时降低空间维度。</p>
|
||
<ul>
|
||
<li><strong>最大池化</strong>取每个窗口中的最大值，保留最强的激活（最突出的特征）。</li>
|
||
<li><strong>平均池化</strong>取均值，平滑特征图。一个 2x2 的池化窗口配合步长 2 会使两个空间维度都减半。</li>
|
||
</ul>
|
||
</li>
|
||
<li>
|
||
<p><strong>全局平均池化（GAP）</strong> 将每个通道的整个空间范围平均为单个数值，生成一个长度等于通道数的向量。GAP 取代了许多现代架构末尾的全连接层，大幅减少了参数量，并起到了结构正则化的作用。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>批归一化（BatchNorm）</strong> 将每个小批量内的激活值归一化为零均值和单位方差，然后应用可学习的缩放和平移（第 06 章）。在 CNN 中，批归一化按通道应用：统计量在跨批次和空间维度上为每个通道独立计算。它稳定了训练，允许使用更高的学习率，并起到轻度正则化的作用。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>丢弃法</strong>（第 06 章）在训练期间随机将神经元置零。</p>
|
||
</li>
|
||
<li>
|
||
<p>在 CNN 中，<strong>空间丢弃法（Dropout2D）</strong> 丢弃整个特征图通道而非单个像素，这更为有效，因为特征图中相邻像素高度相关。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>数据增广</strong>通过在训练期间对每张图像应用随机变换来人为地扩展训练集：水平翻转、随机裁剪、旋转、颜色抖动（调整亮度、对比度、饱和度、色调）以及 cutout（遮挡随机矩形区域）。网络以多种不同形式看到每张图像，迫使其学习变换不变的特征，而非记忆特定的像素模式。</p>
|
||
</li>
|
||
<li>
|
||
<p>高级增广策略包括 <strong>Mixup</strong>（混合两张图像及其标签：<span class="arithmatex">\(\tilde{x} = \lambda x_i + (1-\lambda) x_j\)</span>，<span class="arithmatex">\(\tilde{y} = \lambda y_i + (1-\lambda) y_j\)</span>）、<strong>CutMix</strong>（将一张图像的矩形区域粘贴到另一张图像上，并按面积比例混合标签）以及 <strong>RandAugment</strong>（从一个固定集合中随机采样一系列增广操作，使用单一的强度参数）。</p>
|
||
</li>
|
||
<li>
|
||
<p>CNN 架构的历史是一个逐步走向更深、更高效设计的故事，每一步都解决了限制前代架构的问题。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>LeNet-5</strong>（LeCun 等人，1998 年）是最早的 CNN，专为手写数字识别设计。两个卷积层后接三个全连接层，使用平均池化和 tanh 激活函数。它证明了学习到的滤波器优于手工设计的特征，但按现代标准来看很小（6 万个参数）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>AlexNet</strong>（Krizhevsky 等人，2012 年）以巨大优势赢得了 ImageNet 竞赛，引发了深度学习革命。关键创新：ReLU 激活函数（取代了存在梯度消失问题的 tanh）、用于正则化的丢弃法、数据增广以及在 GPU 上训练。五个卷积层，三个全连接层，6000 万个参数。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>VGG</strong>（Simonyan 和 Zisserman，2014 年）证明，仅使用 3x3 滤波器并深层堆叠效果优于更大的滤波器。两个堆叠的 3x3 滤波器具有与一个 5x5 滤波器相同的感受野，但参数更少（<span class="arithmatex">\(2 \times 3^2 = 18\)</span> 对比 <span class="arithmatex">\(5^2 = 25\)</span>）且多了一个非线性层。VGG-16（16 层）和 VGG-19（19 层）至今仍被广泛用作特征提取器。架构非常简单：卷积块通道数递增（64、128、256、512），每个块后接最大池化。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="VGG 架构：堆叠的 3x3 卷积块，通道深度递增（64→128→256→512），块之间是最大池化，末端是全连接层" src="../../images/vgg_architecture.svg" /></p>
|
||
<ul>
|
||
<li><strong>GoogLeNet/Inception</strong>（Szegedy 等人，2014 年）引入了 <strong>Inception 模块</strong>：不是选择单一的滤波器大小，而是并行使用 1x1、3x3 和 5x5 卷积，将它们的输出拼接起来，让网络决定哪个尺度最有用。1x1 卷积在较大滤波器之前用作瓶颈以减少计算量。GoogLeNet 以比 VGG 少 12 倍的参数（680 万对比 1.38 亿）实现了更高的准确率。</li>
|
||
</ul>
|
||
<p><img alt="Inception 模块：四个并行分支（1×1、3×3、5×5 和池化），带 1×1 瓶颈，沿通道维度拼接" src="../../images/inception_module.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p>Inception 模块同时捕获多个尺度的特征。1x1 滤波器捕获逐点模式，3x3 捕获局部纹理，5x5 捕获更大的结构。拼接将所有视角组合成丰富的表示。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>ResNet</strong>（He 等人，2016 年）解决了<strong>退化问题</strong>：更深的网络表现反而不如较浅的网络，这不是因为过拟合，而是因为更深的网络更难优化。解决方案是<strong>跳跃连接</strong>（残差连接）：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\text{output} = F(x) + x\]</div>
|
||
<ul>
|
||
<li>该层学习残差 <span class="arithmatex">\(F(x) = \text{output} - x\)</span>。如果最优变换接近恒等映射（这在深层网络中很常见），学习一个接近零的残差比学习完整的映射要容易得多。跳跃连接还提供了直接的梯度通道，减少了梯度消失问题。ResNet 训练了 152 层的网络，远超此前任何架构。</li>
|
||
</ul>
|
||
<p><img alt="ResNet 块：输入 x 经过两个卷积层得到 F(x)，然后跳跃连接将 x 加回，得到输出 F(x) + x" src="../../images/resnet_block.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p>当输入和输出维度不同时（由于步长或通道数变化），<strong>投影捷径</strong>会应用一个 1x1 卷积来匹配 <span class="arithmatex">\(x\)</span> 的维度：<span class="arithmatex">\(\text{output} = F(x) + W_s x\)</span>。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>瓶颈块</strong>（用于 ResNet-50 及更深版本）使用三个卷积：1x1 降通道，3x3 进行空间处理，1x1 再将通道数恢复。这比两个 3x3 卷积计算量更小，允许构建更深的网络。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>DenseNet</strong>（Huang 等人，2017 年）将跳跃连接的思想进一步推进：在一个密集块内，每一层都与所有后续层相连。第 <span class="arithmatex">\(l\)</span> 层接收前面所有层的特征图作为输入：<span class="arithmatex">\(x_l = H_l([x_0, x_1, \ldots, x_{l-1}])\)</span>，其中 <span class="arithmatex">\([\cdot]\)</span> 表示沿通道维度的拼接。这促进了特征复用，增强了梯度流动，并减少了总参数量。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="DenseNet 密集块：每一层通过拼接接收前面所有层的特征图，形成密集连接以实现最大程度的特征复用" src="../../images/densenet_block.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>高效架构</strong>面向移动设备和边缘硬件上的部署，这些场景下计算、内存和能耗都受到限制。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>MobileNet</strong>（Howard 等人，2017 年）用<strong>深度可分离卷积</strong>取代了标准卷积，将操作分解为两个步骤：</p>
|
||
<ol>
|
||
<li><strong>深度卷积</strong>：每个输入通道应用一个独立的 <span class="arithmatex">\(k \times k\)</span> 滤波器（不跨通道交互）</li>
|
||
<li><strong>逐点卷积</strong>：应用 1x1 卷积来组合跨通道的信息</li>
|
||
</ol>
|
||
</li>
|
||
<li>
|
||
<p>一个标准 <span class="arithmatex">\(k \times k\)</span> 卷积，输入通道数为 <span class="arithmatex">\(C_{\text{in}}\)</span>，输出通道数为 <span class="arithmatex">\(C_{\text{out}}\)</span>，每个空间位置需要 <span class="arithmatex">\(k^2 \cdot C_{\text{in}} \cdot C_{\text{out}}\)</span> 次乘法。深度可分离卷积需要 <span class="arithmatex">\(k^2 \cdot C_{\text{in}} + C_{\text{in}} \cdot C_{\text{out}}\)</span> 次，减少了大约 <span class="arithmatex">\(k^2\)</span> 倍。对于 3x3 滤波器，这大约便宜 9 倍。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="深度可分离卷积：深度步骤对每个通道应用一个 k×k 滤波器，然后逐点 1×1 卷积混合通道——输出形状相同，操作量约减少 9×" src="../../images/depthwise_separable_conv.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>MobileNet-V2</strong> 引入了<strong>逆残差块</strong>：先用 1x1 卷积扩展通道，在扩展空间中应用深度卷积，再用 1x1 卷积投影回低维。跳跃连接放置在窄（瓶颈）层上，与 ResNet 的模式相反。扩展率通常为 6。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>EfficientNet</strong>（Tan 和 Le，2019 年）引入了<strong>复合缩放</strong>：不是独立地仅缩放深度、或仅缩放宽度、或仅缩放分辨率，而是使用固定比例同时缩放所有三个维度。给定缩放系数 <span class="arithmatex">\(\phi\)</span>：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\text{depth}: d = \alpha^\phi, \quad \text{width}: w = \beta^\phi, \quad \text{resolution}: r = \gamma^\phi\]</div>
|
||
<ul>
|
||
<li>约束条件为 <span class="arithmatex">\(\alpha \cdot \beta^2 \cdot \gamma^2 \approx 2\)</span>（这样 <span class="arithmatex">\(\phi\)</span> 每增加一个单位，总计算量大约翻倍）。通过网格搜索得到基线比例 <span class="arithmatex">\(\alpha = 1.2\)</span>，<span class="arithmatex">\(\beta = 1.1\)</span>，<span class="arithmatex">\(\gamma = 1.15\)</span>。EfficientNet-B0 到 B7 逐步放大，以远少于之前模型的参数和 FLOPs 达到了最先进的准确率。</li>
|
||
</ul>
|
||
<p><img alt="EfficientNet 复合缩放：单独缩放宽度、深度或分辨率，与使用单一系数 φ 同时缩放三者" src="../../images/efficientnet_scaling.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>ShuffleNet</strong> 通过使用<strong>分组卷积</strong>后接<strong>通道混洗</strong>来降低 1x1 卷积（在 MobileNet 风格的架构中占主导）的成本。分组卷积将通道分成多个组，在每个组内独立进行卷积，但这阻止了跨组的信息流动。混洗操作在组之间重新排列通道，以可忽略不计的成本恢复了信息混合。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>迁移学习</strong>是将在一个任务上训练好的模型适配到不同任务的实践。在计算机视觉中，这几乎总是意味着从一个在 ImageNet（140 万张图像，1000 个类别）上预训练的模型开始，适配到特定领域的数据集（医学图像、卫星图像、制造缺陷检测）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>特征提取</strong>：冻结所有卷积层，移除最终的分类头，仅在上面训练一个新的分类头。冻结的层充当通用特征提取器。当目标域与 ImageNet 相似且目标数据集较小时，这种方法效果很好。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>微调</strong>：解冻部分或全部卷积层，以较小的学习率进行训练。预训练的权重作为起点而非固定特征。微调通常先解冻后面的层（这些层捕获高级的、任务特定的特征），再根据需要解冻更早的层。</p>
|
||
</li>
|
||
<li>
|
||
<p>迁移学习之所以有效，是因为 CNN 的早期层学习通用特征（边缘、纹理、颜色），这些特征对各种任务都有用，而后面层学习任务特定的特征。一个用于分类动物的网络，其边缘检测器对分类建筑物仍然有用。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>可视化 CNN</strong> 可以揭示网络学到了什么，并帮助调试意外行为。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>激活图</strong>（特征图）展示了给定输入图像下每个滤波器的输出。早期层的激活图看起来像边缘图；更深层的激活图则越来越抽象，空间上越来越粗糙。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>Grad-CAM</strong>（梯度加权类别激活映射，Selvaraju 等人，2017 年）高亮了输入图像中对模型预测最重要的区域。其工作原理是：</p>
|
||
<ol>
|
||
<li>计算目标类别分数相对于最后一个卷积层特征图的梯度（使用第 03 章的链式法则）</li>
|
||
<li>对这些梯度进行全局平均池化，得到每个通道的重要性权重</li>
|
||
<li>计算特征图的加权组合并应用 ReLU</li>
|
||
</ol>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[L_{\text{Grad-CAM}} = \text{ReLU}\!\left(\sum_k \alpha_k A^k\right), \quad \alpha_k = \frac{1}{Z} \sum_i \sum_j \frac{\partial y^c}{\partial A^k_{ij}}\]</div>
|
||
<ul>
|
||
<li>其中 <span class="arithmatex">\(A^k\)</span> 是第 <span class="arithmatex">\(k\)</span> 个特征图，<span class="arithmatex">\(\alpha_k\)</span> 是通道 <span class="arithmatex">\(k\)</span> 的重要性权重，<span class="arithmatex">\(y^c\)</span> 是类别 <span class="arithmatex">\(c\)</span> 的分数。结果是一个粗糙的热力图，显示哪些区域驱动了分类。应用 ReLU 是因为我们只对具有正影响分类的特征感兴趣。</li>
|
||
</ul>
|
||
<p><img alt="Grad-CAM：一张狗的输入图像，最后一个卷积层的特征图，梯度加权组合，以及叠加在原始图像上的热力图，高亮了狗的脸部" src="../../images/grad_cam.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>特征反演</strong>通过优化一张随机图像使其匹配目标特征（对像素值进行梯度下降），从特征表示中重建输入图像。这揭示了网络在各层保留了哪些信息。浅层几乎能完美重建图像；深层产生的图像可识别但有所扭曲，这表明精细的空间细节丢失了，而语义内容得以保留。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>Deep Dream</strong> 和<strong>神经风格迁移</strong>是特征可视化的创意应用。Deep Dream 最大化选定层中神经元的激活，产生超现实的、放大模式的图像。神经风格迁移优化目标图像，使其同时匹配一张图像的内容特征（来自深层）和另一张图像的风格特征（滤波器激活的 Gram 矩阵，捕获纹理统计信息）。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="colab-notebook">编程任务（使用 CoLab 或 notebook）<a class="headerlink" href="#colab-notebook" title="Permanent link">¶</a></h2>
|
||
<ol>
|
||
<li>
|
||
<p>用 JAX 从头实现一个简单的 CNN，包含两个卷积层、最大池化和一个分类头。在一个合成的二维模式分类任务上训练它。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.lax</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">lax</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="k">def</span><span class="w"> </span><span class="nf">conv2d</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">kernel</span><span class="p">,</span> <span class="n">stride</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="sd">"""简单 2D 卷积，单输入，单滤波器。"""</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="k">return</span> <span class="n">lax</span><span class="o">.</span><span class="n">conv</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">],</span> <span class="n">kernel</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">],</span> <span class="p">(</span><span class="n">stride</span><span class="p">,</span> <span class="n">stride</span><span class="p">),</span> <span class="s1">'SAME'</span><span class="p">)[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">max_pool</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="w"> </span><span class="sd">"""2x2 最大池化。"""</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="n">H</span><span class="p">,</span> <span class="n">W</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="p">[:</span><span class="n">H</span><span class="o">//</span><span class="n">size</span><span class="o">*</span><span class="n">size</span><span class="p">,</span> <span class="p">:</span><span class="n">W</span><span class="o">//</span><span class="n">size</span><span class="o">*</span><span class="n">size</span><span class="p">]</span>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="k">return</span> <span class="n">x</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">H</span><span class="o">//</span><span class="n">size</span><span class="p">,</span> <span class="n">size</span><span class="p">,</span> <span class="n">W</span><span class="o">//</span><span class="n">size</span><span class="p">,</span> <span class="n">size</span><span class="p">)</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="k">def</span><span class="w"> </span><span class="nf">init_cnn</span><span class="p">(</span><span class="n">key</span><span class="p">):</span>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a> <span class="n">k1</span><span class="p">,</span> <span class="n">k2</span><span class="p">,</span> <span class="n">k3</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
|
||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a> <span class="k">return</span> <span class="p">{</span>
|
||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a> <span class="s1">'conv1'</span><span class="p">:</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k1</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.3</span><span class="p">,</span>
|
||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a> <span class="s1">'conv2'</span><span class="p">:</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k2</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.3</span><span class="p">,</span>
|
||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a> <span class="s1">'fc_w'</span><span class="p">:</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k3</span><span class="p">,</span> <span class="p">(</span><span class="mi">64</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.1</span><span class="p">,</span>
|
||
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a> <span class="s1">'fc_b'</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span>
|
||
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a> <span class="p">}</span>
|
||
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>
|
||
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">forward_cnn</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">):</span>
|
||
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a> <span class="c1"># Conv1 -> ReLU -> Pool</span>
|
||
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a> <span class="n">h</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">conv2d</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">params</span><span class="p">[</span><span class="s1">'conv1'</span><span class="p">]))</span>
|
||
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a> <span class="n">h</span> <span class="o">=</span> <span class="n">max_pool</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>
|
||
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a> <span class="c1"># Conv2 -> ReLU -> Pool</span>
|
||
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a> <span class="n">h</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">conv2d</span><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">params</span><span class="p">[</span><span class="s1">'conv2'</span><span class="p">]))</span>
|
||
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a> <span class="n">h</span> <span class="o">=</span> <span class="n">max_pool</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>
|
||
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a> <span class="c1"># Flatten and classify</span>
|
||
<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a> <span class="n">flat</span> <span class="o">=</span> <span class="n">h</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
|
||
<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a> <span class="c1"># Pad or truncate to fixed size</span>
|
||
<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a> <span class="n">flat</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">flat</span><span class="p">,</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">max</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">64</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="n">flat</span><span class="p">))))[:</span><span class="mi">64</span><span class="p">]</span>
|
||
<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a> <span class="n">logit</span> <span class="o">=</span> <span class="p">(</span><span class="n">flat</span> <span class="o">@</span> <span class="n">params</span><span class="p">[</span><span class="s1">'fc_w'</span><span class="p">]</span> <span class="o">+</span> <span class="n">params</span><span class="p">[</span><span class="s1">'fc_b'</span><span class="p">])</span><span class="o">.</span><span class="n">squeeze</span><span class="p">()</span>
|
||
<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a> <span class="k">return</span> <span class="n">jax</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">sigmoid</span><span class="p">(</span><span class="n">logit</span><span class="p">)</span>
|
||
<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>
|
||
<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a><span class="c1"># Generate synthetic data: class 0 = low-freq pattern, class 1 = high-freq</span>
|
||
<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a><span class="k">def</span><span class="w"> </span><span class="nf">make_data</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">200</span><span class="p">):</span>
|
||
<a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a> <span class="n">images</span><span class="p">,</span> <span class="n">labels</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[]</span>
|
||
<a id="__codelineno-0-42" name="__codelineno-0-42" href="#__codelineno-0-42"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-0-43" name="__codelineno-0-43" href="#__codelineno-0-43"></a> <span class="n">k1</span><span class="p">,</span> <span class="n">key</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
|
||
<a id="__codelineno-0-44" name="__codelineno-0-44" href="#__codelineno-0-44"></a> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">4</span><span class="o">*</span><span class="n">jnp</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">32</span><span class="p">),</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">4</span><span class="o">*</span><span class="n">jnp</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span> <span class="mi">32</span><span class="p">))</span>
|
||
<a id="__codelineno-0-45" name="__codelineno-0-45" href="#__codelineno-0-45"></a> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:</span>
|
||
<a id="__codelineno-0-46" name="__codelineno-0-46" href="#__codelineno-0-46"></a> <span class="n">img</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k1</span><span class="p">,</span> <span class="p">(</span><span class="mi">32</span><span class="p">,</span> <span class="mi">32</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.1</span>
|
||
<a id="__codelineno-0-47" name="__codelineno-0-47" href="#__codelineno-0-47"></a> <span class="n">labels</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-0-48" name="__codelineno-0-48" href="#__codelineno-0-48"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-0-49" name="__codelineno-0-49" href="#__codelineno-0-49"></a> <span class="n">img</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">x</span><span class="p">)</span> <span class="o">*</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">y</span><span class="p">)</span> <span class="o">+</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k1</span><span class="p">,</span> <span class="p">(</span><span class="mi">32</span><span class="p">,</span> <span class="mi">32</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.1</span>
|
||
<a id="__codelineno-0-50" name="__codelineno-0-50" href="#__codelineno-0-50"></a> <span class="n">labels</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-0-51" name="__codelineno-0-51" href="#__codelineno-0-51"></a> <span class="n">images</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">img</span><span class="p">)</span>
|
||
<a id="__codelineno-0-52" name="__codelineno-0-52" href="#__codelineno-0-52"></a> <span class="k">return</span> <span class="n">images</span><span class="p">,</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">labels</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">jnp</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
|
||
<a id="__codelineno-0-53" name="__codelineno-0-53" href="#__codelineno-0-53"></a>
|
||
<a id="__codelineno-0-54" name="__codelineno-0-54" href="#__codelineno-0-54"></a><span class="n">key</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
|
||
<a id="__codelineno-0-55" name="__codelineno-0-55" href="#__codelineno-0-55"></a><span class="n">images</span><span class="p">,</span> <span class="n">labels</span> <span class="o">=</span> <span class="n">make_data</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
|
||
<a id="__codelineno-0-56" name="__codelineno-0-56" href="#__codelineno-0-56"></a><span class="n">params</span> <span class="o">=</span> <span class="n">init_cnn</span><span class="p">(</span><span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">0</span><span class="p">))</span>
|
||
<a id="__codelineno-0-57" name="__codelineno-0-57" href="#__codelineno-0-57"></a>
|
||
<a id="__codelineno-0-58" name="__codelineno-0-58" href="#__codelineno-0-58"></a><span class="k">def</span><span class="w"> </span><span class="nf">loss_fn</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">,</span> <span class="n">label</span><span class="p">):</span>
|
||
<a id="__codelineno-0-59" name="__codelineno-0-59" href="#__codelineno-0-59"></a> <span class="n">pred</span> <span class="o">=</span> <span class="n">forward_cnn</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">)</span>
|
||
<a id="__codelineno-0-60" name="__codelineno-0-60" href="#__codelineno-0-60"></a> <span class="k">return</span> <span class="o">-</span><span class="p">(</span><span class="n">label</span> <span class="o">*</span> <span class="n">jnp</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">pred</span> <span class="o">+</span> <span class="mf">1e-7</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">label</span><span class="p">)</span> <span class="o">*</span> <span class="n">jnp</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">pred</span> <span class="o">+</span> <span class="mf">1e-7</span><span class="p">))</span>
|
||
<a id="__codelineno-0-61" name="__codelineno-0-61" href="#__codelineno-0-61"></a>
|
||
<a id="__codelineno-0-62" name="__codelineno-0-62" href="#__codelineno-0-62"></a><span class="n">grad_fn</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span><span class="n">loss_fn</span><span class="p">)</span>
|
||
<a id="__codelineno-0-63" name="__codelineno-0-63" href="#__codelineno-0-63"></a><span class="n">lr</span> <span class="o">=</span> <span class="mf">0.01</span>
|
||
<a id="__codelineno-0-64" name="__codelineno-0-64" href="#__codelineno-0-64"></a>
|
||
<a id="__codelineno-0-65" name="__codelineno-0-65" href="#__codelineno-0-65"></a><span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span><span class="p">):</span>
|
||
<a id="__codelineno-0-66" name="__codelineno-0-66" href="#__codelineno-0-66"></a> <span class="n">total_loss</span> <span class="o">=</span> <span class="mf">0.0</span>
|
||
<a id="__codelineno-0-67" name="__codelineno-0-67" href="#__codelineno-0-67"></a> <span class="k">for</span> <span class="n">img</span><span class="p">,</span> <span class="n">label</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">images</span><span class="p">,</span> <span class="n">labels</span><span class="p">):</span>
|
||
<a id="__codelineno-0-68" name="__codelineno-0-68" href="#__codelineno-0-68"></a> <span class="n">grads</span> <span class="o">=</span> <span class="n">grad_fn</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">,</span> <span class="n">label</span><span class="p">)</span>
|
||
<a id="__codelineno-0-69" name="__codelineno-0-69" href="#__codelineno-0-69"></a> <span class="n">params</span> <span class="o">=</span> <span class="p">{</span><span class="n">k</span><span class="p">:</span> <span class="n">params</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">-</span> <span class="n">lr</span> <span class="o">*</span> <span class="n">grads</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">params</span><span class="p">}</span>
|
||
<a id="__codelineno-0-70" name="__codelineno-0-70" href="#__codelineno-0-70"></a> <span class="n">total_loss</span> <span class="o">+=</span> <span class="n">loss_fn</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">,</span> <span class="n">label</span><span class="p">)</span>
|
||
<a id="__codelineno-0-71" name="__codelineno-0-71" href="#__codelineno-0-71"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Epoch </span><span class="si">{</span><span class="n">epoch</span><span class="si">}</span><span class="s2">: loss = </span><span class="si">{</span><span class="n">total_loss</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="n">images</span><span class="p">)</span><span class="si">:</span><span class="s2">.4f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-72" name="__codelineno-0-72" href="#__codelineno-0-72"></a>
|
||
<a id="__codelineno-0-73" name="__codelineno-0-73" href="#__codelineno-0-73"></a><span class="c1"># Test accuracy</span>
|
||
<a id="__codelineno-0-74" name="__codelineno-0-74" href="#__codelineno-0-74"></a><span class="n">preds</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">forward_cnn</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">)</span> <span class="o">></span> <span class="mf">0.5</span> <span class="k">for</span> <span class="n">img</span> <span class="ow">in</span> <span class="n">images</span><span class="p">])</span>
|
||
<a id="__codelineno-0-75" name="__codelineno-0-75" href="#__codelineno-0-75"></a><span class="n">acc</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">preds</span> <span class="o">==</span> <span class="n">labels</span><span class="p">)</span>
|
||
<a id="__codelineno-0-76" name="__codelineno-0-76" href="#__codelineno-0-76"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Accuracy: </span><span class="si">{</span><span class="n">acc</span><span class="si">:</span><span class="s2">.2%</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>可视化不同滤波器大小如何影响感受野。展示两个堆叠的 3x3 滤波器与一个 5x5 滤波器覆盖相同的感受野，但参数更少。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="k">def</span><span class="w"> </span><span class="nf">compute_receptive_field</span><span class="p">(</span><span class="n">layers</span><span class="p">):</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="sd">"""从一组 (kernel_size, stride) 元组计算感受野大小。"""</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a> <span class="n">rf</span> <span class="o">=</span> <span class="mi">1</span> <span class="c1"># 从 1 个像素开始</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a> <span class="n">stride_product</span> <span class="o">=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a> <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">layers</span><span class="p">:</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a> <span class="n">rf</span> <span class="o">+=</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">stride_product</span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a> <span class="n">stride_product</span> <span class="o">*=</span> <span class="n">s</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a> <span class="k">return</span> <span class="n">rf</span>
|
||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="c1"># Compare architectures</span>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="n">configs</span> <span class="o">=</span> <span class="p">{</span>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a> <span class="s1">'Single 5x5'</span><span class="p">:</span> <span class="p">[(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">)],</span>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a> <span class="s1">'Two 3x3'</span><span class="p">:</span> <span class="p">[(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)],</span>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a> <span class="s1">'Three 3x3'</span><span class="p">:</span> <span class="p">[(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)],</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a> <span class="s1">'Single 7x7'</span><span class="p">:</span> <span class="p">[(</span><span class="mi">7</span><span class="p">,</span> <span class="mi">1</span><span class="p">)],</span>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a> <span class="s1">'3x3 stride 2 + 3x3'</span><span class="p">:</span> <span class="p">[(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)],</span>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="p">}</span>
|
||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a>
|
||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="s1">'Config'</span><span class="si">:</span><span class="s2"><25</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="s1">'RF'</span><span class="si">:</span><span class="s2">>4</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="s1">'Params (per channel)'</span><span class="si">:</span><span class="s2">>20</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="nb">print</span><span class="p">(</span><span class="s1">'-'</span> <span class="o">*</span> <span class="mi">55</span><span class="p">)</span>
|
||
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="k">for</span> <span class="n">name</span><span class="p">,</span> <span class="n">layers</span> <span class="ow">in</span> <span class="n">configs</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
|
||
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a> <span class="n">rf</span> <span class="o">=</span> <span class="n">compute_receptive_field</span><span class="p">(</span><span class="n">layers</span><span class="p">)</span>
|
||
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a> <span class="c1"># Parameters: sum of k^2 for each layer (per input-output channel pair)</span>
|
||
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a> <span class="n">params</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">k</span> <span class="o">*</span> <span class="n">k</span> <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">layers</span><span class="p">)</span>
|
||
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">name</span><span class="si">:</span><span class="s2"><25</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">rf</span><span class="si">:</span><span class="s2">>4</span><span class="si">}</span><span class="s2"> </span><span class="si">{</span><span class="n">params</span><span class="si">:</span><span class="s2">>20</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a>
|
||
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="c1"># Visualise receptive fields</span>
|
||
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
|
||
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="k">for</span> <span class="n">ax</span><span class="p">,</span> <span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">rf_size</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">axes</span><span class="p">,</span> <span class="p">[(</span><span class="s1">'5x5 filter'</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="s1">'Two 3x3 filters'</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="s1">'Three 3x3 filters'</span><span class="p">,</span> <span class="mi">7</span><span class="p">)]):</span>
|
||
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a> <span class="n">grid</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">9</span><span class="p">,</span> <span class="mi">9</span><span class="p">))</span>
|
||
<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a> <span class="n">c</span> <span class="o">=</span> <span class="mi">4</span> <span class="c1"># centre</span>
|
||
<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a> <span class="n">half</span> <span class="o">=</span> <span class="n">rf_size</span> <span class="o">//</span> <span class="mi">2</span>
|
||
<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a> <span class="n">grid</span> <span class="o">=</span> <span class="n">grid</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">c</span><span class="o">-</span><span class="n">half</span><span class="p">:</span><span class="n">c</span><span class="o">+</span><span class="n">half</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="o">-</span><span class="n">half</span><span class="p">:</span><span class="n">c</span><span class="o">+</span><span class="n">half</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</span>
|
||
<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a> <span class="n">ax</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'Blues'</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a> <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="n">name</span><span class="si">}</span><span class="se">\n</span><span class="s1">RF = </span><span class="si">{</span><span class="n">rf_size</span><span class="si">}</span><span class="s1">x</span><span class="si">{</span><span class="n">rf_size</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
|
||
<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a> <span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">9</span><span class="p">));</span> <span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">9</span><span class="p">))</span>
|
||
<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a> <span class="n">ax</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.3</span><span class="p">)</span>
|
||
<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s1">'Receptive Field Comparison'</span><span class="p">)</span>
|
||
<a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">();</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>从头实现 Grad-CAM。给定一个预构建的简单 CNN，计算针对特定类别的梯度加权激活图，并将其可视化为热力图。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">simple_cnn</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">):</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="sd">"""返回预测和最后一个卷积层激活的简单 CNN。"""</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a> <span class="c1"># Conv layer (our "last conv layer" for Grad-CAM)</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a> <span class="n">H</span><span class="p">,</span> <span class="n">W</span> <span class="o">=</span> <span class="n">img</span><span class="o">.</span><span class="n">shape</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a> <span class="n">k</span> <span class="o">=</span> <span class="n">params</span><span class="p">[</span><span class="s1">'conv'</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a> <span class="n">pad</span> <span class="o">=</span> <span class="n">k</span> <span class="o">//</span> <span class="mi">2</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a> <span class="n">img_pad</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">pad</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'edge'</span><span class="p">)</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a> <span class="n">activation_map</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">H</span><span class="p">,</span> <span class="n">W</span><span class="p">))</span>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">H</span><span class="p">):</span>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">W</span><span class="p">):</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a> <span class="n">activation_map</span> <span class="o">=</span> <span class="n">activation_map</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">img_pad</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">k</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span><span class="n">j</span><span class="o">+</span><span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="n">params</span><span class="p">[</span><span class="s1">'conv'</span><span class="p">])</span>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a> <span class="p">)</span>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a> <span class="n">activation_map</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">activation_map</span><span class="p">)</span> <span class="c1"># ReLU</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a> <span class="c1"># Global average pool -> dense -> output</span>
|
||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a> <span class="n">pooled</span> <span class="o">=</span> <span class="n">activation_map</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a> <span class="n">logit</span> <span class="o">=</span> <span class="n">pooled</span> <span class="o">*</span> <span class="n">params</span><span class="p">[</span><span class="s1">'w'</span><span class="p">]</span> <span class="o">+</span> <span class="n">params</span><span class="p">[</span><span class="s1">'b'</span><span class="p">]</span>
|
||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a> <span class="k">return</span> <span class="n">jax</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">sigmoid</span><span class="p">(</span><span class="n">logit</span><span class="p">),</span> <span class="n">activation_map</span>
|
||
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a>
|
||
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="c1"># Create test image: bright region on the left (class indicator)</span>
|
||
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="n">img</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">32</span><span class="p">,</span> <span class="mi">32</span><span class="p">))</span>
|
||
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="n">img</span> <span class="o">=</span> <span class="n">img</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="mi">8</span><span class="p">:</span><span class="mi">24</span><span class="p">,</span> <span class="mi">4</span><span class="p">:</span><span class="mi">16</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</span>
|
||
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="n">img</span> <span class="o">=</span> <span class="n">img</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="mi">5</span><span class="p">:</span><span class="mi">10</span><span class="p">,</span> <span class="mi">20</span><span class="p">:</span><span class="mi">28</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="mf">0.3</span><span class="p">)</span>
|
||
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a>
|
||
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="n">key</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
|
||
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="n">params</span> <span class="o">=</span> <span class="p">{</span>
|
||
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a> <span class="s1">'conv'</span><span class="p">:</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.3</span><span class="p">,</span>
|
||
<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a> <span class="s1">'w'</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="mf">2.0</span><span class="p">),</span>
|
||
<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a> <span class="s1">'b'</span><span class="p">:</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="p">),</span>
|
||
<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="p">}</span>
|
||
<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a>
|
||
<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="c1"># Compute Grad-CAM</span>
|
||
<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="k">def</span><span class="w"> </span><span class="nf">class_score</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">):</span>
|
||
<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a> <span class="n">pred</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">simple_cnn</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">)</span>
|
||
<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a> <span class="k">return</span> <span class="n">pred</span>
|
||
<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a>
|
||
<a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a><span class="c1"># Get activation map and gradients</span>
|
||
<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="n">pred</span><span class="p">,</span> <span class="n">act_map</span> <span class="o">=</span> <span class="n">simple_cnn</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">)</span>
|
||
<a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a><span class="n">grad_fn</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">grad</span><span class="p">(</span><span class="k">lambda</span> <span class="n">img</span><span class="p">:</span> <span class="n">simple_cnn</span><span class="p">(</span><span class="n">params</span><span class="p">,</span> <span class="n">img</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span>
|
||
<a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="n">img_grad</span> <span class="o">=</span> <span class="n">grad_fn</span><span class="p">(</span><span class="n">img</span><span class="p">)</span>
|
||
<a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></a>
|
||
<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a><span class="c1"># Weight = global average of gradients (simplified 1-channel Grad-CAM)</span>
|
||
<a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></a><span class="n">alpha</span> <span class="o">=</span> <span class="n">img_grad</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
|
||
<a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a><span class="n">grad_cam</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">act_map</span><span class="p">)</span> <span class="c1"># ReLU</span>
|
||
<a id="__codelineno-2-50" name="__codelineno-2-50" href="#__codelineno-2-50"></a><span class="n">grad_cam</span> <span class="o">=</span> <span class="p">(</span><span class="n">grad_cam</span> <span class="o">-</span> <span class="n">grad_cam</span><span class="o">.</span><span class="n">min</span><span class="p">())</span> <span class="o">/</span> <span class="p">(</span><span class="n">grad_cam</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">-</span> <span class="n">grad_cam</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> <span class="o">+</span> <span class="mf">1e-8</span><span class="p">)</span>
|
||
<a id="__codelineno-2-51" name="__codelineno-2-51" href="#__codelineno-2-51"></a>
|
||
<a id="__codelineno-2-52" name="__codelineno-2-52" href="#__codelineno-2-52"></a><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
|
||
<a id="__codelineno-2-53" name="__codelineno-2-53" href="#__codelineno-2-53"></a><span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'Input Image'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-2-54" name="__codelineno-2-54" href="#__codelineno-2-54"></a><span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">act_map</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'viridis'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s1">'Activation Map'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-2-55" name="__codelineno-2-55" href="#__codelineno-2-55"></a><span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">img</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'gray'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">)</span>
|
||
<a id="__codelineno-2-56" name="__codelineno-2-56" href="#__codelineno-2-56"></a><span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">grad_cam</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="s1">'jet'</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.4</span><span class="p">)</span>
|
||
<a id="__codelineno-2-57" name="__codelineno-2-57" href="#__codelineno-2-57"></a><span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s1">'Grad-CAM (pred=</span><span class="si">{</span><span class="n">pred</span><span class="si">:</span><span class="s1">.2f</span><span class="si">}</span><span class="s1">)'</span><span class="p">);</span> <span class="n">axes</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'off'</span><span class="p">)</span>
|
||
<a id="__codelineno-2-58" name="__codelineno-2-58" href="#__codelineno-2-58"></a><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">();</span> <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>比较深度可分离卷积与标准卷积。统计两者的参数和 FLOPs，并展示它们在计算量少得多的情况下产生相似的输出。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="k">def</span><span class="w"> </span><span class="nf">standard_conv</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">kernel</span><span class="p">):</span>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="sd">"""标准卷积：(H, W, C_in) * (k, k, C_in, C_out) -> (H, W, C_out)。"""</span>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a> <span class="n">H</span><span class="p">,</span> <span class="n">W</span><span class="p">,</span> <span class="n">C_in</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span>
|
||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a> <span class="n">k</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">C_out</span> <span class="o">=</span> <span class="n">kernel</span><span class="o">.</span><span class="n">shape</span>
|
||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a> <span class="n">pad</span> <span class="o">=</span> <span class="n">k</span> <span class="o">//</span> <span class="mi">2</span>
|
||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a> <span class="n">x_pad</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">((</span><span class="n">pad</span><span class="p">,</span> <span class="n">pad</span><span class="p">),</span> <span class="p">(</span><span class="n">pad</span><span class="p">,</span> <span class="n">pad</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)),</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'constant'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a> <span class="n">out</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">H</span><span class="p">,</span> <span class="n">W</span><span class="p">,</span> <span class="n">C_out</span><span class="p">))</span>
|
||
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">H</span><span class="p">):</span>
|
||
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">W</span><span class="p">):</span>
|
||
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a> <span class="n">patch</span> <span class="o">=</span> <span class="n">x_pad</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">k</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span><span class="n">j</span><span class="o">+</span><span class="n">k</span><span class="p">,</span> <span class="p">:]</span> <span class="c1"># (k, k, C_in)</span>
|
||
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">C_out</span><span class="p">):</span>
|
||
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a> <span class="n">out</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">patch</span> <span class="o">*</span> <span class="n">kernel</span><span class="p">[:,</span> <span class="p">:,</span> <span class="p">:,</span> <span class="n">c</span><span class="p">]))</span>
|
||
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a> <span class="k">return</span> <span class="n">out</span>
|
||
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a>
|
||
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">depthwise_separable_conv</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dw_kernel</span><span class="p">,</span> <span class="n">pw_kernel</span><span class="p">):</span>
|
||
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w"> </span><span class="sd">"""深度可分离：深度卷积 (k,k,C_in) 然后逐点卷积 (C_in, C_out)。"""</span>
|
||
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a> <span class="n">H</span><span class="p">,</span> <span class="n">W</span><span class="p">,</span> <span class="n">C_in</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span>
|
||
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a> <span class="n">k</span> <span class="o">=</span> <span class="n">dw_kernel</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a> <span class="n">pad</span> <span class="o">=</span> <span class="n">k</span> <span class="o">//</span> <span class="mi">2</span>
|
||
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a> <span class="n">x_pad</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">((</span><span class="n">pad</span><span class="p">,</span> <span class="n">pad</span><span class="p">),</span> <span class="p">(</span><span class="n">pad</span><span class="p">,</span> <span class="n">pad</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)),</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'constant'</span><span class="p">)</span>
|
||
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a>
|
||
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a> <span class="c1"># Depthwise: one filter per channel</span>
|
||
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a> <span class="n">dw_out</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">H</span><span class="p">,</span> <span class="n">W</span><span class="p">,</span> <span class="n">C_in</span><span class="p">))</span>
|
||
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">H</span><span class="p">):</span>
|
||
<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">W</span><span class="p">):</span>
|
||
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">C_in</span><span class="p">):</span>
|
||
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a> <span class="n">patch</span> <span class="o">=</span> <span class="n">x_pad</span><span class="p">[</span><span class="n">i</span><span class="p">:</span><span class="n">i</span><span class="o">+</span><span class="n">k</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span><span class="n">j</span><span class="o">+</span><span class="n">k</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span>
|
||
<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a> <span class="n">dw_out</span> <span class="o">=</span> <span class="n">dw_out</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span> <span class="n">c</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">patch</span> <span class="o">*</span> <span class="n">dw_kernel</span><span class="p">[:,</span> <span class="p">:,</span> <span class="n">c</span><span class="p">]))</span>
|
||
<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a>
|
||
<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a> <span class="c1"># Pointwise: 1x1 conv across channels</span>
|
||
<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a> <span class="n">out</span> <span class="o">=</span> <span class="n">dw_out</span> <span class="o">@</span> <span class="n">pw_kernel</span>
|
||
<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a> <span class="k">return</span> <span class="n">out</span>
|
||
<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a>
|
||
<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="c1"># Setup</span>
|
||
<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a><span class="n">H</span><span class="p">,</span> <span class="n">W</span><span class="p">,</span> <span class="n">C_in</span><span class="p">,</span> <span class="n">C_out</span><span class="p">,</span> <span class="n">k</span> <span class="o">=</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">16</span><span class="p">,</span> <span class="mi">32</span><span class="p">,</span> <span class="mi">3</span>
|
||
<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a><span class="n">key</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
|
||
<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a><span class="n">k1</span><span class="p">,</span> <span class="n">k2</span><span class="p">,</span> <span class="n">k3</span><span class="p">,</span> <span class="n">k4</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
|
||
<a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a>
|
||
<a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a><span class="n">x</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k1</span><span class="p">,</span> <span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">W</span><span class="p">,</span> <span class="n">C_in</span><span class="p">))</span>
|
||
<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></a><span class="n">std_kernel</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k2</span><span class="p">,</span> <span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">C_in</span><span class="p">,</span> <span class="n">C_out</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.1</span>
|
||
<a id="__codelineno-3-44" name="__codelineno-3-44" href="#__codelineno-3-44"></a><span class="n">dw_kernel</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k3</span><span class="p">,</span> <span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">C_in</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.1</span>
|
||
<a id="__codelineno-3-45" name="__codelineno-3-45" href="#__codelineno-3-45"></a><span class="n">pw_kernel</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">k4</span><span class="p">,</span> <span class="p">(</span><span class="n">C_in</span><span class="p">,</span> <span class="n">C_out</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.1</span>
|
||
<a id="__codelineno-3-46" name="__codelineno-3-46" href="#__codelineno-3-46"></a>
|
||
<a id="__codelineno-3-47" name="__codelineno-3-47" href="#__codelineno-3-47"></a><span class="c1"># Compare</span>
|
||
<a id="__codelineno-3-48" name="__codelineno-3-48" href="#__codelineno-3-48"></a><span class="n">std_params</span> <span class="o">=</span> <span class="n">k</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="n">C_in</span> <span class="o">*</span> <span class="n">C_out</span>
|
||
<a id="__codelineno-3-49" name="__codelineno-3-49" href="#__codelineno-3-49"></a><span class="n">dw_params</span> <span class="o">=</span> <span class="n">k</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="n">C_in</span> <span class="o">+</span> <span class="n">C_in</span> <span class="o">*</span> <span class="n">C_out</span>
|
||
<a id="__codelineno-3-50" name="__codelineno-3-50" href="#__codelineno-3-50"></a>
|
||
<a id="__codelineno-3-51" name="__codelineno-3-51" href="#__codelineno-3-51"></a><span class="n">std_flops</span> <span class="o">=</span> <span class="n">H</span> <span class="o">*</span> <span class="n">W</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="n">C_in</span> <span class="o">*</span> <span class="n">C_out</span>
|
||
<a id="__codelineno-3-52" name="__codelineno-3-52" href="#__codelineno-3-52"></a><span class="n">dw_flops</span> <span class="o">=</span> <span class="n">H</span> <span class="o">*</span> <span class="n">W</span> <span class="o">*</span> <span class="p">(</span><span class="n">k</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="n">C_in</span> <span class="o">+</span> <span class="n">C_in</span> <span class="o">*</span> <span class="n">C_out</span><span class="p">)</span>
|
||
<a id="__codelineno-3-53" name="__codelineno-3-53" href="#__codelineno-3-53"></a>
|
||
<a id="__codelineno-3-54" name="__codelineno-3-54" href="#__codelineno-3-54"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Standard conv: </span><span class="si">{</span><span class="n">std_params</span><span class="si">:</span><span class="s2">>8,</span><span class="si">}</span><span class="s2"> params, </span><span class="si">{</span><span class="n">std_flops</span><span class="si">:</span><span class="s2">>10,</span><span class="si">}</span><span class="s2"> FLOPs"</span><span class="p">)</span>
|
||
<a id="__codelineno-3-55" name="__codelineno-3-55" href="#__codelineno-3-55"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Depthwise separable conv: </span><span class="si">{</span><span class="n">dw_params</span><span class="si">:</span><span class="s2">>8,</span><span class="si">}</span><span class="s2"> params, </span><span class="si">{</span><span class="n">dw_flops</span><span class="si">:</span><span class="s2">>10,</span><span class="si">}</span><span class="s2"> FLOPs"</span><span class="p">)</span>
|
||
<a id="__codelineno-3-56" name="__codelineno-3-56" href="#__codelineno-3-56"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Parameter reduction: </span><span class="si">{</span><span class="n">std_params</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">dw_params</span><span class="si">:</span><span class="s2">.1f</span><span class="si">}</span><span class="s2">x"</span><span class="p">)</span>
|
||
<a id="__codelineno-3-57" name="__codelineno-3-57" href="#__codelineno-3-57"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"FLOP reduction: </span><span class="si">{</span><span class="n">std_flops</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">dw_flops</span><span class="si">:</span><span class="s2">.1f</span><span class="si">}</span><span class="s2">x"</span><span class="p">)</span>
|
||
<a id="__codelineno-3-58" name="__codelineno-3-58" href="#__codelineno-3-58"></a>
|
||
<a id="__codelineno-3-59" name="__codelineno-3-59" href="#__codelineno-3-59"></a><span class="n">std_out</span> <span class="o">=</span> <span class="n">standard_conv</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">std_kernel</span><span class="p">)</span>
|
||
<a id="__codelineno-3-60" name="__codelineno-3-60" href="#__codelineno-3-60"></a><span class="n">ds_out</span> <span class="o">=</span> <span class="n">depthwise_separable_conv</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">dw_kernel</span><span class="p">,</span> <span class="n">pw_kernel</span><span class="p">)</span>
|
||
<a id="__codelineno-3-61" name="__codelineno-3-61" href="#__codelineno-3-61"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="se">\n</span><span class="s2">Standard output shape: </span><span class="si">{</span><span class="n">std_out</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-3-62" name="__codelineno-3-62" href="#__codelineno-3-62"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Depthwise sep output shape: </span><span class="si">{</span><span class="n">ds_out</span><span class="o">.</span><span class="n">shape</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
</code></pre></div></p>
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