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统计学
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概率论
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概率概念
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分布
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</a>
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贝叶斯
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</a>
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信息论
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机器学习
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经典机器学习
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梯度机器学习
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深度学习
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强化学习
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分布式深度学习
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分布式深度学习
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计算语言学
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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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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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高级文本生成
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</span>
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|
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计算机视觉
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图像基础
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目标检测与分割
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ViT 与生成模型
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视频与 3D 视觉
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音频与语音
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数字信号处理
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</a>
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<span class="md-ellipsis">
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自动语音识别
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</span>
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</a>
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</li>
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<a href="../../chapter%2009%3A%20audio%20and%20speech/03.%20text%20to%20speech%20and%20voice/" class="md-nav__link">
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<span class="md-ellipsis">
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语音合成
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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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说话人与音频分析
|
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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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源分离与降噪
|
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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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<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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多模态表征
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</span>
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</a>
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视觉语言模型
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</span>
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</a>
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<span class="md-ellipsis">
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图像与视频 Token 化
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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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跨模态生成
|
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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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<a href="../../chapter%2010%3A%20multimodal%20learning/05.%20unified%20multimodal%20architectures/" class="md-nav__link">
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<span class="md-ellipsis">
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统一多模态架构
|
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|
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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 class="md-nav__item md-nav__item--nested">
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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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<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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</a>
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<span class="md-ellipsis">
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视觉-语言-动作模型
|
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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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<a href="../../chapter%2011%3A%20autonomous%20systems/04.%20self-driving/" class="md-nav__link">
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自动驾驶
|
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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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<a href="../../chapter%2011%3A%20autonomous%20systems/05.%20space%20and%20extreme%20robotics/" class="md-nav__link">
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<span class="md-ellipsis">
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太空与极端机器人
|
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|
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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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图神经网络
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</span>
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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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几何深度学习
|
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<span class="md-ellipsis">
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|
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硬件基础
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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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AI 推理
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量化
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边缘推理
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扩缩与部署
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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">分布式深度学习<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
|
||
<p><em>分布式训练将计算分散到多个GPU和机器上，以训练单个设备无法容纳或训练太慢的模型。本文件涵盖混合精度、数据并行、模型并行、流水线并行、ZeRO、FSDP、张量并行以及全规约等通信原语——这些对于大规模训练LLM至关重要。</em></p>
|
||
<ul>
|
||
<li>
|
||
<p>在单个GPU上训练大型神经网络最终会遇到瓶颈。模型可能无法放入内存，或者训练可能需要数月。分布式训练将工作分散到多个设备（GPU、TPU或整台机器）上，以更快地训练和训练更大的模型。本文件涵盖了实现这一目标的技术。</p>
|
||
</li>
|
||
<li>
|
||
<p>要理解为何分布式重要，从训练的<strong>计算成本</strong>开始。在一个包含 <span class="arithmatex">\(d_{\text{in}}\)</span> 个输入和 <span class="arithmatex">\(d_{\text{out}}\)</span> 个输出的密集层上，对一批 <span class="arithmatex">\(B\)</span> 个样本进行一次前向传播需要大约 <span class="arithmatex">\(2 \cdot B \cdot d_{\text{in}} \cdot d_{\text{out}}\)</span> 次FLOP（浮点运算）：对输出矩阵的每个元素进行一次乘法和一次加法。反向传播的成本大约是前向传播的两倍（计算相对于输入和权重的梯度），因此一个密集层的一个训练步骤约为 <span class="arithmatex">\(6 \cdot B \cdot d_{\text{in}} \cdot d_{\text{out}}\)</span> 次FLOP。</p>
|
||
</li>
|
||
<li>
|
||
<p>对于隐藏维度为 <span class="arithmatex">\(d\)</span> 的Transformer层，自注意力块涉及四个投影（Q、K、V和输出），每个的成本为 <span class="arithmatex">\(O(B \cdot n \cdot d^2)\)</span> 次FLOP（其中 <span class="arithmatex">\(n\)</span> 是序列长度），加上注意力矩阵计算 <span class="arithmatex">\(O(B \cdot n^2 \cdot d)\)</span>。前馈块有两个密集层，通常扩展到 <span class="arithmatex">\(4d\)</span> 再回来：<span class="arithmatex">\(O(B \cdot n \cdot 8d^2)\)</span>。每层总计：大约 <span class="arithmatex">\(O(B \cdot n \cdot 12d^2 + B \cdot n^2 \cdot d)\)</span>。乘以层数，你就会明白为什么训练GPT规模的模型需要数千个GPU小时。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>内存墙</strong>通常是更严格的约束。在训练期间，GPU内存必须同时容纳四样东西：</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="堆叠柱状图展示训练内存分解：参数、梯度、优化器状态、激活值" src="../../images/training_memory_breakdown.svg" /></p>
|
||
<ul>
|
||
<li><strong>参数</strong>：模型权重。一个70亿参数的模型在FP32中（每个参数4字节）仅权重就需要28 GB。</li>
|
||
<li><strong>梯度</strong>：与参数大小相同。又是28 GB。</li>
|
||
<li><strong>优化器状态</strong>：Adam维护两个额外的缓冲区（一阶和二阶矩估计），每个与参数大小相同。即使模型使用较低精度，这些也以FP32格式保存以确保数值稳定性。对于我们的7B模型，那就是 <span class="arithmatex">\(2 \times 28 = 56\)</span> GB。</li>
|
||
<li>
|
||
<p><strong>激活值</strong>：在前向传播过程中保存下来供反向传播使用的中间值。大小取决于批量大小、序列长度和模型宽度。这通常是最主要的组成部分，并随批量大小线性增长。</p>
|
||
</li>
|
||
<li>
|
||
<p>对于使用FP32 Adam的7B模型：28（参数）+ 28（梯度）+ 56（优化器）= 112 GB，这还没算激活值。单个80 GB的A100 GPU无法容纳。这就是分布式策略至关重要的原因。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>混合精度训练</strong>是第一道防线。不是将所有内容存储在FP32（32位浮点）中，而是使用FP16或BF16（16位）进行前向和反向传播，同时将权重的FP32主副本保留给优化器更新。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>FP16</strong>具有高精度（10位尾数），但范围有限，可能导致上溢/下溢。损失缩放（在反向传播前将损失乘以一个大因子，然后将梯度除以相同因子）缓解了这个问题。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>BF16</strong>（脑浮点）具有与FP32相同的指数范围（8位指数），但精度较低（7位尾数）。它几乎从不溢出，很少需要损失缩放，因此使用更简单。BF16是现代Transformer训练的默认选择。</p>
|
||
</li>
|
||
<li>
|
||
<p>混合精度大致将激活值和梯度的内存减半（前向/反向传播期间的主要成本），同时将优化器状态保留在FP32中以确保数值稳定性。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>数据并行</strong>是最简单的分布式策略。你在 <span class="arithmatex">\(N\)</span> 个GPU上复制整个模型，将每个小批量分成 <span class="arithmatex">\(N\)</span> 个相等的块，并将一个块发送到每个GPU。每个GPU在其块上独立运行前向和反向传播。然后梯度在所有GPU上平均（使用全规约操作），每个GPU更新其本地模型副本。</p>
|
||
</li>
|
||
<li>
|
||
<p>从模型的角度来看，这相当于使用大了 <span class="arithmatex">\(N\)</span> 倍的小批量进行训练。如果每个GPU处理一个大小为 <span class="arithmatex">\(B\)</span> 的批次，则有效批量大小为 <span class="arithmatex">\(N \cdot B\)</span>。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="并排比较：数据并行复制模型并分割数据，模型并行分割模型并分享数据" src="../../images/data_model_parallelism.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p>梯度平均可以同步或异步进行。<strong>同步SGD</strong>等待所有GPU完成后再进行平均，确保与使用更大批量的单GPU训练数学上等价。缺点是，最慢的GPU（"掉队者"）会拖慢所有人。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>异步SGD</strong>让每个GPU独立地更新一个共享的参数服务器，无需等待。这消除了掉队者问题，但引入了"陈旧梯度"：一个GPU可能基于略微过时的参数计算梯度。陈旧梯度增加了噪声，可能减缓收敛。在实践中，带高效通信的同步SGD更受青睐。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>梯度累积</strong>是一种软件技巧，用于在有限硬件上模拟更大的批量大小。不必每个小批量做一次更新，而是运行多次前向/反向传播并累积梯度，然后做一次更新。这与更大批量得到相同的结果，而无需更多GPU内存用于激活值（一次只有一个小批量的激活值在内存中）。</p>
|
||
</li>
|
||
<li>
|
||
<p>当模型本身太大无法放入单个GPU时，需要<strong>模型并行</strong>。有两种主要形式。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>张量并行</strong>将单个层分割到多个GPU上。一个大的矩阵乘法 <span class="arithmatex">\(Y = XW\)</span> 可以按列分割：将 <span class="arithmatex">\(W\)</span> 分区为 <span class="arithmatex">\([W_1, W_2]\)</span> 分布在两个GPU上，并行计算 <span class="arithmatex">\(Y_1 = XW_1\)</span> 和 <span class="arithmatex">\(Y_2 = XW_2\)</span>，然后拼接。这适用于注意力投影和前馈层。它需要GPU之间快速通信（通常是节点内的NVLink），因为每层都必须组合部分结果。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>流水线并行</strong>将不同的层分配到不同的GPU上。GPU 0运行第1-4层，GPU 1运行第5-8层，依此类推。数据像流水线一样流经整个管道。朴素的方法有一个"流水线气泡"：当GPU 0处理微批次1的前向传播时，GPU 1-3处于空闲状态。<strong>微批处理</strong>通过将小批量分割成更小的微批次来缓解这个问题，这些微批次按顺序流经流水线，使所有GPU大部分时间保持忙碌。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>混合并行</strong>结合了数据并行、张量并行和流水线并行。一个典型的大模型设置可能使用节点内的张量并行（8个GPU通过快速NVLink连接）、跨节点的流水线并行以及跨节点组的数据并行。这就是GPT-4和Llama等模型的训练方式。</p>
|
||
</li>
|
||
<li>
|
||
<p>分布式训练的效率在很大程度上取决于<strong>通信</strong>。关键操作是<strong>全规约（all-reduce）</strong>：给定 <span class="arithmatex">\(N\)</span> 个GPU上各有一个值，计算总和（或平均值）并将结果分发给所有GPU。</p>
|
||
</li>
|
||
<li>
|
||
<p>朴素的全规约将所有数据发送到一个GPU，求和，然后广播回来。通信量为 <span class="arithmatex">\(O(N)\)</span>，并在根节点造成瓶颈。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>环全规约（Ring all-reduce）</strong> 要高效得多。将 <span class="arithmatex">\(N\)</span> 个GPU排列成一个环。每个GPU将其数据分割成 <span class="arithmatex">\(N\)</span> 块。在 <span class="arithmatex">\(N - 1\)</span> 步中，每个GPU向邻居发送一块，并从另一个邻居接收一块，累加部分和。再经过 <span class="arithmatex">\(N - 1\)</span> 步后，完整的总和传播到所有GPU。每个GPU的总数据传输量：数据大小的 <span class="arithmatex">\(2(N-1)/N\)</span> 倍，随着 <span class="arithmatex">\(N\)</span> 的增长趋近于 <span class="arithmatex">\(2\times\)</span>。关键在于，这不随 <span class="arithmatex">\(N\)</span> 增加，使其带宽最优。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="四个GPU排列成环，每个将梯度块传递给邻居，直到所有GPU都得到完整总和" src="../../images/ring_allreduce.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>参数服务器</strong>是一种替代架构，其中专用服务器节点保存模型参数。工作节点计算梯度并将其发送到服务器，服务器更新参数并将其发送回来。这更简单，但可能在服务器处造成通信瓶颈。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>NCCL</strong>（NVIDIA集合通信库）是GPU间通信的标准库。它提供了全规约、全收集、广播和其他集合操作的高效实现，自动为网络拓扑选择最佳算法。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>缩放定律</strong>描述了模型性能如何随计算量、数据量和模型大小而提升。原始的Kaplan等人（2020）缩放定律发现，损失随每个因素以幂律方式下降：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[L(N) \propto N^{-\alpha_N}, \quad L(D) \propto D^{-\alpha_D}, \quad L(C) \propto C^{-\alpha_C}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>其中 <span class="arithmatex">\(N\)</span> 是参数数量，<span class="arithmatex">\(D\)</span> 是数据集大小，<span class="arithmatex">\(C\)</span> 是计算预算。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>Chinchilla缩放定律</strong>（Hoffmann等人，2022）表明大多数模型训练不足：对于给定的计算预算，应该训练一个更小的模型，使用比以前认为的更多的数据。最优比例大约是每参数20个token。一个7B模型应该看到大约140B个token，而不是Llama 1在65B模型上使用的300B个token。这一发现将领域转向了"计算最优"训练。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>混合专家（MoE）</strong> 是一种在不按比例增加计算量的情况下扩展模型容量的架构。每个Transformer层不是使用一个前馈网络，而是有 <span class="arithmatex">\(N\)</span> 个"专家"网络（每个都是一个标准FFN）。一个<strong>门控网络</strong>（路由器）检查每个token并将其发送到top-<span class="arithmatex">\(K\)</span>个专家（通常 <span class="arithmatex">\(K = 1\)</span> 或 <span class="arithmatex">\(K = 2\)</span>）。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="token通过门控网络路由到选定的专家，使用top-K稀疏路由和加权输出组合" src="../../images/moe_routing.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p>总参数量要大得多（因为有 <span class="arithmatex">\(N\)</span> 个专家），但每个token的FLOPs大致保持不变（因为每个token只有 <span class="arithmatex">\(K\)</span> 个专家激活）。例如，Mixtral 8x7B共有47B个参数，但每次前向传播只用大约13B，以较小模型的代价获得更大模型的性能。</p>
|
||
</li>
|
||
<li>
|
||
<p>MoE带来了挑战。<strong>负载均衡</strong>：如果路由器将大多数token发送到同一个专家，其他专家就被浪费了。辅助损失鼓励均匀路由。<strong>通信</strong>：不同的专家可能位于不同的GPU上，因此路由token需要全对全通信，这很昂贵。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>容错</strong>在训练运行持续数周或数月、涉及数千个GPU时至关重要。如果单个GPU失效，你不想丢失所有进度。<strong>检查点</strong>定期将模型权重、优化器状态和训练状态（学习率、步数、数据位置）保存到磁盘。如果发生故障，你可以从最近的检查点重新开始。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>梯度检查点</strong>（也称为激活重计算）是一种内存优化，而非容错机制。在前向传播过程中，不是保存所有激活值供反向传播使用，而是只在某些检查点保存激活值。在反向传播过程中，从检查点重新计算缺失的激活值。这以计算换取内存：它使前向传播成本增加约33%，但可以将激活内存减少 <span class="arithmatex">\(\sqrt{L}\)</span> 倍（其中 <span class="arithmatex">\(L\)</span> 是层数）。</p>
|
||
</li>
|
||
<li>
|
||
<p>综合起来，训练前沿模型结合了所有这些技术：BF16混合精度、使用环全规约在数千个GPU上进行数据并行、节点内的张量并行、跨节点的流水线并行、减少内存的梯度检查点、提高参数效率的MoE，以及用于容错的定期检查点。系统工程与算法设计一样具有挑战性。</p>
|
||
</li>
|
||
<li>
|
||
<p>总结分布式训练工具包：</p>
|
||
</li>
|
||
</ul>
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>技术</th>
|
||
<th>作用</th>
|
||
<th>权衡</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td>混合精度 (BF16)</td>
|
||
<td>将激活值/梯度的内存减半</td>
|
||
<td>轻微数值差异</td>
|
||
</tr>
|
||
<tr>
|
||
<td>数据并行</td>
|
||
<td>在GPU间扩展批量大小</td>
|
||
<td>梯度同步的通信开销</td>
|
||
</tr>
|
||
<tr>
|
||
<td>张量并行</td>
|
||
<td>在GPU间分割层</td>
|
||
<td>需要快速互联</td>
|
||
</tr>
|
||
<tr>
|
||
<td>流水线并行</td>
|
||
<td>在GPU间分割模型阶段</td>
|
||
<td>流水线气泡（计算浪费）</td>
|
||
</tr>
|
||
<tr>
|
||
<td>梯度累积</td>
|
||
<td>模拟大批量</td>
|
||
<td>更慢（多次前向/反向传播）</td>
|
||
</tr>
|
||
<tr>
|
||
<td>梯度检查点</td>
|
||
<td>减少激活内存</td>
|
||
<td>约多33%计算</td>
|
||
</tr>
|
||
<tr>
|
||
<td>环全规约</td>
|
||
<td>高效的梯度平均</td>
|
||
<td>大模型受限于带宽</td>
|
||
</tr>
|
||
<tr>
|
||
<td>MoE</td>
|
||
<td>更多容量，相同FLOPs</td>
|
||
<td>负载均衡、路由复杂性</td>
|
||
</tr>
|
||
<tr>
|
||
<td>缩放定律</td>
|
||
<td>指导计算分配</td>
|
||
<td>经验公式，未必在所有规模都成立</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<h2 id="colab">编程任务（使用CoLab或笔记本）<a class="headerlink" href="#colab" title="Permanent link">¶</a></h2>
|
||
<ol>
|
||
<li>
|
||
<p>计算Transformer层的FLOPs和内存需求。给定隐藏维度 <span class="arithmatex">\(d\)</span>、序列长度 <span class="arithmatex">\(n\)</span>、批量大小 <span class="arithmatex">\(B\)</span> 和层数，估计总训练成本。
|
||
<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.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="k">def</span><span class="w"> </span><span class="nf">transformer_layer_flops</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">B</span><span class="p">):</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="sd">"""一个Transformer层前向传播的近似FLOPs。"""</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="c1"># QKV投影：3 * (B * n * d * d) * 2（乘法-加法）</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">qkv_flops</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">B</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="n">d</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="c1"># 注意力：(B * n * n * d) * 2 用于QK^T，(B * n * n * d) * 2 用于attn*V</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="n">attn_flops</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">B</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">d</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="c1"># 输出投影：(B * n * d * d) * 2</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="n">out_flops</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">B</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="n">d</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="c1"># FFN：两层，d->4d 和 4d->d：2 * (B * n * d * 4d) * 2</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="n">ffn_flops</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">B</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">d</span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="k">return</span> <span class="n">qkv_flops</span> <span class="o">+</span> <span class="n">attn_flops</span> <span class="o">+</span> <span class="n">out_flops</span> <span class="o">+</span> <span class="n">ffn_flops</span>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">transformer_layer_memory</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">dtype_bytes</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="w"> </span><span class="sd">"""一个层的近似激活内存（字节）。"""</span>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a> <span class="c1"># QKV：3 * B * n * d</span>
|
||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a> <span class="n">qkv_mem</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">B</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="n">dtype_bytes</span>
|
||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a> <span class="c1"># 注意力权重：B * heads * n * n（近似 B * n * n * sizeof）</span>
|
||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a> <span class="n">attn_mem</span> <span class="o">=</span> <span class="n">B</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="n">dtype_bytes</span>
|
||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a> <span class="c1"># FFN中间值：B * n * 4d</span>
|
||
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a> <span class="n">ffn_mem</span> <span class="o">=</span> <span class="n">B</span> <span class="o">*</span> <span class="n">n</span> <span class="o">*</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="n">dtype_bytes</span>
|
||
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a> <span class="k">return</span> <span class="n">qkv_mem</span> <span class="o">+</span> <span class="n">attn_mem</span> <span class="o">+</span> <span class="n">ffn_mem</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="c1"># 示例：GPT-2规模</span>
|
||
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="n">d</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">L</span> <span class="o">=</span> <span class="mi">1024</span><span class="p">,</span> <span class="mi">1024</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">24</span>
|
||
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a><span class="n">fwd_flops</span> <span class="o">=</span> <span class="n">transformer_layer_flops</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">B</span><span class="p">)</span>
|
||
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a><span class="n">total_flops</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">L</span> <span class="o">*</span> <span class="n">fwd_flops</span> <span class="c1"># 前向+反向的3倍</span>
|
||
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="n">act_mem</span> <span class="o">=</span> <span class="n">L</span> <span class="o">*</span> <span class="n">transformer_layer_memory</span><span class="p">(</span><span class="n">d</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">B</span><span class="p">)</span>
|
||
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="n">param_count</span> <span class="o">=</span> <span class="n">L</span> <span class="o">*</span> <span class="p">(</span><span class="mi">12</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="n">d</span> <span class="o">+</span> <span class="mi">13</span> <span class="o">*</span> <span class="n">d</span><span class="p">)</span> <span class="c1"># 近似</span>
|
||
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>
|
||
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"模型：d=</span><span class="si">{</span><span class="n">d</span><span class="si">}</span><span class="s2">, n=</span><span class="si">{</span><span class="n">n</span><span class="si">}</span><span class="s2">, B=</span><span class="si">{</span><span class="n">B</span><span class="si">}</span><span class="s2">, L=</span><span class="si">{</span><span class="n">L</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"参数：</span><span class="si">{</span><span class="n">param_count</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e6</span><span class="si">:</span><span class="s2">.0f</span><span class="si">}</span><span class="s2">M"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"每步FLOPs：</span><span class="si">{</span><span class="n">total_flops</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e12</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> TFLOPs"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"激活内存：</span><span class="si">{</span><span class="n">act_mem</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e9</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> GB (BF16)"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"参数内存 (FP32)：</span><span class="si">{</span><span class="n">param_count</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e9</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> GB"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Adam优化器内存：</span><span class="si">{</span><span class="n">param_count</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">8</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e9</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> GB"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"总训练内存：</span><span class="si">{</span><span class="p">(</span><span class="n">param_count</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">16</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">act_mem</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">1e9</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2"> GB"</span><span class="p">)</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>模拟数据并行训练。将数据集分割到多个"虚拟GPU"上，独立计算梯度，平均它们，并验证结果与单GPU训练匹配。
|
||
<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</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">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-1-3" 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="c1"># 简单线性模型：y = wx + b</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></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">0</span><span class="p">)</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></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">key</span><span class="p">,</span> <span class="p">(</span><span class="mi">64</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">w_true</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="mf">1.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">])</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">y</span> <span class="o">=</span> <span class="n">X</span> <span class="o">@</span> <span class="n">w_true</span> <span class="o">+</span> <span class="mf">0.1</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">key</span><span class="p">,</span> <span class="p">(</span><span class="mi">64</span><span class="p">,))</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">loss_fn</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a> <span class="k">return</span> <span class="n">jnp</span><span class="o">.</span><span class="n">mean</span><span class="p">((</span><span class="n">X</span> <span class="o">@</span> <span class="n">w</span> <span class="o">-</span> <span class="n">y</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</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="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-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="c1"># 单GPU：全批量梯度</span>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="n">w</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">4</span><span class="p">)</span>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="n">grad_single</span> <span class="o">=</span> <span class="n">grad_fn</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="c1"># 数据并行：分割到4个"GPU"上</span>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="n">n_gpus</span> <span class="o">=</span> <span class="mi">4</span>
|
||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="n">chunk_size</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">X</span><span class="p">)</span> <span class="o">//</span> <span class="n">n_gpus</span>
|
||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="n">grads</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></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_gpus</span><span class="p">):</span>
|
||
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a> <span class="n">X_chunk</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">chunk_size</span><span class="p">:(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">chunk_size</span><span class="p">]</span>
|
||
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a> <span class="n">y_chunk</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">chunk_size</span><span class="p">:(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">chunk_size</span><span class="p">]</span>
|
||
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a> <span class="n">grads</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">grad_fn</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">X_chunk</span><span class="p">,</span> <span class="n">y_chunk</span><span class="p">))</span>
|
||
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
|
||
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="c1"># 全规约：平均梯度</span>
|
||
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="n">grad_parallel</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">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="n">grads</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a>
|
||
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="nb">print</span><span class="p">(</span><span class="s2">"单GPU梯度："</span><span class="p">,</span> <span class="n">grad_single</span><span class="p">)</span>
|
||
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="nb">print</span><span class="p">(</span><span class="s2">"数据并行梯度（平均）："</span><span class="p">,</span> <span class="n">grad_parallel</span><span class="p">)</span>
|
||
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"匹配：</span><span class="si">{</span><span class="n">jnp</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">grad_single</span><span class="p">,</span><span class="w"> </span><span class="n">grad_parallel</span><span class="p">,</span><span class="w"> </span><span class="n">atol</span><span class="o">=</span><span class="mf">1e-5</span><span class="p">)</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a>
|
||
<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="c1"># 训练两者并比较</span>
|
||
<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="n">w_single</span><span class="p">,</span> <span class="n">w_parallel</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">4</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">4</span><span class="p">)</span>
|
||
<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="n">lr</span> <span class="o">=</span> <span class="mf">0.1</span>
|
||
<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="k">for</span> <span class="n">step</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
|
||
<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a> <span class="n">w_single</span> <span class="o">=</span> <span class="n">w_single</span> <span class="o">-</span> <span class="n">lr</span> <span class="o">*</span> <span class="n">grad_fn</span><span class="p">(</span><span class="n">w_single</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
|
||
<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a>
|
||
<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a> <span class="n">grads</span> <span class="o">=</span> <span class="p">[</span><span class="n">grad_fn</span><span class="p">(</span><span class="n">w_parallel</span><span class="p">,</span> <span class="n">X</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">chunk_size</span><span class="p">:(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">chunk_size</span><span class="p">],</span>
|
||
<a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a> <span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="o">*</span><span class="n">chunk_size</span><span class="p">:(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">chunk_size</span><span class="p">])</span> <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_gpus</span><span class="p">)]</span>
|
||
<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a> <span class="n">avg_grad</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">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="n">grads</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a> <span class="n">w_parallel</span> <span class="o">=</span> <span class="n">w_parallel</span> <span class="o">-</span> <span class="n">lr</span> <span class="o">*</span> <span class="n">avg_grad</span>
|
||
<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a>
|
||
<a id="__codelineno-1-46" name="__codelineno-1-46" href="#__codelineno-1-46"></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">100步之后："</span><span class="p">)</span>
|
||
<a id="__codelineno-1-47" name="__codelineno-1-47" href="#__codelineno-1-47"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"单GPU权重：</span><span class="si">{</span><span class="n">w_single</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-1-48" name="__codelineno-1-48" href="#__codelineno-1-48"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"数据并行权重：</span><span class="si">{</span><span class="n">w_parallel</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-1-49" name="__codelineno-1-49" href="#__codelineno-1-49"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"最大差异：</span><span class="si">{</span><span class="n">jnp</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">w_single</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">w_parallel</span><span class="p">))</span><span class="si">:</span><span class="s2">.2e</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>实现一个简单的混合专家层。创建一个门控网络，将token路由到top-K个专家并组合它们的输出。
|
||
<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>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="k">def</span><span class="w"> </span><span class="nf">expert_fn</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">W1</span><span class="p">,</span> <span class="n">b1</span><span class="p">,</span> <span class="n">W2</span><span class="p">,</span> <span class="n">b2</span><span class="p">):</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="sd">"""简单的2层FFN专家。"""</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></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">x</span> <span class="o">@</span> <span class="n">W1</span> <span class="o">+</span> <span class="n">b1</span><span class="p">)</span> <span class="c1"># ReLU</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a> <span class="k">return</span> <span class="n">h</span> <span class="o">@</span> <span class="n">W2</span> <span class="o">+</span> <span class="n">b2</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">moe_layer</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">gate_W</span><span class="p">,</span> <span class="n">experts_params</span><span class="p">,</span> <span class="n">top_k</span><span class="o">=</span><span class="mi">2</span><span class="p">):</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w"> </span><span class="sd">"""</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="sd"> MoE前向传播。</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="sd"> x: (batch, d_model)</span>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="sd"> gate_W: (d_model, n_experts)</span>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="sd"> experts_params: 每个专家的 (W1, b1, W2, b2) 列表</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="sd"> """</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a> <span class="n">n_experts</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">experts_params</span><span class="p">)</span>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a> <span class="c1"># 门控：计算路由分数</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a> <span class="n">gate_logits</span> <span class="o">=</span> <span class="n">x</span> <span class="o">@</span> <span class="n">gate_W</span> <span class="c1"># (batch, n_experts)</span>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a> <span class="n">gate_probs</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">softmax</span><span class="p">(</span><span class="n">gate_logits</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a> <span class="c1"># Top-K选择</span>
|
||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a> <span class="n">top_k_indices</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="o">-</span><span class="n">gate_probs</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)[:,</span> <span class="p">:</span><span class="n">top_k</span><span class="p">]</span>
|
||
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a> <span class="n">top_k_probs</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">take_along_axis</span><span class="p">(</span><span class="n">gate_probs</span><span class="p">,</span> <span class="n">top_k_indices</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a> <span class="c1"># 重新归一化</span>
|
||
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a> <span class="n">top_k_probs</span> <span class="o">=</span> <span class="n">top_k_probs</span> <span class="o">/</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">top_k_probs</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a>
|
||
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a> <span class="c1"># 计算专家输出（简化：运行所有专家，稍后掩码）</span>
|
||
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a> <span class="n">expert_outputs</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span>
|
||
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a> <span class="n">expert_fn</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">experts_params</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <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_experts</span><span class="p">)</span>
|
||
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a> <span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span> <span class="c1"># (batch, n_experts, d_model)</span>
|
||
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a>
|
||
<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a> <span class="c1"># 收集top-K专家输出并加权</span>
|
||
<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a> <span class="n">batch_idx</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])[:,</span> <span class="kc">None</span><span class="p">]</span>
|
||
<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a> <span class="n">selected_outputs</span> <span class="o">=</span> <span class="n">expert_outputs</span><span class="p">[</span><span class="n">batch_idx</span><span class="p">,</span> <span class="n">top_k_indices</span><span class="p">]</span> <span class="c1"># (batch, top_k, d_model)</span>
|
||
<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a> <span class="n">output</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">selected_outputs</span> <span class="o">*</span> <span class="n">top_k_probs</span><span class="p">[:,</span> <span class="p">:,</span> <span class="kc">None</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a>
|
||
<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a> <span class="k">return</span> <span class="n">output</span><span class="p">,</span> <span class="n">gate_probs</span>
|
||
<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a>
|
||
<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="c1"># 设置</span>
|
||
<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></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-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a><span class="n">batch</span><span class="p">,</span> <span class="n">d_model</span><span class="p">,</span> <span class="n">d_ff</span><span class="p">,</span> <span class="n">n_experts</span> <span class="o">=</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">4</span>
|
||
<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a>
|
||
<a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a><span class="c1"># 初始化专家</span>
|
||
<a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="n">experts_params</span> <span class="o">=</span> <span class="p">[]</span>
|
||
<a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></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_experts</span><span class="p">):</span>
|
||
<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a> <span class="n">k1</span><span class="p">,</span> <span class="n">k2</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> <span class="mi">3</span><span class="p">)[</span><span class="mi">0</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">split</span><span class="p">(</span><span class="n">key</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="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><span class="mi">2</span><span class="p">]</span>
|
||
<a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></a> <span class="n">experts_params</span><span class="o">.</span><span class="n">append</span><span class="p">((</span>
|
||
<a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a> <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">d_model</span><span class="p">,</span> <span class="n">d_ff</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.1</span><span class="p">,</span>
|
||
<a id="__codelineno-2-50" name="__codelineno-2-50" href="#__codelineno-2-50"></a> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">d_ff</span><span class="p">),</span>
|
||
<a id="__codelineno-2-51" name="__codelineno-2-51" href="#__codelineno-2-51"></a> <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">d_ff</span><span class="p">,</span> <span class="n">d_model</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.1</span><span class="p">,</span>
|
||
<a id="__codelineno-2-52" name="__codelineno-2-52" href="#__codelineno-2-52"></a> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">d_model</span><span class="p">),</span>
|
||
<a id="__codelineno-2-53" name="__codelineno-2-53" href="#__codelineno-2-53"></a> <span class="p">))</span>
|
||
<a id="__codelineno-2-54" name="__codelineno-2-54" href="#__codelineno-2-54"></a>
|
||
<a id="__codelineno-2-55" name="__codelineno-2-55" href="#__codelineno-2-55"></a><span class="n">key</span><span class="p">,</span> <span class="n">subkey</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-2-56" name="__codelineno-2-56" href="#__codelineno-2-56"></a><span class="n">gate_W</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">subkey</span><span class="p">,</span> <span class="p">(</span><span class="n">d_model</span><span class="p">,</span> <span class="n">n_experts</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.1</span>
|
||
<a id="__codelineno-2-57" name="__codelineno-2-57" href="#__codelineno-2-57"></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">key</span><span class="p">,</span> <span class="p">(</span><span class="n">batch</span><span class="p">,</span> <span class="n">d_model</span><span class="p">))</span>
|
||
<a id="__codelineno-2-58" name="__codelineno-2-58" href="#__codelineno-2-58"></a>
|
||
<a id="__codelineno-2-59" name="__codelineno-2-59" href="#__codelineno-2-59"></a><span class="n">output</span><span class="p">,</span> <span class="n">gate_probs</span> <span class="o">=</span> <span class="n">moe_layer</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">gate_W</span><span class="p">,</span> <span class="n">experts_params</span><span class="p">,</span> <span class="n">top_k</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
|
||
<a id="__codelineno-2-60" name="__codelineno-2-60" href="#__codelineno-2-60"></a>
|
||
<a id="__codelineno-2-61" name="__codelineno-2-61" href="#__codelineno-2-61"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"输入形状：</span><span class="si">{</span><span class="n">x</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-2-62" name="__codelineno-2-62" href="#__codelineno-2-62"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"输出形状：</span><span class="si">{</span><span class="n">output</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-2-63" name="__codelineno-2-63" href="#__codelineno-2-63"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"门控概率（第一个样本）：</span><span class="si">{</span><span class="n">gate_probs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-2-64" name="__codelineno-2-64" href="#__codelineno-2-64"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"专家使用率（批量平均）："</span><span class="p">)</span>
|
||
<a id="__codelineno-2-65" name="__codelineno-2-65" href="#__codelineno-2-65"></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_experts</span><span class="p">):</span>
|
||
<a id="__codelineno-2-66" name="__codelineno-2-66" href="#__codelineno-2-66"></a> <span class="n">usage</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">gate_probs</span><span class="p">[:,</span> <span class="n">i</span><span class="p">])</span>
|
||
<a id="__codelineno-2-67" name="__codelineno-2-67" href="#__codelineno-2-67"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">" 专家 </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">usage</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
</code></pre></div></p>
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