{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d7a3e66e",
   "metadata": {
    "origin_pos": 0
   },
   "source": [
    "# 多GPU训练\n",
    ":label:`sec_multi_gpu`\n",
    "\n",
    "到目前为止，我们讨论了如何在CPU和GPU上高效地训练模型，同时在 :numref:`sec_auto_para`中展示了深度学习框架如何在CPU和GPU之间自动地并行化计算和通信，还在 :numref:`sec_use_gpu`中展示了如何使用`nvidia-smi`命令列出计算机上所有可用的GPU。\n",
    "但是我们没有讨论如何真正实现深度学习训练的并行化。\n",
    "是否一种方法，以某种方式分割数据到多个设备上，并使其能够正常工作呢？\n",
    "本节将详细介绍如何从零开始并行地训练网络，\n",
    "这里需要运用小批量随机梯度下降算法（详见 :numref:`sec_minibatch_sgd`）。\n",
    "后面我还讲介绍如何使用高级API并行训练网络（请参阅 :numref:`sec_multi_gpu_concise`）。\n",
    "\n",
    "## 问题拆分\n",
    "\n",
    "我们从一个简单的计算机视觉问题和一个稍稍过时的网络开始。\n",
    "这个网络有多个卷积层和汇聚层，最后可能有几个全连接的层，看起来非常类似于LeNet :cite:`LeCun.Bottou.Bengio.ea.1998`或AlexNet :cite:`Krizhevsky.Sutskever.Hinton.2012`。\n",
    "假设我们有多个GPU（如果是桌面服务器则有$2$个，AWS g4dn.12xlarge上有$4$个，p3.16xlarge上有$8$个，p2.16xlarge上有$16$个）。\n",
    "我们希望以一种方式对训练进行拆分，为实现良好的加速比，还能同时受益于简单且可重复的设计选择。\n",
    "毕竟，多个GPU同时增加了内存和计算能力。\n",
    "简而言之，对于需要分类的小批量训练数据，我们有以下选择。\n",
    "\n",
    "第一种方法，在多个GPU之间拆分网络。\n",
    "也就是说，每个GPU将流入特定层的数据作为输入，跨多个后续层对数据进行处理，然后将数据发送到下一个GPU。\n",
    "与单个GPU所能处理的数据相比，我们可以用更大的网络处理数据。\n",
    "此外，每个GPU占用的*显存*（memory footprint）可以得到很好的控制，虽然它只是整个网络显存的一小部分。\n",
    "\n",
    "然而，GPU的接口之间需要的密集同步可能是很难办的，特别是层之间计算的工作负载不能正确匹配的时候，\n",
    "还有层之间的接口需要大量的数据传输的时候（例如：激活值和梯度，数据量可能会超出GPU总线的带宽）。\n",
    "此外，计算密集型操作的顺序对拆分来说也是非常重要的，这方面的最好研究可参见 :cite:`Mirhoseini.Pham.Le.ea.2017`，其本质仍然是一个困难的问题，目前还不清楚研究是否能在特定问题上实现良好的线性缩放。\n",
    "综上所述，除非存框架或操作系统本身支持将多个GPU连接在一起，否则不建议这种方法。\n",
    "\n",
    "第二种方法，拆分层内的工作。\n",
    "例如，将问题分散到$4$个GPU，每个GPU生成$16$个通道的数据，而不是在单个GPU上计算$64$个通道。\n",
    "对于全连接的层，同样可以拆分输出单元的数量。\n",
    " :numref:`fig_alexnet_original`描述了这种设计，其策略用于处理显存非常小（当时为2GB）的GPU。\n",
    "当通道或单元的数量不太小时，使计算性能有良好的提升。\n",
    "此外，由于可用的显存呈线性扩展，多个GPU能够处理不断变大的网络。\n",
    "\n",
    "![由于GPU显存有限，原有AlexNet设计中的模型并行](../img/alexnet-original.svg)\n",
    ":label:`fig_alexnet_original`\n",
    "\n",
    "然而，我们需要大量的同步或*屏障操作*（barrier operation），因为每一层都依赖于所有其他层的结果。\n",
    "此外，需要传输的数据量也可能比跨GPU拆分层时还要大。\n",
    "因此，基于带宽的成本和复杂性，我们同样不推荐这种方法。\n",
    "\n",
    "最后一种方法，跨多个GPU对数据进行拆分。\n",
    "这种方式下，所有GPU尽管有不同的观测结果，但是执行着相同类型的工作。\n",
    "在完成每个小批量数据的训练之后，梯度在GPU上聚合。\n",
    "这种方法最简单，并可以应用于任何情况，同步只需要在每个小批量数据处理之后进行。\n",
    "也就是说，当其他梯度参数仍在计算时，完成计算的梯度参数就可以开始交换。\n",
    "而且，GPU的数量越多，小批量包含的数据量就越大，从而就能提高训练效率。\n",
    "但是，添加更多的GPU并不能让我们训练更大的模型。\n",
    "\n",
    "![在多个GPU上并行化。从左到右：原始问题、网络并行、分层并行、数据并行](../img/splitting.svg)\n",
    ":label:`fig_splitting`\n",
    "\n",
    " :numref:`fig_splitting`中比较了多个GPU上不同的并行方式。\n",
    "总体而言，只要GPU的显存足够大，数据并行是最方便的。\n",
    "有关分布式训练分区的详细描述，请参见 :cite:`Li.Andersen.Park.ea.2014`。\n",
    "在深度学习的早期，GPU的显存曾经是一个棘手的问题，然而如今除了非常特殊的情况，这个问题已经解决。\n",
    "下面我们将重点讨论数据并行性。\n",
    "\n",
    "## 数据并行性\n",
    "\n",
    "假设一台机器有$k$个GPU。\n",
    "给定需要训练的模型，虽然每个GPU上的参数值都是相同且同步的，但是每个GPU都将独立地维护一组完整的模型参数。\n",
    "例如， :numref:`fig_data_parallel`演示了在$k=2$时基于数据并行方法训练模型。\n",
    "\n",
    "![利用两个GPU上的数据，并行计算小批量随机梯度下降](../img/data-parallel.svg)\n",
    ":label:`fig_data_parallel`\n",
    "\n",
    "一般来说，$k$个GPU并行训练过程如下：\n",
    "\n",
    "* 在任何一次训练迭代中，给定的随机的小批量样本都将被分成$k$个部分，并均匀地分配到GPU上；\n",
    "* 每个GPU根据分配给它的小批量子集，计算模型参数的损失和梯度；\n",
    "* 将$k$个GPU中的局部梯度聚合，以获得当前小批量的随机梯度；\n",
    "* 聚合梯度被重新分发到每个GPU中；\n",
    "* 每个GPU使用这个小批量随机梯度，来更新它所维护的完整的模型参数集。\n",
    "\n",
    "\n",
    "在实践中请注意，当在$k$个GPU上训练时，需要扩大小批量的大小为$k$的倍数，这样每个GPU都有相同的工作量，就像只在单个GPU上训练一样。\n",
    "因此，在16-GPU服务器上可以显著地增加小批量数据量的大小，同时可能还需要相应地提高学习率。\n",
    "还请注意， :numref:`sec_batch_norm`中的批量规范化也需要调整，例如，为每个GPU保留单独的批量规范化参数。\n",
    "\n",
    "下面我们将使用一个简单网络来演示多GPU训练。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9b75d971",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T06:56:31.500723Z",
     "iopub.status.busy": "2023-08-18T06:56:31.500272Z",
     "iopub.status.idle": "2023-08-18T06:56:33.774318Z",
     "shell.execute_reply": "2023-08-18T06:56:33.773366Z"
    },
    "origin_pos": 2,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "from torch import nn\n",
    "from torch.nn import functional as F\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f734e92e",
   "metadata": {
    "origin_pos": 4
   },
   "source": [
    "## [**简单网络**]\n",
    "\n",
    "我们使用 :numref:`sec_lenet`中介绍的（稍加修改的）LeNet，\n",
    "从零开始定义它，从而详细说明参数交换和同步。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e7ea3d2d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T06:56:33.791043Z",
     "iopub.status.busy": "2023-08-18T06:56:33.790376Z",
     "iopub.status.idle": "2023-08-18T06:56:33.803921Z",
     "shell.execute_reply": "2023-08-18T06:56:33.803009Z"
    },
    "origin_pos": 6,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "# 初始化模型参数\n",
    "scale = 0.01\n",
    "W1 = torch.randn(size=(20, 1, 3, 3)) * scale\n",
    "b1 = torch.zeros(20)\n",
    "W2 = torch.randn(size=(50, 20, 5, 5)) * scale\n",
    "b2 = torch.zeros(50)\n",
    "W3 = torch.randn(size=(800, 128)) * scale\n",
    "b3 = torch.zeros(128)\n",
    "W4 = torch.randn(size=(128, 10)) * scale\n",
    "b4 = torch.zeros(10)\n",
    "params = [W1, b1, W2, b2, W3, b3, W4, b4]\n",
    "\n",
    "# 定义模型\n",
    "def lenet(X, params):\n",
    "    h1_conv = F.conv2d(input=X, weight=params[0], bias=params[1])\n",
    "    h1_activation = F.relu(h1_conv)\n",
    "    h1 = F.avg_pool2d(input=h1_activation, kernel_size=(2, 2), stride=(2, 2))\n",
    "    h2_conv = F.conv2d(input=h1, weight=params[2], bias=params[3])\n",
    "    h2_activation = F.relu(h2_conv)\n",
    "    h2 = F.avg_pool2d(input=h2_activation, kernel_size=(2, 2), stride=(2, 2))\n",
    "    h2 = h2.reshape(h2.shape[0], -1)\n",
    "    h3_linear = torch.mm(h2, params[4]) + params[5]\n",
    "    h3 = F.relu(h3_linear)\n",
    "    y_hat = torch.mm(h3, params[6]) + params[7]\n",
    "    return y_hat\n",
    "\n",
    "# 交叉熵损失函数\n",
    "loss = nn.CrossEntropyLoss(reduction='none')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0720668",
   "metadata": {
    "origin_pos": 8
   },
   "source": [
    "## 数据同步\n",
    "\n",
    "对于高效的多GPU训练，我们需要两个基本操作。\n",
    "首先，我们需要[**向多个设备分发参数**]并附加梯度（`get_params`）。\n",
    "如果没有参数，就不可能在GPU上评估网络。\n",
    "第二，需要跨多个设备对参数求和，也就是说，需要一个`allreduce`函数。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "327866dd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T06:56:33.808310Z",
     "iopub.status.busy": "2023-08-18T06:56:33.807838Z",
     "iopub.status.idle": "2023-08-18T06:56:33.812526Z",
     "shell.execute_reply": "2023-08-18T06:56:33.811610Z"
    },
    "origin_pos": 10,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def get_params(params, device):\n",
    "    new_params = [p.to(device) for p in params]\n",
    "    for p in new_params:\n",
    "        p.requires_grad_()\n",
    "    return new_params"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0810efa1",
   "metadata": {
    "origin_pos": 12
   },
   "source": [
    "通过将模型参数复制到一个GPU。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "acbfd8fb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T06:56:33.816628Z",
     "iopub.status.busy": "2023-08-18T06:56:33.816173Z",
     "iopub.status.idle": "2023-08-18T06:56:35.081408Z",
     "shell.execute_reply": "2023-08-18T06:56:35.080442Z"
    },
    "origin_pos": 13,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b1 权重: tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
      "       device='cuda:0', requires_grad=True)\n",
      "b1 梯度: None\n"
     ]
    }
   ],
   "source": [
    "new_params = get_params(params, d2l.try_gpu(0))\n",
    "print('b1 权重:', new_params[1])\n",
    "print('b1 梯度:', new_params[1].grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1785343",
   "metadata": {
    "origin_pos": 14
   },
   "source": [
    "由于还没有进行任何计算，因此权重参数的梯度仍然为零。\n",
    "假设现在有一个向量分布在多个GPU上，下面的[**`allreduce`函数将所有向量相加，并将结果广播给所有GPU**]。\n",
    "请注意，我们需要将数据复制到累积结果的设备，才能使函数正常工作。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "08d61f96",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T06:56:35.085160Z",
     "iopub.status.busy": "2023-08-18T06:56:35.084535Z",
     "iopub.status.idle": "2023-08-18T06:56:35.089528Z",
     "shell.execute_reply": "2023-08-18T06:56:35.088692Z"
    },
    "origin_pos": 16,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def allreduce(data):\n",
    "    for i in range(1, len(data)):\n",
    "        data[0][:] += data[i].to(data[0].device)\n",
    "    for i in range(1, len(data)):\n",
    "        data[i][:] = data[0].to(data[i].device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "649811d7",
   "metadata": {
    "origin_pos": 18
   },
   "source": [
    "通过在不同设备上创建具有不同值的向量并聚合它们。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5ddb502b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T06:56:35.092907Z",
     "iopub.status.busy": "2023-08-18T06:56:35.092390Z",
     "iopub.status.idle": "2023-08-18T06:56:36.054582Z",
     "shell.execute_reply": "2023-08-18T06:56:36.053711Z"
    },
    "origin_pos": 20,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "allreduce之前：\n",
      " tensor([[1., 1.]], device='cuda:0') \n",
      " tensor([[2., 2.]], device='cuda:1')\n",
      "allreduce之后：\n",
      " tensor([[3., 3.]], device='cuda:0') \n",
      " tensor([[3., 3.]], device='cuda:1')\n"
     ]
    }
   ],
   "source": [
    "data = [torch.ones((1, 2), device=d2l.try_gpu(i)) * (i + 1) for i in range(2)]\n",
    "print('allreduce之前：\\n', data[0], '\\n', data[1])\n",
    "allreduce(data)\n",
    "print('allreduce之后：\\n', data[0], '\\n', data[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "173fee39",
   "metadata": {
    "origin_pos": 22
   },
   "source": [
    "## 数据分发\n",
    "\n",
    "我们需要一个简单的工具函数，[**将一个小批量数据均匀地分布在多个GPU上**]。\n",
    "例如，有两个GPU时，我们希望每个GPU可以复制一半的数据。\n",
    "因为深度学习框架的内置函数编写代码更方便、更简洁，所以在$4 \\times 5$矩阵上使用它进行尝试。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8964df34",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T06:56:36.058211Z",
     "iopub.status.busy": "2023-08-18T06:56:36.057647Z",
     "iopub.status.idle": "2023-08-18T06:56:36.067247Z",
     "shell.execute_reply": "2023-08-18T06:56:36.066423Z"
    },
    "origin_pos": 24,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input : tensor([[ 0,  1,  2,  3,  4],\n",
      "        [ 5,  6,  7,  8,  9],\n",
      "        [10, 11, 12, 13, 14],\n",
      "        [15, 16, 17, 18, 19]])\n",
      "load into [device(type='cuda', index=0), device(type='cuda', index=1)]\n",
      "output: (tensor([[0, 1, 2, 3, 4],\n",
      "        [5, 6, 7, 8, 9]], device='cuda:0'), tensor([[10, 11, 12, 13, 14],\n",
      "        [15, 16, 17, 18, 19]], device='cuda:1'))\n"
     ]
    }
   ],
   "source": [
    "data = torch.arange(20).reshape(4, 5)\n",
    "devices = [torch.device('cuda:0'), torch.device('cuda:1')]\n",
    "split = nn.parallel.scatter(data, devices)\n",
    "print('input :', data)\n",
    "print('load into', devices)\n",
    "print('output:', split)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c313718",
   "metadata": {
    "origin_pos": 26
   },
   "source": [
    "为了方便以后复用，我们定义了可以同时拆分数据和标签的`split_batch`函数。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "abd5b51e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-08-18T06:56:36.070742Z",
     "iopub.status.busy": "2023-08-18T06:56:36.070215Z",
     "iopub.status.idle": "2023-08-18T06:56:36.074876Z",
     "shell.execute_reply": "2023-08-18T06:56:36.074084Z"
    },
    "origin_pos": 28,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "#@save\n",
    "def split_batch(X, y, devices):\n",
    "    \"\"\"将X和y拆分到多个设备上\"\"\"\n",
    "    assert X.shape[0] == y.shape[0]\n",
    "    return (nn.parallel.scatter(X, devices),\n",
    "            nn.parallel.scatter(y, devices))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd16b450",
   "metadata": {
    "origin_pos": 30
   },
   "source": [
    "## 训练\n",
    "\n",
    "现在我们可以[**在一个小批量上实现多GPU训练**]。\n",
    "在多个GPU之间同步数据将使用刚才讨论的辅助函数`allreduce`和`split_and_load`。\n",
    "我们不需要编写任何特定的代码来实现并行性。\n",
    "因为计算图在小批量内的设备之间没有任何依赖关系，因此它是“自动地”并行执行。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1d569999",
   "metadata": {
    "execution": {
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   "source": [
    "def train_batch(X, y, device_params, devices, lr):\n",
    "    X_shards, y_shards = split_batch(X, y, devices)\n",
    "    # 在每个GPU上分别计算损失\n",
    "    ls = [loss(lenet(X_shard, device_W), y_shard).sum()\n",
    "          for X_shard, y_shard, device_W in zip(\n",
    "              X_shards, y_shards, device_params)]\n",
    "    for l in ls:  # 反向传播在每个GPU上分别执行\n",
    "        l.backward()\n",
    "    # 将每个GPU的所有梯度相加，并将其广播到所有GPU\n",
    "    with torch.no_grad():\n",
    "        for i in range(len(device_params[0])):\n",
    "            allreduce(\n",
    "                [device_params[c][i].grad for c in range(len(devices))])\n",
    "    # 在每个GPU上分别更新模型参数\n",
    "    for param in device_params:\n",
    "        d2l.sgd(param, lr, X.shape[0]) # 在这里，我们使用全尺寸的小批量"
   ]
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   "source": [
    "现在，我们可以[**定义训练函数**]。\n",
    "与前几章中略有不同：训练函数需要分配GPU并将所有模型参数复制到所有设备。\n",
    "显然，每个小批量都是使用`train_batch`函数来处理多个GPU。\n",
    "我们只在一个GPU上计算模型的精确度，而让其他GPU保持空闲，尽管这是相对低效的，但是使用方便且代码简洁。\n"
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   "source": [
    "def train(num_gpus, batch_size, lr):\n",
    "    train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)\n",
    "    devices = [d2l.try_gpu(i) for i in range(num_gpus)]\n",
    "    # 将模型参数复制到num_gpus个GPU\n",
    "    device_params = [get_params(params, d) for d in devices]\n",
    "    num_epochs = 10\n",
    "    animator = d2l.Animator('epoch', 'test acc', xlim=[1, num_epochs])\n",
    "    timer = d2l.Timer()\n",
    "    for epoch in range(num_epochs):\n",
    "        timer.start()\n",
    "        for X, y in train_iter:\n",
    "            # 为单个小批量执行多GPU训练\n",
    "            train_batch(X, y, device_params, devices, lr)\n",
    "            torch.cuda.synchronize()\n",
    "        timer.stop()\n",
    "        # 在GPU0上评估模型\n",
    "        animator.add(epoch + 1, (d2l.evaluate_accuracy_gpu(\n",
    "            lambda x: lenet(x, device_params[0]), test_iter, devices[0]),))\n",
    "    print(f'测试精度：{animator.Y[0][-1]:.2f}，{timer.avg():.1f}秒/轮，'\n",
    "          f'在{str(devices)}')"
   ]
  },
  {
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   "source": [
    "让我们看看[**在单个GPU上运行**]效果得有多好。\n",
    "首先使用的批量大小是$256$，学习率是$0.2$。\n"
   ]
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "测试精度：0.84，2.7秒/轮，在[device(type='cuda', index=0)]\n"
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    },
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    "保持批量大小和学习率不变，并[**增加为2个GPU**]，我们可以看到测试精度与之前的实验基本相同。\n",
    "不同的GPU个数在算法寻优方面是相同的。\n",
    "不幸的是，这里没有任何有意义的加速：模型实在太小了；而且数据集也太小了。在这个数据集中，我们实现的多GPU训练的简单方法受到了巨大的Python开销的影响。\n",
    "在未来，我们将遇到更复杂的模型和更复杂的并行化方法。\n",
    "尽管如此，让我们看看Fashion-MNIST数据集上会发生什么。\n"
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     "text": [
      "测试精度：0.83，3.6秒/轮，在[device(type='cuda', index=0), device(type='cuda', index=1)]\n"
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    "## 小结\n",
    "\n",
    "* 有多种方法可以在多个GPU上拆分深度网络的训练。拆分可以在层之间、跨层或跨数据上实现。前两者需要对数据传输过程进行严格编排，而最后一种则是最简单的策略。\n",
    "* 数据并行训练本身是不复杂的，它通过增加有效的小批量数据量的大小提高了训练效率。\n",
    "* 在数据并行中，数据需要跨多个GPU拆分，其中每个GPU执行自己的前向传播和反向传播，随后所有的梯度被聚合为一，之后聚合结果向所有的GPU广播。\n",
    "* 小批量数据量更大时，学习率也需要稍微提高一些。\n",
    "\n",
    "## 练习\n",
    "\n",
    "1. 在$k$个GPU上进行训练时，将批量大小从$b$更改为$k \\cdot b$，即按GPU的数量进行扩展。\n",
    "1. 比较不同学习率时模型的精确度，随着GPU数量的增加学习率应该如何扩展？\n",
    "1. 实现一个更高效的`allreduce`函数用于在不同的GPU上聚合不同的参数？为什么这样的效率更高？\n",
    "1. 实现模型在多GPU下测试精度的计算。\n"
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   "source": [
    "[Discussions](https://discuss.d2l.ai/t/2800)\n"
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