{
"cells": [
{
"cell_type": "markdown",
"id": "59b31683",
"metadata": {
"origin_pos": 0
},
"source": [
"# 多层感知机的从零开始实现\n",
":label:`sec_mlp_scratch`\n",
"\n",
"我们已经在 :numref:`sec_mlp`中描述了多层感知机（MLP），\n",
"现在让我们尝试自己实现一个多层感知机。\n",
"为了与之前softmax回归（ :numref:`sec_softmax_scratch` ）\n",
"获得的结果进行比较，\n",
"我们将继续使用Fashion-MNIST图像分类数据集\n",
"（ :numref:`sec_fashion_mnist`）。\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "ffbb0fc1",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T06:59:21.394152Z",
"iopub.status.busy": "2023-08-18T06:59:21.393407Z",
"iopub.status.idle": "2023-08-18T06:59:24.364157Z",
"shell.execute_reply": "2023-08-18T06:59:24.362977Z"
},
"origin_pos": 2,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"import torch\n",
"from torch import nn\n",
"from d2l import torch as d2l"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "0be61c4f",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T06:59:24.369567Z",
"iopub.status.busy": "2023-08-18T06:59:24.368990Z",
"iopub.status.idle": "2023-08-18T06:59:24.501326Z",
"shell.execute_reply": "2023-08-18T06:59:24.500151Z"
},
"origin_pos": 5,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"batch_size = 256\n",
"train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)"
]
},
{
"cell_type": "markdown",
"id": "8236e2cd",
"metadata": {
"origin_pos": 6
},
"source": [
"## 初始化模型参数\n",
"\n",
"回想一下，Fashion-MNIST中的每个图像由\n",
"$28 \\times 28 = 784$个灰度像素值组成。\n",
"所有图像共分为10个类别。\n",
"忽略像素之间的空间结构，\n",
"我们可以将每个图像视为具有784个输入特征\n",
"和10个类的简单分类数据集。\n",
"首先，我们将[**实现一个具有单隐藏层的多层感知机，\n",
"它包含256个隐藏单元**]。\n",
"注意，我们可以将这两个变量都视为超参数。\n",
"通常，我们选择2的若干次幂作为层的宽度。\n",
"因为内存在硬件中的分配和寻址方式，这么做往往可以在计算上更高效。\n",
"\n",
"我们用几个张量来表示我们的参数。\n",
"注意，对于每一层我们都要记录一个权重矩阵和一个偏置向量。\n",
"跟以前一样，我们要为损失关于这些参数的梯度分配内存。\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "7730f280",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T06:59:24.508163Z",
"iopub.status.busy": "2023-08-18T06:59:24.506257Z",
"iopub.status.idle": "2023-08-18T06:59:24.520861Z",
"shell.execute_reply": "2023-08-18T06:59:24.519861Z"
},
"origin_pos": 8,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"num_inputs, num_outputs, num_hiddens = 784, 10, 256\n",
"\n",
"W1 = nn.Parameter(torch.randn(\n",
" num_inputs, num_hiddens, requires_grad=True) * 0.01)\n",
"b1 = nn.Parameter(torch.zeros(num_hiddens, requires_grad=True))\n",
"W2 = nn.Parameter(torch.randn(\n",
" num_hiddens, num_outputs, requires_grad=True) * 0.01)\n",
"b2 = nn.Parameter(torch.zeros(num_outputs, requires_grad=True))\n",
"\n",
"params = [W1, b1, W2, b2]"
]
},
{
"cell_type": "markdown",
"id": "2700dfe8",
"metadata": {
"origin_pos": 11
},
"source": [
"## 激活函数\n",
"\n",
"为了确保我们对模型的细节了如指掌，\n",
"我们将[**实现ReLU激活函数**]，\n",
"而不是直接调用内置的`relu`函数。\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "5f46a813",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T06:59:24.528151Z",
"iopub.status.busy": "2023-08-18T06:59:24.526356Z",
"iopub.status.idle": "2023-08-18T06:59:24.533695Z",
"shell.execute_reply": "2023-08-18T06:59:24.532654Z"
},
"origin_pos": 13,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"def relu(X):\n",
" a = torch.zeros_like(X)\n",
" return torch.max(X, a)"
]
},
{
"cell_type": "markdown",
"id": "741dbe39",
"metadata": {
"origin_pos": 16
},
"source": [
"## 模型\n",
"\n",
"因为我们忽略了空间结构，\n",
"所以我们使用`reshape`将每个二维图像转换为一个长度为`num_inputs`的向量。\n",
"只需几行代码就可以(**实现我们的模型**)。\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b3d9923a",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T06:59:24.541482Z",
"iopub.status.busy": "2023-08-18T06:59:24.539621Z",
"iopub.status.idle": "2023-08-18T06:59:24.547435Z",
"shell.execute_reply": "2023-08-18T06:59:24.546468Z"
},
"origin_pos": 18,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"def net(X):\n",
" X = X.reshape((-1, num_inputs))\n",
" H = relu(X@W1 + b1) # 这里“@”代表矩阵乘法\n",
" return (H@W2 + b2)"
]
},
{
"cell_type": "markdown",
"id": "bd600c14",
"metadata": {
"origin_pos": 21
},
"source": [
"## 损失函数\n",
"\n",
"由于我们已经从零实现过softmax函数（ :numref:`sec_softmax_scratch`），\n",
"因此在这里我们直接使用高级API中的内置函数来计算softmax和交叉熵损失。\n",
"回想一下我们之前在 :numref:`subsec_softmax-implementation-revisited`中\n",
"对这些复杂问题的讨论。\n",
"我们鼓励感兴趣的读者查看损失函数的源代码，以加深对实现细节的了解。\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "f55fe0ea",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T06:59:24.554675Z",
"iopub.status.busy": "2023-08-18T06:59:24.552824Z",
"iopub.status.idle": "2023-08-18T06:59:24.560084Z",
"shell.execute_reply": "2023-08-18T06:59:24.559049Z"
},
"origin_pos": 23,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"loss = nn.CrossEntropyLoss(reduction='none')"
]
},
{
"cell_type": "markdown",
"id": "b3a03c3a",
"metadata": {
"origin_pos": 25
},
"source": [
"## 训练\n",
"\n",
"幸运的是，[**多层感知机的训练过程与softmax回归的训练过程完全相同**]。\n",
"可以直接调用`d2l`包的`train_ch3`函数（参见 :numref:`sec_softmax_scratch` ），\n",
"将迭代周期数设置为10，并将学习率设置为0.1.\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "c83cc0c7",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T06:59:24.567796Z",
"iopub.status.busy": "2023-08-18T06:59:24.566005Z",
"iopub.status.idle": "2023-08-18T07:00:19.750339Z",
"shell.execute_reply": "2023-08-18T07:00:19.748990Z"
},
"origin_pos": 27,
"tab": [
"pytorch"
]
},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"num_epochs, lr = 10, 0.1\n",
"updater = torch.optim.SGD(params, lr=lr)\n",
"d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, updater)"
]
},
{
"cell_type": "markdown",
"id": "4da98919",
"metadata": {
"origin_pos": 30
},
"source": [
"为了对学习到的模型进行评估，我们将[**在一些测试数据上应用这个模型**]。\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "8230ba7c",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:00:19.755336Z",
"iopub.status.busy": "2023-08-18T07:00:19.754506Z",
"iopub.status.idle": "2023-08-18T07:00:20.323813Z",
"shell.execute_reply": "2023-08-18T07:00:20.322738Z"
},
"origin_pos": 31,
"tab": [
"pytorch"
]
},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"d2l.predict_ch3(net, test_iter)"
]
},
{
"cell_type": "markdown",
"id": "c97420c6",
"metadata": {
"origin_pos": 32
},
"source": [
"## 小结\n",
"\n",
"* 手动实现一个简单的多层感知机是很容易的。然而如果有大量的层，从零开始实现多层感知机会变得很麻烦（例如，要命名和记录模型的参数）。\n",
"\n",
"## 练习\n",
"\n",
"1. 在所有其他参数保持不变的情况下，更改超参数`num_hiddens`的值，并查看此超参数的变化对结果有何影响。确定此超参数的最佳值。\n",
"1. 尝试添加更多的隐藏层，并查看它对结果有何影响。\n",
"1. 改变学习速率会如何影响结果？保持模型架构和其他超参数（包括轮数）不变，学习率设置为多少会带来最好的结果？\n",
"1. 通过对所有超参数（学习率、轮数、隐藏层数、每层的隐藏单元数）进行联合优化，可以得到的最佳结果是什么？\n",
"1. 描述为什么涉及多个超参数更具挑战性。\n",
"1. 如果想要构建多个超参数的搜索方法，请想出一个聪明的策略。\n"
]
},
{
"cell_type": "markdown",
"id": "d0e00850",
"metadata": {
"origin_pos": 34,
"tab": [
"pytorch"
]
},
"source": [
"[Discussions](https://discuss.d2l.ai/t/1804)\n"
]
}
],
"metadata": {
"language_info": {
"name": "python"
},
"required_libs": []
},
"nbformat": 4,
"nbformat_minor": 5
}