1857 lines
108 KiB
Plaintext
1857 lines
108 KiB
Plaintext
{
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"cells": [
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"metadata": {
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"source": [
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"# 多层感知机的从零开始实现\n",
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":label:`sec_mlp_scratch`\n",
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"\n",
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"我们已经在 :numref:`sec_mlp`中描述了多层感知机（MLP），\n",
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"现在让我们尝试自己实现一个多层感知机。\n",
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"为了与之前softmax回归（ :numref:`sec_softmax_scratch` ）\n",
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"获得的结果进行比较，\n",
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"我们将继续使用Fashion-MNIST图像分类数据集\n",
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"（ :numref:`sec_fashion_mnist`）。\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "ffbb0fc1",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T06:59:21.394152Z",
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"origin_pos": 2,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [],
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"source": [
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"import torch\n",
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"from torch import nn\n",
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"from d2l import torch as d2l"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "0be61c4f",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T06:59:24.369567Z",
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},
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"origin_pos": 5,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [],
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"source": [
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"batch_size = 256\n",
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"train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8236e2cd",
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"metadata": {
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"origin_pos": 6
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},
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"source": [
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"## 初始化模型参数\n",
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"\n",
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"回想一下，Fashion-MNIST中的每个图像由\n",
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"$28 \\times 28 = 784$个灰度像素值组成。\n",
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"所有图像共分为10个类别。\n",
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"忽略像素之间的空间结构，\n",
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"我们可以将每个图像视为具有784个输入特征\n",
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"和10个类的简单分类数据集。\n",
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"首先，我们将[**实现一个具有单隐藏层的多层感知机，\n",
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"它包含256个隐藏单元**]。\n",
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"注意，我们可以将这两个变量都视为超参数。\n",
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"通常，我们选择2的若干次幂作为层的宽度。\n",
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"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",
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"\n",
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"我们用几个张量来表示我们的参数。\n",
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"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",
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"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"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "7730f280",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T06:59:24.508163Z",
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"origin_pos": 8,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [],
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"source": [
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||
"num_inputs, num_outputs, num_hiddens = 784, 10, 256\n",
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"\n",
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"W1 = nn.Parameter(torch.randn(\n",
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" num_inputs, num_hiddens, requires_grad=True) * 0.01)\n",
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"b1 = nn.Parameter(torch.zeros(num_hiddens, requires_grad=True))\n",
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||
"W2 = nn.Parameter(torch.randn(\n",
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" num_hiddens, num_outputs, requires_grad=True) * 0.01)\n",
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"b2 = nn.Parameter(torch.zeros(num_outputs, requires_grad=True))\n",
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"\n",
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||
"params = [W1, b1, W2, b2]"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2700dfe8",
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"metadata": {
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"origin_pos": 11
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},
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"source": [
|
||
"## 激活函数\n",
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||
"\n",
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"为了确保我们对模型的细节了如指掌，\n",
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"我们将[**实现ReLU激活函数**]，\n",
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"而不是直接调用内置的`relu`函数。\n"
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||
]
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||
},
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{
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||
"cell_type": "code",
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||
"execution_count": 4,
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||
"id": "5f46a813",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T06:59:24.528151Z",
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"iopub.status.busy": "2023-08-18T06:59:24.526356Z",
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"iopub.status.idle": "2023-08-18T06:59:24.533695Z",
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"shell.execute_reply": "2023-08-18T06:59:24.532654Z"
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},
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"origin_pos": 13,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [],
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||
"source": [
|
||
"def relu(X):\n",
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" a = torch.zeros_like(X)\n",
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||
" return torch.max(X, a)"
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||
]
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},
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{
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"cell_type": "markdown",
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"id": "741dbe39",
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"metadata": {
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"origin_pos": 16
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},
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"source": [
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||
"## 模型\n",
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"\n",
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"因为我们忽略了空间结构，\n",
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"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"
|
||
]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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||
"id": "b3d9923a",
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"metadata": {
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"execution": {
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"iopub.execute_input": "2023-08-18T06:59:24.541482Z",
|
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"iopub.status.busy": "2023-08-18T06:59:24.539621Z",
|
||
"iopub.status.idle": "2023-08-18T06:59:24.547435Z",
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"shell.execute_reply": "2023-08-18T06:59:24.546468Z"
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},
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||
"origin_pos": 18,
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"tab": [
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||
"pytorch"
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||
]
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||
},
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||
"outputs": [],
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||
"source": [
|
||
"def net(X):\n",
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||
" 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)"
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||
]
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||
},
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{
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"cell_type": "markdown",
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"id": "bd600c14",
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"metadata": {
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"origin_pos": 21
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},
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"source": [
|
||
"## 损失函数\n",
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||
"\n",
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||
"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",
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||
"回想一下我们之前在 :numref:`subsec_softmax-implementation-revisited`中\n",
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||
"对这些复杂问题的讨论。\n",
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||
"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"
|
||
]
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||
},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "f55fe0ea",
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"metadata": {
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"execution": {
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"iopub.status.busy": "2023-08-18T06:59:24.552824Z",
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"iopub.status.idle": "2023-08-18T06:59:24.560084Z",
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"shell.execute_reply": "2023-08-18T06:59:24.559049Z"
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},
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"origin_pos": 23,
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"tab": [
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"pytorch"
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]
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},
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"outputs": [],
|
||
"source": [
|
||
"loss = nn.CrossEntropyLoss(reduction='none')"
|
||
]
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||
},
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{
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"cell_type": "markdown",
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"id": "b3a03c3a",
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"metadata": {
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},
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"source": [
|
||
"## 训练\n",
|
||
"\n",
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||
"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"
|
||
]
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||
},
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{
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"cell_type": "code",
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"origin_pos": 27,
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"pytorch"
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]
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"## 小结\n",
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"\n",
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"* 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",
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"\n",
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"\n",
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"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",
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"1. 尝试添加更多的隐藏层，并查看它对结果有何影响。\n",
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||
"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",
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"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",
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"1. 描述为什么涉及多个超参数更具挑战性。\n",
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"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"
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]
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"tab": [
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"pytorch"
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]
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},
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"source": [
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]
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}
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],
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