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machine-learning/05_feedforward/05_feedforward.ipynb
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"# 前馈神经网络\n",
"\n",
"目录\n",
"\n",
"- 多层感知机\n",
"- 多层感知机从零开始实现\n",
"- 多层感知机的简洁实现"
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"## 多层感知机\n",
"\n",
"简要介绍一些常见的激活函数"
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"%matplotlib inline\n",
"import torch\n",
"from d2l import torch as d2l"
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"ReLU提供了一种非常简单的非线性变换\n",
"$$\\operatorname{ReLU}(x) = \\max(x, 0)$$"
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"source": [
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"source": [
"y.backward(torch.ones_like(x), retain_graph=True)\n",
"d2l.plot(x.detach(), x.grad, 'x', 'grad of relu', figsize=(5, 2.5))"
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"对于一个定义域在$\\mathbb{R}$中的输入,\n",
"*sigmoid函数*将输入变换为区间(0, 1)上的输出\n",
"$$\\operatorname{sigmoid}(x) = \\frac{1}{1 + \\exp(-x)}$$"
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"source": [
"Tanh(双曲正切)函数也能将其输入压缩转换到区间(-1, 1)上\n",
"$$\\operatorname{tanh}(x) = \\frac{1 - \\exp(-2x)}{1 + \\exp(-2x)}$$"
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"source": [
"y = torch.tanh(x)\n",
"d2l.plot(x.detach(), y.detach(), 'x', 'tanh(x)', figsize=(5, 2.5))"
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},
{
"cell_type": "code",
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"id": "4fe3ec86-9940-4d1f-946a-0efeb5ab4c37",
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"tab": [
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"source": [
"x.grad.data.zero_() # 清除以前的梯度\n",
"y.backward(torch.ones_like(x),retain_graph=True)\n",
"d2l.plot(x.detach(), x.grad, 'x', 'grad of tanh', figsize=(5, 2.5))"
]
},
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"id": "641485cc-5306-49ec-8cbc-97601d8922af",
"metadata": {
"slideshow": {
"slide_type": "-"
},
"tags": []
},
"source": [
"## 多层感知机从零开始实现\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "850f9472-762c-4525-9376-ac170b27db83",
"metadata": {
"origin_pos": 4,
"tab": [
"pytorch"
]
},
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"source": [
"import torch\n",
"from torch import nn\n",
"from d2l import torch as d2l\n",
"\n",
"batch_size = 256\n",
"train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)"
]
},
{
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"id": "667c9915-0f1c-4f28-9176-40a7cdafdf36",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"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"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "44bea74f-6f0f-4807-9473-b251c2c1ac28",
"metadata": {
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"tab": [
"pytorch"
]
},
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"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": "da8f4700-315d-4249-83d0-bae1a4807d01",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"实现ReLU激活函数"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "68d398da-b046-4ad2-8c72-d5f2544bf68f",
"metadata": {
"origin_pos": 11,
"tab": [
"pytorch"
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},
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"source": [
"def relu(X):\n",
" a = torch.zeros_like(X)\n",
" return torch.max(X, a)"
]
},
{
"cell_type": "markdown",
"id": "0dc3b5a5-dce1-4027-bf78-260fefb376df",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"实现我们的模型"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "cdfb32c3-c3a4-46cf-89c4-e4e1ab46cb20",
"metadata": {
"origin_pos": 19,
"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)\n",
"\n",
"loss = nn.CrossEntropyLoss(reduction='none')"
]
},
{
"cell_type": "markdown",
"id": "3c233b99-3507-40c0-a185-bc8da9c16f68",
"metadata": {
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"slide_type": "slide"
}
},
"source": [
"多层感知机的训练过程与softmax回归的训练过程完全相同"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "c6254fc2-e783-4305-80d0-52b5bbf5108d",
"metadata": {
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"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)"
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},
{
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"metadata": {
"slideshow": {
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},
"source": [
"在一些测试数据上应用这个模型"
]
},
{
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"id": "fcc61869-115c-408e-affd-ef36327ac7b8",
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"tab": [
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"text/plain": [
"<Figure size 900x150 with 6 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"d2l.predict_ch3(net, test_iter)"
]
},
{
"cell_type": "markdown",
"id": "e35e6756-4c65-4a63-a512-41c831045596",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"## 多层感知机的简洁实现\n",
"\n",
"通过高级API更简洁地实现多层感知机"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "31883579-70e2-4930-ae26-72a7e7a2cce2",
"metadata": {
"origin_pos": 2,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"import torch\n",
"from torch import nn\n",
"from d2l import torch as d2l"
]
},
{
"cell_type": "markdown",
"id": "2547eec8-64d0-4a97-9e3e-75bd80db3c98",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"隐藏层\n",
"包含256个隐藏单元,并使用了ReLU激活函数"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "8316e7aa-873e-436b-bee5-9d5cf7c1e298",
"metadata": {
"origin_pos": 6,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"net = nn.Sequential(nn.Flatten(),\n",
" nn.Linear(784, 256),\n",
" nn.ReLU(),\n",
" nn.Linear(256, 10))\n",
"\n",
"def init_weights(m):\n",
" if type(m) == nn.Linear:\n",
" nn.init.normal_(m.weight, std=0.01)\n",
"\n",
"net.apply(init_weights);"
]
},
{
"cell_type": "markdown",
"id": "4a347357-8fac-4cf6-9baa-0a8d8d7c9790",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"训练过程"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "6d2b9cb2-e525-46e4-9283-0d059148d0e0",
"metadata": {
"origin_pos": 12,
"tab": [
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