{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Neural Networks\n", "===============\n", "\n", "使用torch.nn包来构建神经网络。\n", "\n", "上一讲已经讲过了``autograd``，``nn``包依赖``autograd``包来定义模型并求导。\n", "一个``nn.Module``包含各个层和一个``forward(input)``方法，该方法返回``output``。\n", "\n", "\n", "\n", "例如：\n", "\n", "![](https://pytorch.org/tutorials/_images/mnist.png)\n", "\n", "它是一个简单的前馈神经网络，它接受一个输入，然后一层接着一层地传递，最后输出计算的结果。\n", "\n", "神经网络的典型训练过程如下：\n", "\n", "1. 定义包含一些可学习的参数(或者叫权重)神经网络模型； \n", "2. 在数据集上迭代； \n", "3. 通过神经网络处理输入； \n", "4. 计算损失(输出结果和正确值的差值大小)；\n", "5. 将梯度反向传播回网络的参数； \n", "6. 更新网络的参数，主要使用如下简单的更新原则： \n", "``weight = weight - learning_rate * gradient``\n", "\n", " \n", "\n", "定义网络\n", "------------------\n", "\n", "开始定义一个网络：\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Net(\n", " (conv1): Conv2d(1, 6, kernel_size=(5, 5), stride=(1, 1))\n", " (conv2): Conv2d(6, 16, kernel_size=(5, 5), stride=(1, 1))\n", " (fc1): Linear(in_features=400, out_features=120, bias=True)\n", " (fc2): Linear(in_features=120, out_features=84, bias=True)\n", " (fc3): Linear(in_features=84, out_features=10, bias=True)\n", ")\n" ] } ], "source": [ "import torch\n", "import torch.nn as nn\n", "import torch.nn.functional as F\n", "\n", "\n", "class Net(nn.Module):\n", "\n", " def __init__(self):\n", " super(Net, self).__init__()\n", " # 1 input image channel, 6 output channels, 5x5 square convolution\n", " # kernel\n", " self.conv1 = nn.Conv2d(1, 6, 5)\n", " self.conv2 = nn.Conv2d(6, 16, 5)\n", " # an affine operation: y = Wx + b\n", " self.fc1 = nn.Linear(16 * 5 * 5, 120)\n", " self.fc2 = nn.Linear(120, 84)\n", " self.fc3 = nn.Linear(84, 10)\n", "\n", " def forward(self, x):\n", " # Max pooling over a (2, 2) window\n", " x = F.max_pool2d(F.relu(self.conv1(x)), (2, 2))\n", " # If the size is a square you can only specify a single number\n", " x = F.max_pool2d(F.relu(self.conv2(x)), 2)\n", " x = x.view(-1, self.num_flat_features(x))\n", " x = F.relu(self.fc1(x))\n", " x = F.relu(self.fc2(x))\n", " x = self.fc3(x)\n", " return x\n", "\n", " def num_flat_features(self, x):\n", " size = x.size()[1:] # all dimensions except the batch dimension\n", " num_features = 1\n", " for s in size:\n", " num_features *= s\n", " return num_features\n", "\n", "\n", "net = Net()\n", "print(net)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "在模型中必须要定义 ``forward`` 函数，``backward``\n", "函数（用来计算梯度）会被``autograd``自动创建。\n", "可以在 ``forward`` 函数中使用任何针对 Tensor 的操作。\n", "\n", " ``net.parameters()``返回可被学习的参数（权重）列表和值\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10\n", "torch.Size([6, 1, 5, 5])\n" ] } ], "source": [ "params = list(net.parameters())\n", "print(len(params))\n", "print(params[0].size()) # conv1's .weight" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "测试随机输入32×32。\n", "注：这个网络（LeNet）期望的输入大小是32×32，如果使用MNIST数据集来训练这个网络，请把图片大小重新调整到32×32。\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tensor([[ 0.1120, 0.0713, 0.1014, -0.0696, -0.1210, 0.0084, -0.0206, 0.1366,\n", " -0.0455, -0.0036]], grad_fn=)\n" ] } ], "source": [ "input = torch.randn(1, 1, 32, 32)\n", "out = net(input)\n", "print(out)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "将所有参数的梯度缓存清零，然后进行随机梯度的的反向传播：\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "net.zero_grad()\n", "out.backward(torch.randn(1, 10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Note

``torch.nn`` 只支持小批量输入。整个 ``torch.nn``\n", "包都只支持小批量样本，而不支持单个样本。\n", "\n", " 例如，``nn.Conv2d`` 接受一个4维的张量，\n", " ``每一维分别是sSamples * nChannels * Height * Width（样本数*通道数*高*宽）``。\n", "\n", " 如果你有单个样本，只需使用 ``input.unsqueeze(0)`` 来添加其它的维数

\n", "\n", "在继续之前，我们回顾一下到目前为止用到的类。\n", "\n", "**回顾:**\n", " - ``torch.Tensor``：一个用过自动调用 ``backward()``实现支持自动梯度计算的 *多维数组* ，\n", " 并且保存关于这个向量的*梯度* w.r.t.\n", " - ``nn.Module``：神经网络模块。封装参数、移动到GPU上运行、导出、加载等。\n", " - ``nn.Parameter``：一种变量，当把它赋值给一个``Module``时，被 *自动* 地注册为一个参数。\n", " - ``autograd.Function``：实现一个自动求导操作的前向和反向定义，每个变量操作至少创建一个函数节点，每一个``Tensor``的操作都回创建一个接到创建``Tensor``和 *编码其历史* 的函数的``Function``节点。\n", "\n", "**重点如下：**\n", " - 定义一个网络\n", " - 处理输入，调用backword\n", "\n", "**还剩：**\n", " - 计算损失\n", " - 更新网络权重\n", "\n", "损失函数\n", "-------------\n", "一个损失函数接受一对 (output, target) 作为输入，计算一个值来估计网络的输出和目标值相差多少。\n", "\n", "***译者注：output为网络的输出，target为实际值***\n", "\n", "nn包中有很多不同的[损失函数](https://pytorch.org/docs/nn.html#loss-functions)。\n", "``nn.MSELoss``是一个比较简单的损失函数，它计算输出和目标间的**均方误差**，\n", "例如：\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "tensor(0.8109, grad_fn=)\n" ] } ], "source": [ "output = net(input)\n", "target = torch.randn(10) # 随机值作为样例\n", "target = target.view(1, -1) # 使target和output的shape相同\n", "criterion = nn.MSELoss()\n", "\n", "loss = criterion(output, target)\n", "print(loss)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "现在，如果在反向过程中跟随``loss`` ， 使用它的\n", "``.grad_fn`` 属性，将看到如下所示的计算图。\n", "\n", "::\n", "\n", " input -> conv2d -> relu -> maxpool2d -> conv2d -> relu -> maxpool2d\n", " -> view -> linear -> relu -> linear -> relu -> linear\n", " -> MSELoss\n", " -> loss\n", "\n", "所以，当我们调用 ``loss.backward()``时,整张计算图都会\n", "根据loss进行微分，而且图中所有设置为``requires_grad=True``的张量\n", "将会拥有一个随着梯度累积的``.grad`` 张量。\n", "\n", "为了说明，让我们向后退几步:\n", "\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "\n" ] } ], "source": [ "print(loss.grad_fn) # MSELoss\n", "print(loss.grad_fn.next_functions[0][0]) # Linear\n", "print(loss.grad_fn.next_functions[0][0].next_functions[0][0]) # ReLU" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "反向传播\n", "--------\n", "调用loss.backward()获得反向传播的误差。\n", "\n", "但是在调用前需要清除已存在的梯度，否则梯度将被累加到已存在的梯度。\n", "\n", "现在，我们将调用loss.backward()，并查看conv1层的偏差（bias）项在反向传播前后的梯度。\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "conv1.bias.grad before backward\n", "tensor([0., 0., 0., 0., 0., 0.])\n", "conv1.bias.grad after backward\n", "tensor([ 0.0051, 0.0042, 0.0026, 0.0152, -0.0040, -0.0036])\n" ] } ], "source": [ "net.zero_grad() # 清除梯度\n", "\n", "print('conv1.bias.grad before backward')\n", "print(net.conv1.bias.grad)\n", "\n", "loss.backward()\n", "\n", "print('conv1.bias.grad after backward')\n", "print(net.conv1.bias.grad)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "如何使用损失函数\n", "\n", "**稍后阅读：**\n", "\n", " `nn`包，包含了各种用来构成深度神经网络构建块的模块和损失函数，完整的文档请查看[here](https://pytorch.org/docs/nn)。\n", "\n", "**剩下的最后一件事:**\n", "\n", " - 新网络的权重\n", "\n", "更新权重\n", "------------------\n", "在实践中最简单的权重更新规则是随机梯度下降（SGD）：\n", "\n", " ``weight = weight - learning_rate * gradient``\n", "\n", "我们可以使用简单的Python代码实现这个规则：\n", "\n", "```python\n", "\n", "learning_rate = 0.01\n", "for f in net.parameters():\n", " f.data.sub_(f.grad.data * learning_rate)\n", "```\n", "但是当使用神经网络是想要使用各种不同的更新规则时，比如SGD、Nesterov-SGD、Adam、RMSPROP等，PyTorch中构建了一个包``torch.optim``实现了所有的这些规则。\n", "使用它们非常简单：\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "import torch.optim as optim\n", "\n", "# create your optimizer\n", "optimizer = optim.SGD(net.parameters(), lr=0.01)\n", "\n", "# in your training loop:\n", "optimizer.zero_grad() # zero the gradient buffers\n", "output = net(input)\n", "loss = criterion(output, target)\n", "loss.backward()\n", "optimizer.step() # Does the update" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ".. 注意::\n", " \n", " 观察如何使用``optimizer.zero_grad()``手动将梯度缓冲区设置为零。\n", " 这是因为梯度是按Backprop部分中的说明累积的。\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 1 }