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动手学深度学习7.7. 稠密连接网络（DenseNet）-笔记练习（PyTorch）

news 来源：原创 2024/9/20 0:12:55

本节课程地址：本节无视频

本节教材地址：7.7. 稠密连接网络（DenseNet） — 动手学深度学习 2.0.0 documentation (d2l.ai)

本节开源代码：...>d2l-zh>pytorch>chapter_multilayer-perceptrons>densenet.ipynb

稠密连接网络（DenseNet）

ResNet极大地改变了如何参数化深层网络中函数的观点。 稠密连接网络（DenseNet）（1608.06993 (arxiv.org)）在某种程度上是ResNet的逻辑扩展。让我们先从数学上了解一下。

从ResNet到DenseNet

回想一下任意函数的泰勒展开式（Taylor expansion），它把这个函数分解成越来越高阶的项。在 x 接近0时，

$f(x) = f(0) + f'(0) x + \frac{f''(0)}{2!} x^2 + \frac{f'''(0)}{3!} x^3 + \ldots.$

同样，ResNet将函数展开为

$f(\mathbf{x}) = \mathbf{x} + g(\mathbf{x}).$

也就是说，ResNet将 $f$ 分解为两部分：一个简单的线性项和一个复杂的非线性项。那么再向前拓展一步，如果我们想将 $f$ 拓展成超过两部分的信息呢？一种方案便是DenseNet。

如图7.7.1 所示，ResNet和DenseNet的关键区别在于，DenseNet输出是连接（用图中的 [,] 表示）而不是如ResNet的简单相加。因此，在应用越来越复杂的函数序列后，我们执行从 $\mathbf{x}$ 到其展开式的映射：

$\mathbf{x} \to \left[ \mathbf{x}, f_1(\mathbf{x}), f_2([\mathbf{x}, f_1(\mathbf{x})]), f_3([\mathbf{x}, f_1(\mathbf{x}), f_2([\mathbf{x}, f_1(\mathbf{x})])]), \ldots\right].$

最后，将这些展开式结合到多层感知机中，再次减少特征的数量。实现起来非常简单：我们不需要添加术语，而是将它们连接起来。 DenseNet这个名字由变量之间的“稠密连接”而得来，最后一层与之前的所有层紧密相连。稠密连接如图7.7.2 所示。

稠密网络主要由2部分构成：稠密块（dense block）和过渡层（transition layer）。前者定义如何连接输入和输出，而后者则控制通道数量，使其不会太复杂。

(稠密块体)

DenseNet使用了ResNet改良版的“批量规范化、激活和卷积”架构（参见 7.6节中的练习）。我们首先实现一下这个架构。

import torch
from torch import nn
from d2l import torch as d2ldef conv_block(input_channels, num_channels):return nn.Sequential(nn.BatchNorm2d(input_channels), nn.ReLU(),nn.Conv2d(input_channels, num_channels, kernel_size=3, padding=1))

一个稠密块由多个卷积块组成，每个卷积块使用相同数量的输出通道。然而，在前向传播中，我们将每个卷积块的输入和输出在通道维上连结。

class DenseBlock(nn.Module):def __init__(self, num_convs, input_channels, num_channels):super(DenseBlock, self).__init__()layer = []for i in range(num_convs):layer.append(conv_block(num_channels * i + input_channels, num_channels))self.net = nn.Sequential(*layer)def forward(self, X):for blk in self.net:Y = blk(X)# 连接通道维度上每个块的输入和输出X = torch.cat((X, Y), dim=1)return X

在下面的例子中，我们[定义一个]有2个输出通道数为10的(DenseBlock)。使用通道数为3的输入时，我们会得到通道数为 3+2×10=23 的输出。卷积块的通道数控制了输出通道数相对于输入通道数的增长，因此也被称为增长率（growth rate）。

blk = DenseBlock(2, 3, 10)
X = torch.randn(4, 3, 8, 8)
Y = blk(X)
Y.shape
torch.Size([4, 23, 8, 8])

[过渡层]

由于每个稠密块都会带来通道数的增加，使用过多则会过于复杂化模型。而过渡层可以用来控制模型复杂度。它通过 1×1 卷积层来减小通道数，并使用步幅为2的平均汇聚层减半高和宽，从而进一步降低模型复杂度。

def transition_block(input_channels, num_channels):return nn.Sequential(nn.BatchNorm2d(input_channels), nn.ReLU(),nn.Conv2d(input_channels, num_channels, kernel_size=1),nn.AvgPool2d(kernel_size=2, stride=2))

对上一个例子中稠密块的输出[使用]通道数为10的[过渡层]。此时输出的通道数减为10，高和宽均减半。

blk = transition_block(23, 10)
blk(Y).shape
torch.Size([4, 10, 4, 4])

[DenseNet模型]

我们来构造DenseNet模型。DenseNet首先使用同ResNet一样的单卷积层和最大汇聚层。

b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),nn.BatchNorm2d(64), nn.ReLU(),nn.MaxPool2d(kernel_size=3, stride=2, padding=1))

接下来，类似于ResNet使用的4个残差块，DenseNet使用的是4个稠密块。与ResNet类似，我们可以设置每个稠密块使用多少个卷积层。这里我们设成4，从而与 7.6节的ResNet-18保持一致。稠密块里的卷积层通道数（即增长率）设为32，所以每个稠密块将增加128个通道。

在每个模块之间，ResNet通过步幅为2的残差块减小高和宽，DenseNet则使用过渡层来减半高和宽，并减半通道数。

# num_channels为当前的通道数
num_channels, growth_rate = 64, 32
num_convs_in_dense_blocks = [4, 4, 4, 4]
blks = []
for i, num_convs in enumerate(num_convs_in_dense_blocks):blks.append(DenseBlock(num_convs, num_channels, growth_rate))# 上一个稠密块的输出通道数num_channels += num_convs * growth_rate# 在稠密块之间添加一个转换层，使通道数量减半if i != len(num_convs_in_dense_blocks) - 1:blks.append(transition_block(num_channels, num_channels // 2))num_channels = num_channels // 2

与ResNet类似，最后接上全局汇聚层和全连接层来输出结果。

net = nn.Sequential(b1, *blks,nn.BatchNorm2d(num_channels), nn.ReLU(),nn.AdaptiveAvgPool2d((1, 1)),nn.Flatten(),nn.Linear(num_channels, 10))
X = torch.rand(size=(1, 1, 224, 224))
for layer in net:X = layer(X)print(layer.__class__.__name__,'output shape:\t', X.shape)

输出结果：
Sequential output shape: torch.Size([1, 64, 56, 56])
DenseBlock output shape: torch.Size([1, 192, 56, 56])
Sequential output shape: torch.Size([1, 96, 28, 28])
DenseBlock output shape: torch.Size([1, 224, 28, 28])
Sequential output shape: torch.Size([1, 112, 14, 14])
DenseBlock output shape: torch.Size([1, 240, 14, 14])
Sequential output shape: torch.Size([1, 120, 7, 7])
DenseBlock output shape: torch.Size([1, 248, 7, 7])
BatchNorm2d output shape: torch.Size([1, 248, 7, 7])
ReLU output shape: torch.Size([1, 248, 7, 7])
AdaptiveAvgPool2d output shape: torch.Size([1, 248, 1, 1])
Flatten output shape: torch.Size([1, 248])
Linear output shape: torch.Size([1, 10])

[训练模型]

由于这里使用了比较深的网络，本节里我们将输入高和宽从224降到96来简化计算。

lr, num_epochs, batch_size = 0.1, 10, 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, resize=96)
d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())

输出结果：
loss 0.141, train acc 0.948, test acc 0.837
3424.4 examples/sec on cuda:0

小结

在跨层连接上，不同于ResNet中将输入与输出相加，稠密连接网络（DenseNet）在通道维上连结输入与输出。
DenseNet的主要构建模块是稠密块和过渡层。
在构建DenseNet时，我们需要通过添加过渡层来控制网络的维数，从而再次减少通道的数量。

练习

为什么我们在过渡层使用平均汇聚层而不是最大汇聚层？

解：
可能原因：

平均汇聚层对输入特征图的所有像素进行平均，有助于保留特征图中的整体信息，而不仅仅是最大值，可以提供更平滑的梯度和更稳定的训练过程。
最大汇聚层可能会丢失一些重要信息，因为它只保留每个区域的最大值。相比之下，平均汇聚层通过考虑所有像素来减少信息丢失。
平均汇聚层有助于梯度在网络中的流动，因为它不会像最大汇聚层那样在反向传播时导致梯度截断的问题。

2. DenseNet的优点之一是其模型参数比ResNet小。为什么呢？
解：
得益于以下几个设计：

DenseNet通过将前面所有层的输出在通道维度上连结起来，形成下一层的输入，这样每一层都接收到了来自前面所有层的特征图。这意味着网络可以重用特征，而不是在每一层重新学习相同的特征，从而减少了参数数量。
DenseNet的主要构建模块是稠密块，在稠密块中，所有层共享相同的卷积核尺寸和步长，从而减少了模型的复杂性和参数数量。
DenseNet使用1×1卷积和平均汇聚层作为过渡层，以降低特征图的空间维度，有助于控制模型的大小，因为它减少了后续层的输入维度，从而减少了参数数量。

3. DenseNet一个诟病的问题是内存或显存消耗过多。

1）真的是这样吗？可以把输入形状换成 224×224，来看看实际的显存消耗。

2）有另一种方法来减少显存消耗吗？需要改变框架么？

解：
1）DenseNet确实显存消耗大，输入形状换成224×224时，会报错：GPU内存不足，batch_size为256时，显存为8.08 GB。
显存计算如下：

2）可以减小输入尺寸或者减小通道数来减少显存消耗，不需要改变框架，但可能影响模型性能；
或者降低模型深度，需要改变框架。

4. 实现DenseNet论文 :cite:Huang.Liu.Van-Der-Maaten.ea.2017表1所示的不同DenseNet版本。
解：
论文链接：https://arxiv.org/pdf/1608.06993
表1：

不同DenseNet版本实现如下：

#DenseNet-121
def conv_block_v2(input_channels, num_channels):return nn.Sequential(nn.BatchNorm2d(input_channels), nn.ReLU(),nn.Conv2d(input_channels, num_channels, kernel_size=1), nn.BatchNorm2d(num_channels), nn.ReLU(),nn.Conv2d(num_channels, num_channels, kernel_size=3, padding=1))
class DenseBlock(nn.Module):def __init__(self, num_convs, input_channels, num_channels):super(DenseBlock, self).__init__()layer = []for i in range(num_convs):layer.append(conv_block_v2(num_channels * i + input_channels, num_channels))self.net = nn.Sequential(*layer)def forward(self, X):for blk in self.net:Y = blk(X)# 连接通道维度上每个块的输入和输出X = torch.cat((X, Y), dim=1)return X
# b1不变
b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),nn.BatchNorm2d(64), nn.ReLU(),nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
num_channels, growth_rate = 64, 32
# 稠密块的数目更改
num_convs_in_dense_blocks = [6, 12, 24, 16]
blks = []
for i, num_convs in enumerate(num_convs_in_dense_blocks):blks.append(DenseBlock(num_convs, num_channels, growth_rate))num_channels += num_convs * growth_rateif i != len(num_convs_in_dense_blocks) - 1:blks.append(transition_block(num_channels, num_channels // 2))num_channels = num_channels // 2
net121 = nn.Sequential(b1, *blks,nn.BatchNorm2d(num_channels), nn.ReLU(),nn.AdaptiveAvgPool2d((1, 1)),nn.Flatten(),nn.Linear(num_channels, 10))X = torch.rand(size=(1, 1, 224, 224))
for layer in net121:X = layer(X)print(layer.__class__.__name__,'output shape:\t', X.shape)

输出结果：
Sequential output shape: torch.Size([1, 64, 56, 56])
DenseBlock output shape: torch.Size([1, 256, 56, 56])
Sequential output shape: torch.Size([1, 128, 28, 28])
DenseBlock output shape: torch.Size([1, 512, 28, 28])
Sequential output shape: torch.Size([1, 256, 14, 14])
DenseBlock output shape: torch.Size([1, 1024, 14, 14])
Sequential output shape: torch.Size([1, 512, 7, 7])
DenseBlock output shape: torch.Size([1, 1024, 7, 7])
BatchNorm2d output shape: torch.Size([1, 1024, 7, 7])
ReLU output shape: torch.Size([1, 1024, 7, 7])
AdaptiveAvgPool2d output shape: torch.Size([1, 1024, 1, 1])
Flatten output shape: torch.Size([1, 1024])
Linear output shape: torch.Size([1, 10])

#DenseNet-169
# b1不变
b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),nn.BatchNorm2d(64), nn.ReLU(),nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
num_channels, growth_rate = 64, 32
# 稠密块的数目更改
num_convs_in_dense_blocks = [6, 12, 32, 32]
blks = []
for i, num_convs in enumerate(num_convs_in_dense_blocks):blks.append(DenseBlock(num_convs, num_channels, growth_rate))num_channels += num_convs * growth_rateif i != len(num_convs_in_dense_blocks) - 1:blks.append(transition_block(num_channels, num_channels // 2))num_channels = num_channels // 2
net169 = nn.Sequential(b1, *blks,nn.BatchNorm2d(num_channels), nn.ReLU(),nn.AdaptiveAvgPool2d((1, 1)),nn.Flatten(),nn.Linear(num_channels, 10))X = torch.rand(size=(1, 1, 224, 224))
for layer in net169:X = layer(X)print(layer.__class__.__name__,'output shape:\t', X.shape)

输出结果：
Sequential output shape: torch.Size([1, 64, 56, 56])
DenseBlock output shape: torch.Size([1, 256, 56, 56])
Sequential output shape: torch.Size([1, 128, 28, 28])
DenseBlock output shape: torch.Size([1, 512, 28, 28])
Sequential output shape: torch.Size([1, 256, 14, 14])
DenseBlock output shape: torch.Size([1, 1280, 14, 14])
Sequential output shape: torch.Size([1, 640, 7, 7])
DenseBlock output shape: torch.Size([1, 1664, 7, 7])
BatchNorm2d output shape: torch.Size([1, 1664, 7, 7])
ReLU output shape: torch.Size([1, 1664, 7, 7])
AdaptiveAvgPool2d output shape: torch.Size([1, 1664, 1, 1])
Flatten output shape: torch.Size([1, 1664])
Linear output shape: torch.Size([1, 10])

#DenseNet-201
# b1不变
b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),nn.BatchNorm2d(64), nn.ReLU(),nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
num_channels, growth_rate = 64, 32
# 稠密块的数目更改
num_convs_in_dense_blocks = [6, 12, 48, 32]
blks = []
for i, num_convs in enumerate(num_convs_in_dense_blocks):blks.append(DenseBlock(num_convs, num_channels, growth_rate))num_channels += num_convs * growth_rateif i != len(num_convs_in_dense_blocks) - 1:blks.append(transition_block(num_channels, num_channels // 2))num_channels = num_channels // 2
net201 = nn.Sequential(b1, *blks,nn.BatchNorm2d(num_channels), nn.ReLU(),nn.AdaptiveAvgPool2d((1, 1)),nn.Flatten(),nn.Linear(num_channels, 10))X = torch.rand(size=(1, 1, 224, 224))
for layer in net201:X = layer(X)print(layer.__class__.__name__,'output shape:\t', X.shape)

输出结果：
Sequential output shape: torch.Size([1, 64, 56, 56])
DenseBlock output shape: torch.Size([1, 256, 56, 56])
Sequential output shape: torch.Size([1, 128, 28, 28])
DenseBlock output shape: torch.Size([1, 512, 28, 28])
Sequential output shape: torch.Size([1, 256, 14, 14])
DenseBlock output shape: torch.Size([1, 1792, 14, 14])
Sequential output shape: torch.Size([1, 896, 7, 7])
DenseBlock output shape: torch.Size([1, 1920, 7, 7])
BatchNorm2d output shape: torch.Size([1, 1920, 7, 7])
ReLU output shape: torch.Size([1, 1920, 7, 7])
AdaptiveAvgPool2d output shape: torch.Size([1, 1920, 1, 1])
Flatten output shape: torch.Size([1, 1920])
Linear output shape: torch.Size([1, 10])

#DenseNet-264
# b1不变
b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),nn.BatchNorm2d(64), nn.ReLU(),nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
num_channels, growth_rate = 64, 32
# 稠密块的数目更改
num_convs_in_dense_blocks = [6, 12, 64, 48]
blks = []
for i, num_convs in enumerate(num_convs_in_dense_blocks):blks.append(DenseBlock(num_convs, num_channels, growth_rate))num_channels += num_convs * growth_rateif i != len(num_convs_in_dense_blocks) - 1:blks.append(transition_block(num_channels, num_channels // 2))num_channels = num_channels // 2
net264 = nn.Sequential(b1, *blks,nn.BatchNorm2d(num_channels), nn.ReLU(),nn.AdaptiveAvgPool2d((1, 1)),nn.Flatten(),nn.Linear(num_channels, 10))X = torch.rand(size=(1, 1, 224, 224))
for layer in net264:X = layer(X)print(layer.__class__.__name__,'output shape:\t', X.shape)

输出结果：
Sequential output shape: torch.Size([1, 64, 56, 56])
DenseBlock output shape: torch.Size([1, 256, 56, 56])
Sequential output shape: torch.Size([1, 128, 28, 28])
DenseBlock output shape: torch.Size([1, 512, 28, 28])
Sequential output shape: torch.Size([1, 256, 14, 14])
DenseBlock output shape: torch.Size([1, 2304, 14, 14])
Sequential output shape: torch.Size([1, 1152, 7, 7])
DenseBlock output shape: torch.Size([1, 2688, 7, 7])
BatchNorm2d output shape: torch.Size([1, 2688, 7, 7])
ReLU output shape: torch.Size([1, 2688, 7, 7])
AdaptiveAvgPool2d output shape: torch.Size([1, 2688, 1, 1])
Flatten output shape: torch.Size([1, 2688])
Linear output shape: torch.Size([1, 10])

5. 应用DenseNet的思想设计一个基于多层感知机的模型。将其应用于4.10节中的房价预测任务。

解：
应用DenseNet思想设计的MLP，与4.10节相同超参数时，提交Kaggle的预测结果更好些，为0.15165（原为0.16715）。

import hashlib
import os
import tarfile
import zipfile
import requests
import numpy as np
import pandas as pd
import torch
from torch import nn
from d2l import torch as d2l
# 数据准备
def download(name, cache_dir=os.path.join('..', 'data')):  #@save"""下载一个DATA_HUB中的文件，返回本地文件名"""assert name in DATA_HUB, f"{name} 不存在于 {DATA_HUB}"url, sha1_hash = DATA_HUB[name]os.makedirs(cache_dir, exist_ok=True)fname = os.path.join(cache_dir, url.split('/')[-1])if os.path.exists(fname):sha1 = hashlib.sha1()with open(fname, 'rb') as f:while True:data = f.read(1048576)if not data:breaksha1.update(data)if sha1.hexdigest() == sha1_hash:return fname  # 命中缓存print(f'正在从{url}下载{fname}...')r = requests.get(url, stream=True, verify=True)with open(fname, 'wb') as f:f.write(r.content)return fnameDATA_HUB = dict()
DATA_URL = 'http://d2l-data.s3-accelerate.amazonaws.com/'
DATA_HUB['kaggle_house_train'] = (  #@saveDATA_URL + 'kaggle_house_pred_train.csv','585e9cc93e70b39160e7921475f9bcd7d31219ce')DATA_HUB['kaggle_house_test'] = (  #@saveDATA_URL + 'kaggle_house_pred_test.csv','fa19780a7b011d9b009e8bff8e99922a8ee2eb90')train_data = pd.read_csv(download('kaggle_house_train'))
test_data = pd.read_csv(download('kaggle_house_test'))
# 数据预处理
all_features = pd.concat((train_data.iloc[:, 1:-1], test_data.iloc[:, 1:]))numeric_features = all_features.dtypes[all_features.dtypes != 'object'].index
all_features[numeric_features] = all_features[numeric_features].apply(lambda x: (x - x.mean()) / (x.std()))
all_features[numeric_features] = all_features[numeric_features].fillna(0)all_features = pd.get_dummies(all_features, dummy_na=True)
all_features = all_features * 1n_train = train_data.shape[0]
train_features = torch.tensor(all_features[:n_train].values, dtype=torch.float32)
test_features = torch.tensor(all_features[n_train:].values, dtype=torch.float32)
train_labels = torch.tensor(train_data.SalePrice.values.reshape(-1, 1), dtype=torch.float32)
# 根据DenseNet设计MLP
def conv_block_1d(input_channels, num_channels):return nn.Sequential(nn.BatchNorm1d(input_channels), nn.ReLU(),nn.Conv1d(input_channels, growth_rate, kernel_size=3, padding=1))class DenseBlock_1d(nn.Module):def __init__(self, num_convs, input_channels, num_channels):super(DenseBlock_1d, self).__init__()layer = []for i in range(num_convs):layer.append(conv_block_1d(num_channels * i + input_channels, num_channels))self.net = nn.Sequential(*layer)def forward(self, X):for blk in self.net:Y = blk(X)# 连接通道维度上每个块的输入和输出X = torch.cat((X, Y), dim=1)return Xdef transition_block_1d(input_channels, num_channels):return nn.Sequential(nn.BatchNorm1d(input_channels), nn.ReLU(),nn.Conv1d(input_channels, num_channels, kernel_size=1),nn.AvgPool1d(kernel_size=2, stride=2))b1 = nn.Sequential(nn.Conv1d(1, 64, kernel_size=7, stride=2, padding=3),nn.BatchNorm1d(64), nn.ReLU(),nn.MaxPool1d(kernel_size=3, stride=2, padding=1))
num_channels, growth_rate = 64, 16
num_convs_in_dense_blocks = [4, 4, 4, 4]
blks = []
for i, num_convs in enumerate(num_convs_in_dense_blocks):blks.append(DenseBlock_1d(num_convs, num_channels, growth_rate))# 上一个稠密块的输出通道数num_channels += num_convs * growth_rate# 在稠密块之间添加一个转换层，使通道数量减半if i != len(num_convs_in_dense_blocks) - 1:blks.append(transition_block_1d(num_channels, num_channels // 2))num_channels = num_channels // 2def get_net():net = nn.Sequential(b1, *blks,nn.BatchNorm1d(num_channels), nn.ReLU(),nn.AdaptiveAvgPool1d((1)),nn.Flatten(),nn.Linear(num_channels, 1))return net
# 训练
loss = nn.MSELoss()def log_rmse(net, features, labels):# 将features reshape成(batch_size,input_channels,width)features = features.unsqueeze(1)clipped_preds = torch.clamp(net(features), 1, float('inf'))rmse = torch.sqrt(loss(torch.log(clipped_preds),torch.log(labels)))return rmse.item()def train(net, train_features, train_labels, test_features, test_labels,num_epochs, learning_rate, weight_decay, batch_size):train_ls, test_ls = [], []train_iter = d2l.load_array((train_features, train_labels), batch_size)optimizer = torch.optim.Adam(net.parameters(),lr = learning_rate,weight_decay = weight_decay)for epoch in range(num_epochs):for X, y in train_iter:optimizer.zero_grad()# 将X reshape成(batch_size,input_channels,width)X = X.unsqueeze(1)l = loss(net(X), y)l.backward()optimizer.step()train_ls.append(log_rmse(net, train_features, train_labels))if test_labels is not None:test_ls.append(log_rmse(net, test_features, test_labels))return train_ls, test_lsdef get_k_fold_data(k, i, X, y):assert k > 1fold_size = X.shape[0] // kX_train, y_train = None, Nonefor j in range(k):idx = slice(j * fold_size, (j + 1) * fold_size)X_part, y_part = X[idx, :], y[idx]if j == i:X_valid, y_valid = X_part, y_partelif X_train is None:X_train, y_train = X_part, y_partelse:X_train = torch.cat([X_train, X_part], 0)y_train = torch.cat([y_train, y_part], 0)return X_train, y_train, X_valid, y_validdef k_fold(k, X_train, y_train, num_epochs, learning_rate, weight_decay,batch_size):train_l_sum, valid_l_sum = 0, 0for i in range(k):data = get_k_fold_data(k, i, X_train, y_train)net = get_net()train_ls, valid_ls = train(net, *data, num_epochs, learning_rate,weight_decay, batch_size)train_l_sum += train_ls[-1]valid_l_sum += valid_ls[-1]if i == 0:d2l.plot(list(range(1, num_epochs + 1)), [train_ls, valid_ls],xlabel='epoch', ylabel='rmse', xlim=[1, num_epochs],legend=['train', 'valid'], yscale='log')print(f'折{i + 1}，训练log rmse{float(train_ls[-1]):f}, 'f'验证log rmse{float(valid_ls[-1]):f}')return train_l_sum / k, valid_l_sum / kk, num_epochs, lr, weight_decay, batch_size = 5, 100, 5, 0, 64
train_l, valid_l = k_fold(k, train_features, train_labels, num_epochs, lr,weight_decay, batch_size)
print(f'{k}-折验证: 平均训练log rmse: {float(train_l):f}, 'f'平均验证log rmse: {float(valid_l):f}')

输出结果：
折1，训练log rmse0.075542, 验证log rmse0.147438
折2，训练log rmse0.050742, 验证log rmse0.137624
折3，训练log rmse0.046990, 验证log rmse0.124749
折4，训练log rmse0.040194, 验证log rmse0.110081
折5，训练log rmse0.024984, 验证log rmse0.085519
5-折验证: 平均训练log rmse: 0.047690, 平均验证log rmse: 0.121082

# 预测
def train_and_pred(train_features, test_features, train_labels, test_data,num_epochs, lr, weight_decay, batch_size):net = get_net()train_ls, _ = train(net, train_features, train_labels, None, None,num_epochs, lr, weight_decay, batch_size)d2l.plot(np.arange(1, num_epochs + 1), [train_ls], xlabel='epoch',ylabel='log rmse', xlim=[1, num_epochs], yscale='log')print(f'训练log rmse：{float(train_ls[-1]):f}')# 将网络应用于测试集。# 将test_features reshape成(batch_size,input_channels,width)test_features = test_features.unsqueeze(1)preds = net(test_features).detach().numpy()# 将其重新格式化以导出到Kaggletest_data['SalePrice'] = pd.Series(preds.reshape(1, -1)[0])submission = pd.concat([test_data['Id'], test_data['SalePrice']], axis=1)submission.to_csv('submission.csv', index=False)train_and_pred(train_features, test_features, train_labels, test_data,num_epochs, lr, weight_decay, batch_size)

输出结果：
训练log rmse：0.044846