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）
:cite:`Huang.Liu.Van-Der-Maaten.ea.2017`\ 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\ :math:`x`\ 接近0时，
.. math:: 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
.. math:: f(\mathbf{x}) = \mathbf{x} + g(\mathbf{x}).
也就是说，ResNet将\ :math:`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\ :math:`f`\ 拓展成超过两部分的信息呢？
一种方案便是DenseNet。
.. _fig_densenet_block:
.. figure:: ../img/densenet-block.svg
ResNet（左）与
DenseNet（右）在跨层连接上的主要区别：使用相加和使用连结。
如
:numref:`fig_densenet_block`\ 所示，ResNet和DenseNet的关键区别在于，DenseNet输出是\ *连接*\ （用图中的\ :math:`[,]`\ 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\ :math:`\mathbf{x}`\ 到其展开式的映射：
.. math::
\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 :numref:`fig_densenet`\ 所示。
.. _fig_densenet:
.. figure:: ../img/densenet.svg
稠密连接。
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
:numref:`sec_resnet`\ 中的练习）。 我们首先实现一下这个架构。
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\diilbookstyleinputcell
.. code:: python
from mindspore import nn, ops
from d2l import mindspore as d2l
def conv_block(input_channels, num_channels):
return nn.SequentialCell([
nn.BatchNorm2d(input_channels), nn.ReLU(),
nn.Conv2d(input_channels, num_channels, kernel_size=3, padding=1,
pad_mode='pad')])
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\diilbookstyleinputcell
.. code:: python
import torch
from torch import nn
from d2l import torch as d2l
def 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))
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\diilbookstyleinputcell
.. code:: python
class DenseBlock(nn.Cell):
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.CellList(layer)
self.concat = ops.Concat(axis=1)
def construct(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 = self.concat((X, Y))
return X
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\diilbookstyleinputcell
.. code:: python
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
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\diilbookstyleinputcell
.. code:: python
blk = DenseBlock(2, 3, 10)
X = ops.randn(4, 3, 8, 8)
Y = blk(X)
Y.shape
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
(4, 23, 8, 8)
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\diilbookstyleinputcell
.. code:: python
blk = DenseBlock(2, 3, 10)
X = torch.randn(4, 3, 8, 8)
Y = blk(X)
Y.shape
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
torch.Size([4, 23, 8, 8])
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\diilbookstyleinputcell
.. code:: python
def transition_block(input_channels, num_channels):
return nn.SequentialCell([
nn.BatchNorm2d(input_channels), nn.ReLU(),
nn.Conv2d(input_channels, num_channels, kernel_size=1),
nn.AvgPool2d(kernel_size=2, stride=2)])
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\diilbookstyleinputcell
.. code:: python
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))
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\diilbookstyleinputcell
.. code:: python
blk = transition_block(23, 10)
blk(Y).shape
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
(4, 10, 4, 4)
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\diilbookstyleinputcell
.. code:: python
blk = transition_block(23, 10)
blk(Y).shape
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
torch.Size([4, 10, 4, 4])
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\diilbookstyleinputcell
.. code:: python
b1 = nn.SequentialCell([
nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3, pad_mode='pad'),
nn.BatchNorm2d(64), nn.ReLU(),
d2l.MaxPool2d(kernel_size=3, stride=2, padding=1)])
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\diilbookstyleinputcell
.. code:: python
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))
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\diilbookstyleinputcell
.. code:: python
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
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\diilbookstyleinputcell
.. code:: python
# 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
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\diilbookstyleinputcell
.. code:: python
net = nn.SequentialCell([
b1, *blks,
nn.BatchNorm2d(num_channels), nn.ReLU(),
nn.AdaptiveMaxPool2d((1, 1)),
nn.Flatten(),
nn.Dense(num_channels, 10)])
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\diilbookstyleinputcell
.. code:: python
net = nn.Sequential(
b1, *blks,
nn.BatchNorm2d(num_channels), nn.ReLU(),
nn.AdaptiveAvgPool2d((1, 1)),
nn.Flatten(),
nn.Linear(num_channels, 10))
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\diilbookstyleinputcell
.. code:: python
lr, num_epochs, batch_size = 0.1, 3, 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)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.281, train acc 0.896, test acc 0.877
9107.4 examples/sec
.. figure:: output_densenet_e82156_75_1.png
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\diilbookstyleinputcell
.. code:: python
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())
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.140, train acc 0.949, test acc 0.764
11162.1 examples/sec on cuda:0
.. figure:: output_densenet_e82156_78_1.svg
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