.. _sec_lenet:
卷积神经网络（LeNet）
=====================
通过之前几节，我们学习了构建一个完整卷积神经网络的所需组件。
回想一下，之前我们将softmax回归模型（
:numref:`sec_softmax_scratch`\ ）和多层感知机模型（
:numref:`sec_mlp_scratch`\ ）应用于Fashion-MNIST数据集中的服装图片。
为了能够应用softmax回归和多层感知机，我们首先将每个大小为\ :math:`28\times28`\ 的图像展平为一个784维的固定长度的一维向量，然后用全连接层对其进行处理。
而现在，我们已经掌握了卷积层的处理方法，我们可以在图像中保留空间结构。
同时，用卷积层代替全连接层的另一个好处是：模型更简洁、所需的参数更少。
本节将介绍LeNet，它是最早发布的卷积神经网络之一，因其在计算机视觉任务中的高效性能而受到广泛关注。
这个模型是由AT&T贝尔实验室的研究员Yann
LeCun在1989年提出的（并以其命名），目的是识别图像
:cite:`LeCun.Bottou.Bengio.ea.1998`\ 中的手写数字。 当时，Yann
LeCun发表了第一篇通过反向传播成功训练卷积神经网络的研究，这项工作代表了十多年来神经网络研究开发的成果。
当时，LeNet取得了与支持向量机（support vector
machines）性能相媲美的成果，成为监督学习的主流方法。
LeNet被广泛用于自动取款机（ATM）机中，帮助识别处理支票的数字。
时至今日，一些自动取款机仍在运行Yann LeCun和他的同事Leon
Bottou在上世纪90年代写的代码呢！
LeNet
-----
总体来看，LeNet（LeNet-5）由两个部分组成：
- 卷积编码器：由两个卷积层组成;
- 全连接层密集块：由三个全连接层组成。
该架构如 :numref:`img_lenet`\ 所示。
.. _img_lenet:
.. figure:: ../img/lenet.svg
LeNet中的数据流。输入是手写数字，输出为10种可能结果的概率。
每个卷积块中的基本单元是一个卷积层、一个sigmoid激活函数和平均汇聚层。请注意，虽然ReLU和最大汇聚层更有效，但它们在20世纪90年代还没有出现。每个卷积层使用\ :math:`5\times 5`\ 卷积核和一个sigmoid激活函数。这些层将输入映射到多个二维特征输出，通常同时增加通道的数量。第一卷积层有6个输出通道，而第二个卷积层有16个输出通道。每个\ :math:`2\times2`\ 池操作（步幅2）通过空间下采样将维数减少4倍。卷积的输出形状由批量大小、通道数、高度、宽度决定。
为了将卷积块的输出传递给稠密块，我们必须在小批量中展平每个样本。换言之，我们将这个四维输入转换成全连接层所期望的二维输入。这里的二维表示的第一个维度索引小批量中的样本，第二个维度给出每个样本的平面向量表示。LeNet的稠密块有三个全连接层，分别有120、84和10个输出。因为我们在执行分类任务，所以输出层的10维对应于最后输出结果的数量。
通过下面的LeNet代码，可以看出用深度学习框架实现此类模型非常简单。我们只需要实例化一个\ ``Sequential``\ 块并将需要的层连接在一起。
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\diilbookstyleinputcell
.. code:: python
from mxnet import autograd, gluon, init, np, npx
from mxnet.gluon import nn
from d2l import mxnet as d2l
npx.set_np()
net = nn.Sequential()
net.add(nn.Conv2D(channels=6, kernel_size=5, padding=2, activation='sigmoid'),
nn.AvgPool2D(pool_size=2, strides=2),
nn.Conv2D(channels=16, kernel_size=5, activation='sigmoid'),
nn.AvgPool2D(pool_size=2, strides=2),
# 默认情况下，“Dense”会自动将形状为（批量大小，通道数，高度，宽度）的输入，
# 转换为形状为（批量大小，通道数*高度*宽度）的输入
nn.Dense(120, activation='sigmoid'),
nn.Dense(84, activation='sigmoid'),
nn.Dense(10))
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\diilbookstyleinputcell
.. code:: python
import torch
from torch import nn
from d2l import torch as d2l
net = nn.Sequential(
nn.Conv2d(1, 6, kernel_size=5, padding=2), nn.Sigmoid(),
nn.AvgPool2d(kernel_size=2, stride=2),
nn.Conv2d(6, 16, kernel_size=5), nn.Sigmoid(),
nn.AvgPool2d(kernel_size=2, stride=2),
nn.Flatten(),
nn.Linear(16 * 5 * 5, 120), nn.Sigmoid(),
nn.Linear(120, 84), nn.Sigmoid(),
nn.Linear(84, 10))
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\diilbookstyleinputcell
.. code:: python
import tensorflow as tf
from d2l import tensorflow as d2l
def net():
return tf.keras.models.Sequential([
tf.keras.layers.Conv2D(filters=6, kernel_size=5, activation='sigmoid',
padding='same'),
tf.keras.layers.AvgPool2D(pool_size=2, strides=2),
tf.keras.layers.Conv2D(filters=16, kernel_size=5,
activation='sigmoid'),
tf.keras.layers.AvgPool2D(pool_size=2, strides=2),
tf.keras.layers.Flatten(),
tf.keras.layers.Dense(120, activation='sigmoid'),
tf.keras.layers.Dense(84, activation='sigmoid'),
tf.keras.layers.Dense(10)])
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\diilbookstyleinputcell
.. code:: python
import warnings
from d2l import paddle as d2l
warnings.filterwarnings("ignore")
import paddle
from paddle import nn, optimizer
net = nn.Sequential(
nn.Conv2D(1, 6, kernel_size=5, padding=2), nn.Sigmoid(),
nn.AvgPool2D(kernel_size=2, stride=2),
nn.Conv2D(6, 16, kernel_size=5), nn.Sigmoid(),
nn.AvgPool2D(kernel_size=2, stride=2),
nn.Flatten(),
nn.Linear(16 * 5 * 5, 120), nn.Sigmoid(),
nn.Linear(120, 84), nn.Sigmoid(),
nn.Linear(84, 10))
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
W0818 09:30:59.183962 118149 gpu_resources.cc:61] Please NOTE: device: 0, GPU Compute Capability: 7.0, Driver API Version: 11.8, Runtime API Version: 11.8
W0818 09:30:59.215307 118149 gpu_resources.cc:91] device: 0, cuDNN Version: 8.7.
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\diilbookstyleinputcell
.. code:: python
X = np.random.uniform(size=(1, 1, 28, 28))
net.initialize()
for layer in net:
X = layer(X)
print(layer.name, 'output shape:\t', X.shape)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
conv0 output shape: (1, 6, 28, 28)
pool0 output shape: (1, 6, 14, 14)
conv1 output shape: (1, 16, 10, 10)
pool1 output shape: (1, 16, 5, 5)
dense0 output shape: (1, 120)
dense1 output shape: (1, 84)
dense2 output shape: (1, 10)
[07:27:48] ../src/storage/storage.cc:196: Using Pooled (Naive) StorageManager for CPU
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\diilbookstyleinputcell
.. code:: python
X = torch.rand(size=(1, 1, 28, 28), dtype=torch.float32)
for layer in net:
X = layer(X)
print(layer.__class__.__name__,'output shape: \t',X.shape)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
Conv2d output shape: torch.Size([1, 6, 28, 28])
Sigmoid output shape: torch.Size([1, 6, 28, 28])
AvgPool2d output shape: torch.Size([1, 6, 14, 14])
Conv2d output shape: torch.Size([1, 16, 10, 10])
Sigmoid output shape: torch.Size([1, 16, 10, 10])
AvgPool2d output shape: torch.Size([1, 16, 5, 5])
Flatten output shape: torch.Size([1, 400])
Linear output shape: torch.Size([1, 120])
Sigmoid output shape: torch.Size([1, 120])
Linear output shape: torch.Size([1, 84])
Sigmoid output shape: torch.Size([1, 84])
Linear output shape: torch.Size([1, 10])
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\diilbookstyleinputcell
.. code:: python
X = tf.random.uniform((1, 28, 28, 1))
for layer in net().layers:
X = layer(X)
print(layer.__class__.__name__, 'output shape: \t', X.shape)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
Conv2D output shape: (1, 28, 28, 6)
AveragePooling2D output shape: (1, 14, 14, 6)
Conv2D output shape: (1, 10, 10, 16)
AveragePooling2D output shape: (1, 5, 5, 16)
Flatten output shape: (1, 400)
Dense output shape: (1, 120)
Dense output shape: (1, 84)
Dense output shape: (1, 10)
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\diilbookstyleinputcell
.. code:: python
X = paddle.rand((1, 1, 28, 28), 'float32')
for layer in net:
X = layer(X)
print(layer.__class__.__name__, 'output shape: \t', X.shape)
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
Conv2D output shape: [1, 6, 28, 28]
Sigmoid output shape: [1, 6, 28, 28]
AvgPool2D output shape: [1, 6, 14, 14]
Conv2D output shape: [1, 16, 10, 10]
Sigmoid output shape: [1, 16, 10, 10]
AvgPool2D output shape: [1, 16, 5, 5]
Flatten output shape: [1, 400]
Linear output shape: [1, 120]
Sigmoid output shape: [1, 120]
Linear output shape: [1, 84]
Sigmoid output shape: [1, 84]
Linear output shape: [1, 10]
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为了进行评估，我们需要对
:numref:`sec_softmax_scratch`\ 中描述的\ ``evaluate_accuracy``\ 函数进行轻微的修改。
由于完整的数据集位于内存中，因此在模型使用GPU计算数据集之前，我们需要将其复制到显存中。
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\diilbookstyleinputcell
.. code:: python
def evaluate_accuracy_gpu(net, data_iter, device=None): #@save
"""使用GPU计算模型在数据集上的精度"""
if not device: # 查询第一个参数所在的第一个设备
device = list(net.collect_params().values())[0].list_ctx()[0]
metric = d2l.Accumulator(2) # 正确预测的数量，总预测的数量
for X, y in data_iter:
X, y = X.as_in_ctx(device), y.as_in_ctx(device)
metric.add(d2l.accuracy(net(X), y), d2l.size(y))
return metric[0] / metric[1]
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为了进行评估，我们需要对
:numref:`sec_softmax_scratch`\ 中描述的\ ``evaluate_accuracy``\ 函数进行轻微的修改。
由于完整的数据集位于内存中，因此在模型使用GPU计算数据集之前，我们需要将其复制到显存中。
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\diilbookstyleinputcell
.. code:: python
def evaluate_accuracy_gpu(net, data_iter, device=None): #@save
"""使用GPU计算模型在数据集上的精度"""
if isinstance(net, nn.Module):
net.eval() # 设置为评估模式
if not device:
device = next(iter(net.parameters())).device
# 正确预测的数量，总预测的数量
metric = d2l.Accumulator(2)
with torch.no_grad():
for X, y in data_iter:
if isinstance(X, list):
# BERT微调所需的（之后将介绍）
X = [x.to(device) for x in X]
else:
X = X.to(device)
y = y.to(device)
metric.add(d2l.accuracy(net(X), y), y.numel())
return metric[0] / metric[1]
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\diilbookstyleinputcell
.. code:: python
def evaluate_accuracy_gpu(net, data_iter, device=None): #@save
"""使用GPU计算模型在数据集上的精度"""
if isinstance(net, nn.Layer):
net.eval() # 设置为评估模式
if not device:
device = next(iter(net.parameters())).place
paddle.set_device("gpu:{}".format(str(device)[-2]))
# 正确预测的数量，总预测的数量
metric = d2l.Accumulator(2)
with paddle.no_grad():
for X, y in data_iter:
if isinstance(X, list):
# BERT微调所需的
X = [paddle.to_tensor(x, place=device) for x in X]
else:
X = paddle.to_tensor(X, place=device)
y = paddle.to_tensor(y, place=device)
metric.add(d2l.accuracy(net(X), y), y.numel())
return metric[0] / metric[1]
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\diilbookstyleinputcell
.. code:: python
#@save
def train_ch6(net, train_iter, test_iter, num_epochs, lr, device):
"""用GPU训练模型(在第六章定义)"""
net.initialize(force_reinit=True, ctx=device, init=init.Xavier())
loss = gluon.loss.SoftmaxCrossEntropyLoss()
trainer = gluon.Trainer(net.collect_params(),
'sgd', {'learning_rate': lr})
animator = d2l.Animator(xlabel='epoch', xlim=[1, num_epochs],
legend=['train loss', 'train acc', 'test acc'])
timer, num_batches = d2l.Timer(), len(train_iter)
for epoch in range(num_epochs):
metric = d2l.Accumulator(3) # 训练损失之和，训练准确率之和，样本数
for i, (X, y) in enumerate(train_iter):
timer.start()
# 下面是与“d2l.train_epoch_ch3”的主要不同
X, y = X.as_in_ctx(device), y.as_in_ctx(device)
with autograd.record():
y_hat = net(X)
l = loss(y_hat, y)
l.backward()
trainer.step(X.shape[0])
metric.add(l.sum(), d2l.accuracy(y_hat, y), X.shape[0])
timer.stop()
train_l = metric[0] / metric[2]
train_acc = metric[1] / metric[2]
if (i + 1) % (num_batches // 5) == 0 or i == num_batches - 1:
animator.add(epoch + (i + 1) / num_batches,
(train_l, train_acc, None))
test_acc = evaluate_accuracy_gpu(net, test_iter)
animator.add(epoch + 1, (None, None, test_acc))
print(f'loss {train_l:.3f}, train acc {train_acc:.3f}, '
f'test acc {test_acc:.3f}')
print(f'{metric[2] * num_epochs / timer.sum():.1f} examples/sec '
f'on {str(device)}')
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\diilbookstyleinputcell
.. code:: python
#@save
def train_ch6(net, train_iter, test_iter, num_epochs, lr, device):
"""用GPU训练模型(在第六章定义)"""
def init_weights(m):
if type(m) == nn.Linear or type(m) == nn.Conv2d:
nn.init.xavier_uniform_(m.weight)
net.apply(init_weights)
print('training on', device)
net.to(device)
optimizer = torch.optim.SGD(net.parameters(), lr=lr)
loss = nn.CrossEntropyLoss()
animator = d2l.Animator(xlabel='epoch', xlim=[1, num_epochs],
legend=['train loss', 'train acc', 'test acc'])
timer, num_batches = d2l.Timer(), len(train_iter)
for epoch in range(num_epochs):
# 训练损失之和，训练准确率之和，样本数
metric = d2l.Accumulator(3)
net.train()
for i, (X, y) in enumerate(train_iter):
timer.start()
optimizer.zero_grad()
X, y = X.to(device), y.to(device)
y_hat = net(X)
l = loss(y_hat, y)
l.backward()
optimizer.step()
with torch.no_grad():
metric.add(l * X.shape[0], d2l.accuracy(y_hat, y), X.shape[0])
timer.stop()
train_l = metric[0] / metric[2]
train_acc = metric[1] / metric[2]
if (i + 1) % (num_batches // 5) == 0 or i == num_batches - 1:
animator.add(epoch + (i + 1) / num_batches,
(train_l, train_acc, None))
test_acc = evaluate_accuracy_gpu(net, test_iter)
animator.add(epoch + 1, (None, None, test_acc))
print(f'loss {train_l:.3f}, train acc {train_acc:.3f}, '
f'test acc {test_acc:.3f}')
print(f'{metric[2] * num_epochs / timer.sum():.1f} examples/sec '
f'on {str(device)}')
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\diilbookstyleinputcell
.. code:: python
class TrainCallback(tf.keras.callbacks.Callback): #@save
"""一个以可视化的训练进展的回调"""
def __init__(self, net, train_iter, test_iter, num_epochs, device_name):
self.timer = d2l.Timer()
self.animator = d2l.Animator(
xlabel='epoch', xlim=[1, num_epochs], legend=[
'train loss', 'train acc', 'test acc'])
self.net = net
self.train_iter = train_iter
self.test_iter = test_iter
self.num_epochs = num_epochs
self.device_name = device_name
def on_epoch_begin(self, epoch, logs=None):
self.timer.start()
def on_epoch_end(self, epoch, logs):
self.timer.stop()
test_acc = self.net.evaluate(
self.test_iter, verbose=0, return_dict=True)['accuracy']
metrics = (logs['loss'], logs['accuracy'], test_acc)
self.animator.add(epoch + 1, metrics)
if epoch == self.num_epochs - 1:
batch_size = next(iter(self.train_iter))[0].shape[0]
num_examples = batch_size * tf.data.experimental.cardinality(
self.train_iter).numpy()
print(f'loss {metrics[0]:.3f}, train acc {metrics[1]:.3f}, '
f'test acc {metrics[2]:.3f}')
print(f'{num_examples / self.timer.avg():.1f} examples/sec on '
f'{str(self.device_name)}')
#@save
def train_ch6(net_fn, train_iter, test_iter, num_epochs, lr, device):
"""用GPU训练模型(在第六章定义)"""
device_name = device._device_name
strategy = tf.distribute.OneDeviceStrategy(device_name)
with strategy.scope():
optimizer = tf.keras.optimizers.SGD(learning_rate=lr)
loss = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
net = net_fn()
net.compile(optimizer=optimizer, loss=loss, metrics=['accuracy'])
callback = TrainCallback(net, train_iter, test_iter, num_epochs,
device_name)
net.fit(train_iter, epochs=num_epochs, verbose=0, callbacks=[callback])
return net
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\diilbookstyleinputcell
.. code:: python
#@save
def train_ch6(net, train_iter, test_iter, num_epochs, lr, device):
"""用GPU训练模型(在第六章定义)"""
def init_weights(m):
if type(m) == nn.Linear or type(m) == nn.Conv2D:
nn.initializer.XavierUniform(m.weight)
net.apply(init_weights)
print('training on', device)
net.to(device)
optimizer = paddle.optimizer.SGD(learning_rate=lr, parameters=net.parameters())
loss = nn.CrossEntropyLoss()
animator = d2l.Animator(xlabel='epoch', xlim=[1, num_epochs],
legend=['train loss', 'train acc', 'test acc'])
timer, num_batches = d2l.Timer(), len(train_iter)
for epoch in range(num_epochs):
# 训练损失之和，训练准确率之和，样本数
metric = d2l.Accumulator(3)
net.train()
for i, (X, y) in enumerate(train_iter):
timer.start()
optimizer.clear_grad()
X, y = paddle.to_tensor(X, place=device), paddle.to_tensor(y, place=device)
y_hat = net(X)
l = loss(y_hat, y)
l.backward()
optimizer.step()
with paddle.no_grad():
metric.add(l * X.shape[0], d2l.accuracy(y_hat, y), X.shape[0])
timer.stop()
train_l = metric[0] / metric[2]
train_acc = metric[1] / metric[2]
if (i + 1) % (num_batches // 5) == 0 or i == num_batches - 1:
animator.add(epoch + (i + 1) / num_batches,
(train_l, train_acc, None))
test_acc = evaluate_accuracy_gpu(net, test_iter)
animator.add(epoch + 1, (None, None, test_acc))
print(f'loss {train_l:.3f}, train acc {train_acc:.3f}, '
f'test acc {test_acc:.3f}')
print(f'{metric[2] * num_epochs / timer.sum():.1f} examples/sec '
f'on {str(device)}')
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\diilbookstyleinputcell
.. code:: python
lr, num_epochs = 0.9, 10
train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.473, train acc 0.823, test acc 0.827
35726.4 examples/sec on gpu(0)
.. figure:: output_lenet_4a2e9e_64_1.svg
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.. raw:: latex
\diilbookstyleinputcell
.. code:: python
lr, num_epochs = 0.9, 10
train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
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\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.469, train acc 0.823, test acc 0.779
55296.6 examples/sec on cuda:0
.. figure:: output_lenet_4a2e9e_67_1.svg
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.. raw:: latex
\diilbookstyleinputcell
.. code:: python
lr, num_epochs = 0.9, 10
train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.467, train acc 0.824, test acc 0.828
61444.5 examples/sec on /GPU:0
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
.. figure:: output_lenet_4a2e9e_70_2.svg
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.. raw:: latex
\diilbookstyleinputcell
.. code:: python
lr, num_epochs = 0.9, 10
train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
.. raw:: latex
\diilbookstyleoutputcell
.. parsed-literal::
:class: output
loss 0.439, train acc 0.837, test acc 0.827
30845.8 examples/sec on Place(gpu:0)
.. figure:: output_lenet_4a2e9e_73_1.svg
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`Discussions `__
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