- 🍨 本文为🔗365天深度学习训练营中的学习记录博客
- 🍖 原作者：K同学啊|接辅导、项目定制
1 前言
在计算机视觉领域，卷积神经网络（CNN）已经成为最主流的方法，比如GoogleNet，VGG-16，Incepetion等模型。CNN史上的一个里程碑事件是ResNet模型的出现，ResNet可以训练出更深的CNN模型，从而实现更高的准确率。ResNet模型的核心是通过建立前面层与后面层之间的“短路连接”（shortcut, skip connection），进而训练出更深的CNN网络。
DenseNet模型的基本思路与ResNet一致，但是它建立的是前面所有层与后面层的紧密连接（dense connection），它的名称也是由此而来。DenseNet的另一大特色是通过特征在channel上的的连接来实现特征重用（feature reuse）。这些特点让DenseNet在参数和计算成本更少的情形下实现比ResNet更优的性能，DenseNet也因此斩获CVPR2017的最佳论文奖。
其中DenseNet论文原文地址为：https://arxiv.org/pdf/1608.06993v5.pdf
2 设计理念
相比ResNet，DenseNet提出了一个更激进的密集连接机制：即互相连接所有的层，具体来说就是每个层都会接受前面所有层作为额外的输入。
图3为ResNet网络的残差连接机制，作为对比，图4为DenseNet的密集连接机制。可以看到，ResNet是每个层与前面的某层（一般是2~4层）短路连接在一起，连接方式是通过元素相加。而在DenseNet中，每个层都会与前面所有层在channel维度上链接（concat）在一起（即元素叠加），并作为下一层的输入。
对于一个L层的网络，DenseNet共包含个连接，相比ResNet，这是一种密集连接。而且DenseNet是直接concat来自不同层的特征图，这可以实现特征重用，提升效率，这一特点是DenseNet与ResNet最主要的区别。
2.1 标准神经网络
图2是一个标准的神经网络传播过程示意图，输入和输出的公式是，其中
是一个组合函数，通常包括BN、ReLu、Pooling、Conv等操作，
是第l层的输入的特征图（来自于l-1层的输出）,
是第l层的输出的特征图。
2.2 ResNet
图3是ResNet的网络连接机制，由图可知是跨层相加，输入和输出的公式是
2.3 DenseNet
图4为DenseNet的连接机制，采用跨通道的concat的形式连接，会连接前面所有层作为输入，输入和输出的公式是。这里要注意所有层的输入都来源于前面所有层在channel维度的concat，以下动图形象表示这一操作。
3 网络结构
网络的具体实现细节如图6所示。
CNN网络一般要经过Pooling或者stride>1的Conv来降低特征图的大小，而DenseNet的密集连接方式需要特征图大小保持一致。为了解决这个问题，DenseNet网络中使用DenseBlock+Transition的结构，其中DenseBlock是包含很多层的模块，每个层的特征图大小相同，层与层之间采用密集连接方式。而Transition层是连接两个相邻的DenseBlock，并且通过Pooling使特征图大小降低。图7给出了DenseNet的网络结构，它共包含4个DenseBlock，各个DenseBlock之间通过Transition层连接在一起。
在DenseBlock中，各个层的特征图大小一致，可以在channel维度上连接。DenseBlock中的非线性组合函数的是BN+ReLU+3*3Conv的结构，如图8所示。另外，与ResNet不同，所有DenseBlock中各个层卷积之后均输出k个特征图，即得到的特征图的channel数为
，或者说采用k个卷积核。
在DenseNet称为growth rate，这是一个超参数。一般情况下使用较小的
（比如12），就可以得到较佳的性能。假定输入层的特征图的channel数为
，那么
层输入的channel数为
，因此随着层数的增加，尽管
设定的较小，DenseBlock的输入会非常多，不过这是由于特征重用所造成的，每个层仅有
个特征是自己独有的。
由于后面层的输入会非常大，DenseBlock内部采用bottleneck层来减少计算量，主要是原有的结构中增加1*1Conv，如图9所示，即BN+ReLU+1*1Conv+BN+ReLU+3*3Conv，称为DenseNet-B结构。其中1*1Conv得到个特征图，它起到的作用是降低特征数量，从而提升计算效率。
对于Trasition层，它主要是连接两个相邻的DenseBlock，并且降低特征图大小。Transition层包括一个1*1的卷积和2*2的AvgPooling，结构为BN+ReLU+1*1Conv+2*2AvgPooling。另外，Transition层可以起到压缩模型的作用。假定Transition层的上接DenseBlock得到特征图channels数为，Transition层可以产生
个特征（通过卷积层），其中
是压缩系数（compression rate）。当
时，特征个数经过Transition层没有变化，即无压缩，而当压缩系数小于1时，这种结构称为DenseNet-C，文中使用
。对于使用bootleneck层的DenseBlock结构和压缩系数小于1的Transition组合机构称为DenseNet-BC。
对于ImageNet数据集，图片输入大小为224*224，网络结构采用包含4个DenseBlock的DenseNet-BC，其首先是一个stride=2的7*7卷积层，然后是一个stride=2的3*3MaxPooling层，后面才进入DenseBlock。ImageNet数据集所采用的网络配置如表1所示：
4 效果对比
5 使用Pytroch实现DenseNet121
图11为DenseNet121的具体网络结构，它与表1中的DenseNet121相对应。左边是整个DenseNet121的网络结构，其中粉色为DenseBlock，最右侧为其详细结构，灰色为Transition，中间为其详细结构。
5.1 前期工作
5.1.1 开发环境
电脑系统：ubuntu16.04
编译器：Jupter Lab
语言环境：Python 3.7
深度学习环境：pytorch
5.1.2 设置GPU
如果设备上支持GPU就使用GPU，否则注释掉这部分代码。
import torch
import torch.nn as nn
import torchvision.transforms as transforms
import torchvision
from torchvision import transforms, datasets
import os, PIL, pathlib, warnings
warnings.filterwarnings("ignore")
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
print(device)5.1.3 导入数据
import os,PIL,random,pathlib
data_dir_str = '../data/bird_photos'
data_dir = pathlib.Path(data_dir_str)
print("data_dir:", data_dir, "\n")
data_paths = list(data_dir.glob('*'))
classNames = [str(path).split('/')[-1] for path in data_paths]
print('classNames:', classNames , '\n')
train_transforms = transforms.Compose([
transforms.Resize([224, 224]), # resize输入图片
transforms.ToTensor(), # 将PIL Image或numpy.ndarray转换成tensor
transforms.Normalize(
mean=[0.485, 0.456, 0.406],
std=[0.229, 0.224, 0.225]) # 从数据集中随机抽样计算得到
])
total_data = datasets.ImageFolder(data_dir_str, transform=train_transforms)
print(total_data)
print(total_data.class_to_idx)结果输出如图：
5.1.4 划分数据集
train_size = int(0.8 * len(total_data))
test_size = len(total_data) - train_size
train_dataset, test_dataset = torch.utils.data.random_split(total_data, [train_size, test_size])
print(train_dataset, test_dataset)
batch_size = 4
train_dl = torch.utils.data.DataLoader(train_dataset,
batch_size=batch_size,
shuffle=True,
num_workers=1,
pin_memory=False)
test_dl = torch.utils.data.DataLoader(test_dataset,
batch_size=batch_size,
shuffle=True,
num_workers=1,
pin_memory=False)
for X, y in test_dl:
print("Shape of X [N, C, H, W]:", X.shape)
print("Shape of y:", y.shape, y.dtype)
break
结果输出如图：
5.2 搭建DenseNet121
5.2.1 DenseBlock中的Bottleneck
import torch
from torch import nn
class _DenseLayer(nn.Sequential):
"""
DenseBlock的基本单元（使用bottleneck）
"""
def __init__(self, num_input_features, growth_rate, bn_size, drop_rate):
super(_DenseLayer, self).__init__()
self.add_module("norm1", nn.BatchNorm2d(num_input_features))
self.add_module("relu1", nn.ReLU(inplace=True))
self.add_module("conv1", nn.Conv2d(num_input_features, bn_size*growth_rate,
kernel_size=1, stride=1, bias=False))
self.add_module("norm2", nn.BatchNorm2d(bn_size*growth_rate))
self.add_module("relu2", nn.ReLU(inplace=True))
self.add_module("conv2", nn.Conv2d(bn_size*growth_rate, growth_rate,
kernel_size=3, stride=1, padding=1, bias=False))
self.drop_rate = drop_rate
def forward(self, x):
new_features = super(_DenseLayer, self).forward(x)
if self.drop_rate > 0:
new_features = F.dropout(new_features, p=self.drop_rate, training=self.training)
return torch.cat([x, new_features], 1)5.2.2 DenseBlock层
class _DenseBlock(nn.Sequential):
def __init__(self, num_layer, num_input_features, bn_size, growth_rate, drop_rate):
super(_DenseBlock, self).__init__()
for i in range(num_layer):
layer = _DenseLayer(num_input_features+i*growth_rate,
growth_rate, bn_size, drop_rate)
self.add_module("denselayer%d" % (i+1,), layer)5.2.3 Transition层
class _Transition(nn.Sequential):
def __init__(self, num_input_features, num_output_features):
super(_Transition, self).__init__()
self.add_module("norm", nn.BatchNorm2d(num_input_features))
self.add_module("relu", nn.ReLU(inplace=True))
self.add_module("conv", nn.Conv2d(num_input_features, num_output_features,
kernel_size=1, stride=1, bias=False))
self.add_module("pool", nn.AvgPool2d(2, stride=2)) 5.2.4 DenseNet-BC
import torch.nn.functional as F
#from collections import OrderedDict
import collections
try:
from collections import OrderedDict
except ImportError:
OrderedDict = dict
class DenseNet(nn.Module):
"DenseNet-BC model"
def __init__(self, growth_rate=32, block_config=(6, 12, 24, 16), num_init_features=64,
bn_size=4, compression_rate=0.5, drop_rate=0, num_classes=4):
"""
growth_rate:(int) number of filters used in DenseLayer, 'k' in the paper
block_config:(list of 4 ints) number of layers in each DenseBlock
num_init_features:(int) number of filters in the first Conv2d
bn_size:(int) the factor using in the bottleneck layer
compression_rate:(float) the compression rate used in Trasition Layer
drop_rate:(float) the drop rate after each DenseLayer
num_classes:(int) number of classes for classification
"""
super(DenseNet, self).__init__()
# first Conv2d
self.features = nn.Sequential(OrderedDict([
("conv0", nn.Conv2d(3, num_init_features, kernel_size=7, stride=2, padding=3, bias=False)),
("norm0", nn.BatchNorm2d(num_init_features)),
("relu0", nn.ReLU(inplace=True)),
("pool0", nn.MaxPool2d(3, stride=2, padding=1))
]))
# DenseBlock
num_features = num_init_features
for i,num_layers in enumerate(block_config):
block = _DenseBlock(num_layers, num_features, bn_size, growth_rate, drop_rate)
self.features.add_module("denseblock%d" % (i + 1), block)
num_features += num_layers*growth_rate
if i != len(block_config) - 1:
transition = _Transition(num_features, int(num_features*compression_rate))
self.features.add_module("transition%d" % (i+1), transition)
num_features = int(num_features * compression_rate)
# final bn+relu
self.features.add_module("norm5", nn.BatchNorm2d(num_features))
self.features.add_module("relu5", nn.ReLU(inplace=True))
# classification layer
self.classifier = nn.Linear(num_features, num_classes)
# params initialization
for m in self.modules():
if isinstance(m, nn.Conv2d):
nn.init.kaiming_normal_(m.weight)
elif isinstance(m, nn.BatchNorm2d):
nn.init.constant_(m.bias, 0)
nn.init.constant_(m.weight, 1)
elif isinstance(m, nn.Linear):
nn.init.constant_(m.bias, 0)
def forward(self, x):
features = self.features(x)
out = F.avg_pool2d(features, 7, stride=1).view(features.size(0), -1)
out = self.classifier(out)
return out5.2.5 DenseNet121
import re
def densenet121(pretrained=False, **kwargs):
# DenseNet121
model = DenseNet(num_init_features=64, growth_rate=32, block_config=(6,12,24,16), ** kwargs)
if pretrained:
# '.' are no longer in module names, but pervious _DenseLayer
# has keys 'norm.1','relu.1','conv.1','norm.2','relu.2','conv.2'.
# They are also in the checkpoints in model_urls.This pattern is used
# to find find such keys.
pattern = re.compile(r'^(.*denselayer\d+\.(?:norm|relu\conv))\.((?:[12])\.(?:weight|bias|running_mean|running_var))$')
state_dir = model_zoo.load_url(model_urls['densenet121'])
for key in list(state_dict.key()):
res = pattern.match(key)
if res:
new_key = res.group(1) + res.group(2)
state_dict[new_key] = state_dict[key]
del state_dict[key]
model.load_state_dict(state_dict)
return model
model = densenet121().to(device)
model结果输出如下（由于结果太长，只展示最前面和最后面）：
（中间省略）
5.2.6 查看模型详情
# 统计模型参数量以及其他指标
import torchsummary as summary
summary.summary(model, (3, 224, 224))结果输出如下（由于结果太长，只展示最前面和最后面）：
（中间省略）
5.3 训练模型
5.3.1 编写训练函数
# 训练循环
def train(dataloader, model, loss_fn, optimizer):
size = len(dataloader.dataset) # 训练集的大小
num_batches = len(dataloader) # 批次数目, (size/batch_size，向上取整)
train_loss, train_acc = 0, 0 # 初始化训练损失和正确率
for X, y in dataloader: # 获取图片及其标签
X, y = X.to(device), y.to(device)
# 计算预测误差
pred = model(X) # 网络输出
loss = loss_fn(pred, y) # 计算网络输出pred和真实值y之间的差距，y为真实值，计算二者差值即为损失
# 反向传播
optimizer.zero_grad() # grad属性归零
loss.backward() # 反向传播
optimizer.step() # 每一步自动更新
# 记录acc与loss
train_acc += (pred.argmax(1) == y).type(torch.float).sum().item()
train_loss += loss.item()
train_acc /= size
train_loss /= num_batches
return train_acc, train_loss5.3.2 编写测试函数
def test(dataloader, model, loss_fn):
size = len(dataloader.dataset) # 训练集的大小
num_batches = len(dataloader) # 批次数目, (size/batch_size，向上取整)
test_loss, test_acc = 0, 0 # 初始化测试损失和正确率
# 当不进行训练时，停止梯度更新，节省计算内存消耗
# with torch.no_grad():
for imgs, target in dataloader: # 获取图片及其标签
with torch.no_grad():
imgs, target = imgs.to(device), target.to(device)
# 计算误差
tartget_pred = model(imgs) # 网络输出
loss = loss_fn(tartget_pred, target) # 计算网络输出和真实值之间的差距，targets为真实值，计算二者差值即为损失
# 记录acc与loss
test_loss += loss.item()
test_acc += (tartget_pred.argmax(1) == target).type(torch.float).sum().item()
test_acc /= size
test_loss /= num_batches
return test_acc, test_loss5.3.3 正式训练
import copy
optimizer = torch.optim.Adam(model.parameters(), lr = 1e-4)
loss_fn = nn.CrossEntropyLoss() #创建损失函数
epochs = 40
train_loss = []
train_acc = []
test_loss = []
test_acc = []
best_acc = 0 #设置一个最佳准确率，作为最佳模型的判别指标
if hasattr(torch.cuda, 'empty_cache'):
torch.cuda.empty_cache()
for epoch in range(epochs):
model.train()
epoch_train_acc, epoch_train_loss = train(train_dl, model, loss_fn, optimizer)
#scheduler.step() #更新学习率（调用官方动态学习率接口时使用）
model.eval()
epoch_test_acc, epoch_test_loss = test(test_dl, model, loss_fn)
#保存最佳模型到best_model
if epoch_test_acc > best_acc:
best_acc = epoch_test_acc
best_model = copy.deepcopy(model)
train_acc.append(epoch_train_acc)
train_loss.append(epoch_train_loss)
test_acc.append(epoch_test_acc)
test_loss.append(epoch_test_loss)
#获取当前的学习率
lr = optimizer.state_dict()['param_groups'][0]['lr']
template = ('Epoch: {:2d}. Train_acc: {:.1f}%, Train_loss: {:.3f}, Test_acc:{:.1f}%, Test_loss:{:.3f}, Lr: {:.2E}')
print(template.format(epoch+1, epoch_train_acc*100, epoch_train_loss, epoch_test_acc*100, epoch_test_loss, lr))
PATH = './J3_best_model.pth'
torch.save(model.state_dict(), PATH)
print('Done')结果输出如下：
5.4 结果可视化
import matplotlib.pyplot as plt
#隐藏警告
import warnings
warnings.filterwarnings("ignore") #忽略警告信息
plt.rcParams['font.sans-serif'] = ['SimHei'] # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False # 用来正常显示负号
plt.rcParams['figure.dpi'] = 100 #分辨率
epochs_range = range(epochs)
plt.figure(figsize=(12, 3))
plt.subplot(1, 2, 1)
plt.plot(epochs_range, train_acc, label='Training Accuracy')
plt.plot(epochs_range, test_acc, label='Test Accuracy')
plt.legend(loc='lower right')
plt.title('Training and Validation Accuracy')
plt.subplot(1, 2, 2)
plt.plot(epochs_range, train_loss, label='Training Loss')
plt.plot(epochs_range, test_loss, label='Test Loss')
plt.legend(loc='upper right')
plt.title('Training and Validation Loss')
plt.show()结果输出如下：
6 使用Tensorflow实现DenseNet121
6.1 前期工作
6.1.1 开发环境
电脑系统：ubuntu16.04
编译器：Jupter Lab
语言环境：Python 3.7
深度学习环境：tensorflow
6.1.2 设置GPU
如果设备上支持GPU就使用GPU，否则注释掉这部分代码。
import tensorflow as tf
gpus = tf.config.list_physical_devices("GPU")
if gpus:
tf.config.experimental.set_memory_growth(gpus[0], True) # 设置GPU显存用量按需使用
tf.config.set_visible_devices([gpus[0]], "GPU")6.1.2 导入数据
import matplotlib.pyplot as plt
# 支持中文
plt.rcParams['font.sans-serif'] = ['SimHei'] # 用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False # 用来正常显示负号
import os, PIL, pathlib
import numpy as np
from tensorflow import keras
from tensorflow.keras import layers,models
data_dir = "../data/bird_photos"
data_dir = pathlib.Path(data_dir)
image_count = len(list(data_dir.glob('*/*')))
print("图片总数为：", image_count)6.1.3 加载数据
batch_size = 8
img_height = 224
img_width = 224
train_ds = tf.keras.preprocessing.image_dataset_from_directory(
data_dir,
validation_split=0.2,
subset="training",
seed=123,
image_size=(img_height, img_width),
batch_size=batch_size)
val_ds = tf.keras.preprocessing.image_dataset_from_directory(
data_dir,
validation_split=0.2,
subset="validation",
seed=123,
image_size=(img_height, img_width),
batch_size=batch_size)
class_Names = train_ds.class_names
print("class_Names:",class_Names)输出结果如下：
6.1.4 可视化数据
plt.figure(figsize=(10, 5)) # 图形的宽为10，高为5
plt.suptitle("imshow data")
for images,labels in train_ds.take(1):
for i in range(8):
ax = plt.subplot(2, 4, i+1)
plt.imshow(images[i].numpy().astype("uint8"))
plt.title(class_Names[labels[i]])
plt.axis("off")输出结果如下：
6.1.5 检查数据
for image_batch, lables_batch in train_ds:
print(image_batch.shape)
print(lables_batch.shape)
break输出结果如下：
6.1.6 配置数据集
AUTOTUNE = tf.data.AUTOTUNE
train_ds = train_ds.cache().shuffle(1000).prefetch(buffer_size=AUTOTUNE)
val_ds = val_ds.cache().prefetch(buffer_size=AUTOTUNE)6.2 搭建DenseNet121
6.2.1 DenseNet121
import tensorflow as tf
import tensorflow.keras.layers as layers
from tensorflow.keras import regularizers
# from tensorflow.keras.models import Model
from tensorflow.keras.layers import Input,Activation,BatchNormalization,Flatten
from tensorflow.keras.layers import Dense,Conv2D,MaxPooling2D,ZeroPadding2D,AveragePooling2D
from tensorflow.keras.models import Model
def regularized_padded_conv2d(*args, **kwargs):
"""
带标准化的卷积
"""
return layers.Conv2D(*args, **kwargs,
padding='same',
kernel_regularizer=regularizers.l2(5e-5),
bias_regularizer=regularizers.l2(5e-5),
kernel_initializer='glorot_normal')
def DenseLayer(x, growth_rate, bn_size, drop_rate, layerName):
new_features = layers.BatchNormalization(name=layerName+"_norm1")(x)
new_features = layers.Activation('relu', name=layerName+"_relu1")(new_features)
new_features = regularized_padded_conv2d(filters=bn_size*growth_rate, kernel_size=1, strides=1, use_bias=False, name=layerName+"_conv1")(new_features)
new_features = layers.BatchNormalization(name=layerName+"_norm2")(new_features)
new_features = layers.Activation('relu', name=layerName+"_relu2")(new_features)
new_features = regularized_padded_conv2d(filters=growth_rate, kernel_size=3, strides=1, use_bias=False, name=layerName+"_conv2")(new_features)
if drop_rate > 0:
new_features = layers.Dropout(rate=drop_rate)(new_features)
return layers.concatenate([x, new_features], axis=-1)
def DenseBlock(x, num_layer, bn_size, growth_rate, drop_rate, blockName):
for i in range(num_layer):
x = DenseLayer(x, growth_rate=growth_rate, bn_size=bn_size, drop_rate=drop_rate, layerName=blockName+'_'+str(i+1))
return x
def Transition(x, num_output_features, blockName):
x = layers.BatchNormalization(name=blockName+"_norm")(x)
x = layers.Activation('relu', name=blockName+"_relu")(x)
x = regularized_padded_conv2d(filters=num_output_features, kernel_size=1, strides=1, use_bias=False, name=blockName+"_conv")(x)
x = layers.AveragePooling2D(pool_size=2, strides=2, padding='same', name=blockName+'_pool')(x)
return x
def densenet121(input_shape=[224,224,3], growth_rate=32, block_config=(6, 12, 24, 16), num_init_features=64,
bn_size=4, compression_rate=0.5, drop_rate=0, num_classes=4, classifier_activation='softmax'):
img_input = Input(shape=input_shape)
# first Conv2d
x = regularized_padded_conv2d(filters=num_init_features, kernel_size=7, strides=2, use_bias=False, name="pre_conv")(img_input)
x = layers.BatchNormalization(name="pre_norm")(x)
x = layers.Activation('relu', name="pre_relu")(x)
x = layers.MaxPool2D(pool_size=3, strides=2, padding='same')(x)
# DenseBlock
num_features = num_init_features
for i,num_layer in enumerate(block_config):
x = DenseBlock(x, num_layer=num_layer, bn_size=bn_size, growth_rate=growth_rate, drop_rate=drop_rate, blockName="DenseBlock_"+str(i+1))
num_features += num_layer*growth_rate
if i != len(block_config) - 1:
num_features = int(num_features * compression_rate)
x = Transition(x, num_output_features=num_features, blockName="TransBlock_"+ str(i+1))
# final bn+relu
x = layers.BatchNormalization(name="norm5")(x)
x = layers.Activation('relu', name="relu5")(x)
x = layers.AveragePooling2D(pool_size=7, strides=1, name='pool5')(x) #GlobalAveragePooling2D
# classification layer
x = Dense(num_classes, activation=classifier_activation, name='classifier')(x)
model = Model(img_input, x, name='densenet121')
# # 加载预训练模型
# model.load_weights("resnet50_weights_tf_dim_ordering_tf_kernels.h5")
return model
6.2.2 查看模型详情
model = densenet121()
model.summary()结果如图所示（由于内容较长，只截取前后部分内容）：
（中间部分省略）
6.3 训练模型
# 设置优化器
opt = tf.keras.optimizers.Adam(learning_rate=1e-6)
model.compile(optimizer="adam",
loss='sparse_categorical_crossentropy',
metrics=['accuracy'])
epochs = 40
history = model.fit(
train_ds,
validation_data=val_ds,
epochs=epochs)结果如下图所示：
6.4 模型评估
acc = history.history['accuracy']
val_acc = history.history['val_accuracy']
loss = history.history['loss']
val_loss = history.history['val_loss']
epochs_range = range(epochs)
plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
plt.suptitle("DenseNet test")
plt.plot(epochs_range, acc, label='Training Accuracy')
plt.plot(epochs_range, val_acc, label='Validation Accuracy')
plt.legend(loc='lower right')
plt.title('Training and Validation Accuracy')
plt.subplot(1, 2, 2)
plt.plot(epochs_range, loss, label='Training Loss')
plt.plot(epochs_range, val_loss, label='Validation loss')
plt.legend(loc='upper right')
plt.title('Training and Validation loss')
plt.show()结果如下图所示：
结合训练时的输出结果和模型评估图可以看出，训练的效果不理想，修改了learing_rate效果也不明显，后续继续尝试和分析。
