NNDL 实验五 前馈神经网络（2）自动梯度计算优化问题

目录

  4.3.1 利用预定义算子重新实现前馈神经网络

1，使用pytorch的预定义算子来重新实现二分类任务。

2. 增加一个3个神经元的隐藏层，再次实现二分类，并与1做对比。（必做）

3. 自定义隐藏层层数和每个隐藏层中的神经元个数，尝试找到最优超参数完成二分类。可以适当修改数据集，便于探索超参数。（选做）

  4.4.2 梯度消失问题

4.4.3 死亡ReLU问题

4.3 自动梯度计算
虽然我们能够通过模块化的方式比较好地对神经网络进行组装，但是每个模块的梯度计算过程仍然十分繁琐且容易出错。在深度学习框架中，已经封装了自动梯度计算的功能，我们只需要聚焦模型架构，不再需要耗费精力进行计算梯度。

飞桨提供了paddle.nn.Layer类，来方便快速的实现自己的层和模型。模型和层都可以基于paddle.nn.Layer扩充实现，模型只是一种特殊的层。继承了paddle.nn.Layer类的算子中，可以在内部直接调用其它继承paddle.nn.Layer类的算子，飞桨框架会自动识别算子中内嵌的paddle.nn.Layer类算子，并自动计算它们的梯度，并在优化时更新它们的参数。

pytorch中的相应内容是什么？请简要介绍。

  4.3.1 利用预定义算子重新实现前馈神经网络

1，使用pytorch的预定义算子来重新实现二分类任务。

import torch.nn as nn
import torch.nn.functional as F
#from paddle.nn.initializer import Constant, Normal, Uniform
import torch
from torch.nn.parameter import Parameterclass Model_MLP_L2_V2(torch.nn.Module):def __init__(self, input_size, hidden_size, output_size):super(Model_MLP_L2_V2, self).__init__()# 使用'paddle.nn.Linear'定义线性层。# 其中第一个参数（in_features）为线性层输入维度；第二个参数（out_features）为线性层输出维度# weight_attr为权重参数属性，这里使用'paddle.nn.initializer.Normal'进行随机高斯分布初始化# bias_attr为偏置参数属性，这里使用'paddle.nn.initializer.Constant'进行常量初始化self.fc1 = nn.Linear(input_size, hidden_size,)nn.init.normal_(self.fc1.weight, mean=0, std=1)nn.init.constant_(self.fc1.bias,0)self.fc2 = nn.Linear(hidden_size, output_size,)nn.init.normal_(self.fc2.weight, mean=0, std=1)nn.init.constant_(self.fc2.bias, 0)# 使用'paddle.nn.functional.sigmoid'定义 Logistic 激活函数self.act_fn = torch.sigmoid# 前向计算def forward(self, inputs):z1 = self.fc1(inputs)a1 = self.act_fn(z1)z2 = self.fc2(a1)a2 = self.act_fn(z2)return a2class RunnerV2_2(object):def __init__(self, model, optimizer, metric, loss_fn, **kwargs):self.model = modelself.optimizer = optimizerself.loss_fn = loss_fnself.metric = metric# 记录训练过程中的评估指标变化情况self.train_scores = []self.dev_scores = []# 记录训练过程中的评价指标变化情况self.train_loss = []self.dev_loss = []def train(self, train_set, dev_set, **kwargs):# 将模型切换为训练模式self.model.train()# 传入训练轮数，如果没有传入值则默认为0num_epochs = kwargs.get("num_epochs", 0)# 传入log打印频率，如果没有传入值则默认为100log_epochs = kwargs.get("log_epochs", 100)# 传入模型保存路径，如果没有传入值则默认为"best_model.pdparams"save_path = kwargs.get("save_path", "best_model.pdparams")# log打印函数，如果没有传入则默认为"None"custom_print_log = kwargs.get("custom_print_log", None)# 记录全局最优指标best_score = 0# 进行num_epochs轮训练for epoch in range(num_epochs):X, y = train_set# 获取模型预测logits = self.model(X)# 计算交叉熵损失trn_loss = self.loss_fn(logits, y)self.train_loss.append(trn_loss.item())# 计算评估指标trn_score = self.metric(logits, y).item()self.train_scores.append(trn_score)# 自动计算参数梯度trn_loss.backward()if custom_print_log is not None:# 打印每一层的梯度custom_print_log(self)# 参数更新self.optimizer.step()# 清空梯度self.optimizer.clear_grad()dev_score, dev_loss = self.evaluate(dev_set)# 如果当前指标为最优指标，保存该模型if dev_score > best_score:self.save_model(save_path)print(f"[Evaluate] best accuracy performence has been updated: {best_score:.5f} --> {dev_score:.5f}")best_score = dev_scoreif log_epochs and epoch % log_epochs == 0:print(f"[Train] epoch: {epoch}/{num_epochs}, loss: {trn_loss.item()}")# 模型评估阶段，使用'paddle.no_grad()'控制不计算和存储梯度def evaluate(self, data_set):# 将模型切换为评估模式self.model.eval()X, y = data_set# 计算模型输出logits = self.model(X)# 计算损失函数loss = self.loss_fn(logits, y).item()self.dev_loss.append(loss)# 计算评估指标score = self.metric(logits, y).item()self.dev_scores.append(score)return score, loss# 模型测试阶段，使用'paddle.no_grad()'控制不计算和存储梯度def predict(self, X):# 将模型切换为评估模式self.model.eval()return self.model(X)# 使用'model.state_dict()'获取模型参数，并进行保存def save_model(self, saved_path):torch.save(self.model.state_dict(), saved_path)# 使用'model.set_state_dict'加载模型参数def load_model(self, model_path):state_dict = torch.load(model_path)self.model.set_state_dict(state_dict)

  4.3.2 完善Runner类

class RunnerV2_2(object):def __init__(self, model, optimizer, metric, loss_fn, **kwargs):self.model = modelself.optimizer = optimizerself.loss_fn = loss_fnself.metric = metric# 记录训练过程中的评估指标变化情况self.train_scores = []self.dev_scores = []# 记录训练过程中的评价指标变化情况self.train_loss = []self.dev_loss = []def train(self, train_set, dev_set, **kwargs):# 将模型切换为训练模式self.model.train()# 传入训练轮数，如果没有传入值则默认为0num_epochs = kwargs.get("num_epochs", 0)# 传入log打印频率，如果没有传入值则默认为100log_epochs = kwargs.get("log_epochs", 100)# 传入模型保存路径，如果没有传入值则默认为"best_model.pdparams"save_path = kwargs.get("save_path", "best_model.pdparams")# log打印函数，如果没有传入则默认为"None"custom_print_log = kwargs.get("custom_print_log", None)# 记录全局最优指标best_score = 0# 进行num_epochs轮训练for epoch in range(num_epochs):X, y = train_set# 获取模型预测logits = self.model(X)# 计算交叉熵损失trn_loss = self.loss_fn(logits, y)self.train_loss.append(trn_loss.item())# 计算评估指标trn_score = self.metric(logits, y).item()self.train_scores.append(trn_score)# 清空梯度optimizer.zero_grad()# 自动计算参数梯度trn_loss.backward()if custom_print_log is not None:# 打印每一层的梯度custom_print_log(self)# 参数更新self.optimizer.step()dev_score, dev_loss = self.evaluate(dev_set)#print(dev_score)# 如果当前指标为最优指标，保存该模型if dev_score > best_score:print(f"[Evaluate] best accuracy performence has been updated: {best_score:.5f} --> {dev_score:.5f}")self.save_model(save_path)best_score = dev_scoreif log_epochs and epoch % log_epochs == 0:print(f"[Train] epoch: {epoch}/{num_epochs}, loss: {trn_loss.item()}")# 模型评估阶段，使用'paddle.no_grad()'控制不计算和存储梯度def evaluate(self, data_set):# 将模型切换为评估模式self.model.eval()X, y = data_set# 计算模型输出logits = self.model(X)# 计算损失函数loss = self.loss_fn(logits, y).item()self.dev_loss.append(loss)# 计算评估指标score = self.metric(logits, y).item()self.dev_scores.append(score)return score, loss# 模型测试阶段，使用'paddle.no_grad()'控制不计算和存储梯度def predict(self, X):# 将模型切换为评估模式self.model.eval()return self.model(X)# 使用'model.state_dict()'获取模型参数，并进行保存def save_model(self, saved_path):torch.save(self.model.state_dict(), saved_path)# 使用'model.set_state_dict'加载模型参数def load_model(self, model_path):state_dict = torch.load(model_path)self.model.load_state_dict(state_dict)

  4.3.3 模型训练

#模型训练
# 设置模型
input_size = 2
hidden_size = 5
output_size = 1
model = Model_MLP_L2_V2(input_size=input_size, hidden_size=hidden_size, output_size=output_size)# 设置损失函数
loss_fn = F.binary_cross_entropy# 设置优化器
from nndl.opitimizer import Optimizerlearning_rate = 0.2
optimizer = torch. optim.SGD(model.parameters(),learning_rate )# 设置评价指标
def accuracy(preds, labels):"""输入：- preds：预测值，二分类时，shape=[N, 1]，N为样本数量，多分类时，shape=[N, C]，C为类别数量- labels：真实标签，shape=[N, 1]输出：- 准确率：shape=[1]"""# 判断是二分类任务还是多分类任务，preds.shape[1]=1时为二分类任务，preds.shape[1]>1时为多分类任务if preds.shape[1] == 1:# 二分类时，判断每个概率值是否大于0.5，当大于0.5时，类别为1，否则类别为0# 使用'paddle.cast'将preds的数据类型转换为float32类型p=[]for i in range(len(preds)):#print(preds[i].data)#print(torch.tensor([1]))if preds[i]>0.5:p.append([1])else:p.append([0])p=torch.tensor(p)return torch.mean(torch.eq(p, labels).float())else:# 多分类时，使用'paddle.argmax'计算最大元素索引作为类别preds = torch.argmax(preds,dim=1).int()return torch.mean(torch.eq(preds, labels).float())
metric = accuracy# 其他参数
epoch_num = 1000
saved_path = 'best_model.pdparams'from nndl.dataset import make_moons# 采样1000个样本
n_samples = 1000
X, y = make_moons(n_samples=n_samples, shuffle=True, noise=0.1)num_train = 640
num_dev = 160
num_test = 200X_train, y_train = X[:num_train], y[:num_train]
X_dev, y_dev = X[num_train:num_train + num_dev], y[num_train:num_train + num_dev]
X_test, y_test = X[num_train + num_dev:], y[num_train + num_dev:]y_train = y_train.reshape([-1,1])
y_dev = y_dev.reshape([-1,1])
y_test = y_test.reshape([-1,1])# 实例化RunnerV2类，并传入训练配置
runner = RunnerV2_2(model, optimizer, metric, loss_fn)runner.train([X_train, y_train], [X_dev, y_dev], num_epochs=epoch_num, log_epochs=50, save_path="best_model.pdparams")

[Evaluate] best accuracy performence has been updated: 0.00000 --> 0.53750
[Train] epoch: 0/1000, loss: 0.6784783601760864
[Evaluate] best accuracy performence has been updated: 0.53750 --> 0.62500
[Evaluate] best accuracy performence has been updated: 0.62500 --> 0.70000
[Evaluate] best accuracy performence has been updated: 0.70000 --> 0.71250
[Evaluate] best accuracy performence has been updated: 0.71250 --> 0.72500
[Evaluate] best accuracy performence has been updated: 0.72500 --> 0.73125
[Evaluate] best accuracy performence has been updated: 0.73125 --> 0.73750
[Evaluate] best accuracy performence has been updated: 0.73750 --> 0.74375
[Evaluate] best accuracy performence has been updated: 0.74375 --> 0.75625
[Evaluate] best accuracy performence has been updated: 0.75625 --> 0.76250
[Evaluate] best accuracy performence has been updated: 0.76250 --> 0.77500
[Evaluate] best accuracy performence has been updated: 0.77500 --> 0.78125
[Evaluate] best accuracy performence has been updated: 0.78125 --> 0.78750
[Train] epoch: 50/1000, loss: 0.45302528142929077
[Evaluate] best accuracy performence has been updated: 0.78750 --> 0.79375
[Evaluate] best accuracy performence has been updated: 0.79375 --> 0.80000
[Evaluate] best accuracy performence has been updated: 0.80000 --> 0.80625
[Evaluate] best accuracy performence has been updated: 0.80625 --> 0.81250
[Evaluate] best accuracy performence has been updated: 0.81250 --> 0.81875
[Train] epoch: 100/1000, loss: 0.4056239724159241
[Evaluate] best accuracy performence has been updated: 0.81875 --> 0.82500
[Evaluate] best accuracy performence has been updated: 0.82500 --> 0.83125
[Evaluate] best accuracy performence has been updated: 0.83125 --> 0.83750
[Train] epoch: 150/1000, loss: 0.37505972385406494
[Train] epoch: 200/1000, loss: 0.35232439637184143
[Evaluate] best accuracy performence has been updated: 0.83750 --> 0.84375
[Evaluate] best accuracy performence has been updated: 0.84375 --> 0.85000
[Evaluate] best accuracy performence has been updated: 0.85000 --> 0.85625
[Train] epoch: 250/1000, loss: 0.3344670832157135
[Evaluate] best accuracy performence has been updated: 0.85625 --> 0.86250
[Evaluate] best accuracy performence has been updated: 0.86250 --> 0.86875
[Evaluate] best accuracy performence has been updated: 0.86875 --> 0.87500
[Evaluate] best accuracy performence has been updated: 0.87500 --> 0.88750
[Train] epoch: 300/1000, loss: 0.32032662630081177
[Train] epoch: 350/1000, loss: 0.3092040717601776
[Train] epoch: 400/1000, loss: 0.3005256950855255
[Train] epoch: 450/1000, loss: 0.29379481077194214
[Evaluate] best accuracy performence has been updated: 0.88750 --> 0.89375
[Train] epoch: 500/1000, loss: 0.2885972857475281
[Train] epoch: 550/1000, loss: 0.2846001982688904
[Train] epoch: 600/1000, loss: 0.2815399169921875
[Train] epoch: 650/1000, loss: 0.2792074382305145
[Train] epoch: 700/1000, loss: 0.2774360179901123
[Train] epoch: 750/1000, loss: 0.276093065738678
[Evaluate] best accuracy performence has been updated: 0.89375 --> 0.90000
[Train] epoch: 800/1000, loss: 0.275073766708374
[Train] epoch: 850/1000, loss: 0.27429693937301636
[Train] epoch: 900/1000, loss: 0.27370065450668335
[Train] epoch: 950/1000, loss: 0.27323827147483826

import matplotlib.pyplot as plt
# 可视化观察训练集与验证集的指标变化情况
def plot(runner, fig_name):plt.figure(figsize=(10, 5))epochs = [i for i in range(len(runner.train_scores))]plt.subplot(1, 2, 1)plt.plot(epochs, runner.train_loss, color='#e4007f', label="Train loss")plt.plot(epochs, runner.dev_loss, color='#f19ec2', linestyle='--', label="Dev loss")# 绘制坐标轴和图例plt.ylabel("loss", fontsize='large')plt.xlabel("epoch", fontsize='large')plt.legend(loc='upper right', fontsize='x-large')plt.subplot(1, 2, 2)plt.plot(epochs, runner.train_scores, color='#e4007f', label="Train accuracy")plt.plot(epochs, runner.dev_scores, color='#f19ec2', linestyle='--', label="Dev accuracy")# 绘制坐标轴和图例plt.ylabel("score", fontsize='large')plt.xlabel("epoch", fontsize='large')plt.legend(loc='lower right', fontsize='x-large')plt.savefig(fig_name)plt.show()plot(runner, 'fw-acc.pdf')

4.3.4 性能评价

# 模型评价
runner.load_model("best_model.pdparams")
score, loss = runner.evaluate([X_test, y_test])
print("[Test] score/loss: {:.4f}/{:.4f}".format(score, loss))

[Test] score/loss: 0.8250/0.3055

2. 增加一个3个神经元的隐藏层，再次实现二分类，并与1做对比。（必做）

class Model_MLP_L2_V2(torch.nn.Module):def __init__(self, input_size, hidden_size,hidden_size2, output_size):super(Model_MLP_L2_V2, self).__init__()# 使用'paddle.nn.Linear'定义线性层。# 其中第一个参数（in_features）为线性层输入维度；第二个参数（out_features）为线性层输出维度# weight_attr为权重参数属性，这里使用'paddle.nn.initializer.Normal'进行随机高斯分布初始化# bias_attr为偏置参数属性，这里使用'paddle.nn.initializer.Constant'进行常量初始化self.fc1 = nn.Linear(input_size, hidden_size,)nn.init.normal_(self.fc1.weight, mean=0, std=1)nn.init.constant_(self.fc1.bias,0)self.fc3=nn.Linear(hidden_size,hidden_size2)nn.init.normal_(self.fc3.weight, mean=0, std=1)nn.init.constant_(self.fc3.bias, 0)self.fc2 = nn.Linear(hidden_size2, output_size,)nn.init.normal_(self.fc2.weight, mean=0, std=1)nn.init.constant_(self.fc2.bias, 0)# 使用'paddle.nn.functional.sigmoid'定义 Logistic 激活函数self.act_fn = torch.sigmoid# 前向计算def forward(self, inputs):z1 = self.fc1(inputs)a1 = self.act_fn(z1)z3= self.fc3(a1)a3=self.act_fn(z3)z2 = self.fc2(a3)a2 = self.act_fn(z2)return a2

[Test] score/loss: 0.8600/0.4793

添加一个有4个神经元的隐层后，精确度和损失都有优化。

3. 自定义隐藏层层数和每个隐藏层中的神经元个数，尝试找到最优超参数完成二分类。可以适当修改数据集，便于探索超参数。（选做）

[Test] score/loss: 0.9200/0.2429

两层隐层，节点数分别为5，6

[Test] score/loss: 0.9250/0.2431

三层隐层，节点数位5，6，10，效果略好于两层隐层。

【思考题】对比自定义梯度计算和自动梯度计算的计算性能、计算结果，谈谈自己的看法。

自动梯度计算有很多优势。首先易于实现，出错率低。在计算性能上，自动梯度计算更快，在结果上自动梯度计算也更精确，不容易出错。如果遇到复杂的神经网络，自动梯度计算的优势更大，它可以用简洁的代码实现，如果用自定义梯度计算，实现起来就要复杂得多。

4.4 优化问题
  4.4.1 参数初始化
实现一个神经网络前，需要先初始化模型参数。

class Model_MLP_L2_V4(torch.nn.Module):def __init__(self, input_size, hidden_size, output_size):super(Model_MLP_L2_V4, self).__init__()# 使用'paddle.nn.Linear'定义线性层。# 其中in_features为线性层输入维度；out_features为线性层输出维度# weight_attr为权重参数属性# bias_attr为偏置参数属性self.fc1 = nn.Linear(input_size, hidden_size,)self.fc2 = nn.Linear(hidden_size, output_size,)torch.nn.init.constant_(self.fc1.weight,0)torch.nn.init.constant_(self.fc2.weight, 0)torch.nn.init.constant_(self.fc1.bias, 0)torch.nn.init.constant_(self.fc2.bias, 0)# 使用'paddle.nn.functional.sigmoid'定义 Logistic 激活函数self.act_fn = torch.sigmoid# 前向计算def forward(self, inputs):z1 = self.fc1(inputs)a1 = self.act_fn(z1)z2 = self.fc2(a1)a2 = self.act_fn(z2)return a2

def print_weights(runner):print('The weights of the Layers：')for item in runner.model.state_dict():print(item)print(model.state_dict()[item])

The weights of the Layers：
fc1.weight
tensor([[0., 0.],[0., 0.],[0., 0.],[0., 0.],[0., 0.]])
fc1.bias
tensor([0., 0., 0., 0., 0.])
fc2.weight
tensor([[0., 0., 0., 0., 0.]])
fc2.bias
tensor([0.])
[Evaluate] best accuracy performence has been updated: 0.00000 --> 0.49375
[Train] epoch: 0/2000, loss: 0.6931473016738892

如果对每一层的权重和偏置都用0初始化，那么通过第一遍前向计算，所有隐藏层神经元的激活值都相同；在反向传播时，所有权重的更新也都相同，这样会导致隐藏层神经元没有差异性，出现对称权重现象。

  4.4.2 梯度消失问题

在神经网络的构建过程中，随着网络层数的增加，理论上网络的拟合能力也应该是越来越好的。但是随着网络变深，参数学习更加困难，容易出现梯度消失问题。

由于Sigmoid型函数的饱和性，饱和区的导数更接近于0，误差经过每一层传递都会不断衰减。当网络层数很深时，梯度就会不停衰减，甚至消失，使得整个网络很难训练，这就是所谓的梯度消失问题。
在深度神经网络中，减轻梯度消失问题的方法有很多种，一种简单有效的方式就是使用导数比较大的激活函数，如：ReLU。

from nndl.dataset import make_moons
n_samples = 1000
X, y = make_moons(n_samples=n_samples, shuffle=True, noise=0.1)num_train = 640
num_dev = 160
num_test = 200X_train, y_train = X[:num_train], y[:num_train]
X_dev, y_dev = X[num_train:num_train + num_dev], y[num_train:num_train + num_dev]
X_test, y_test = X[num_train + num_dev:], y[num_train + num_dev:]y_train = y_train.reshape([-1,1])
y_dev = y_dev.reshape([-1,1])
y_test = y_test.reshape([-1,1])
torch.seed()
# 学习率大小
lr = 0.01# 定义网络，激活函数使用sigmoid
model =  Model_MLP_L5(input_size=2, output_size=1, act='sigmoid')# 定义优化器
optimizer = torch. optim.SGD(model.parameters(),lr )# 定义损失函数，使用交叉熵损失函数
loss_fn = F.binary_cross_entropy# 定义评价指标
metric = accuracy# 指定梯度打印函数
custom_print_log=print_grads
# 实例化Runner类
runner = RunnerV2_2(model, optimizer, metric, loss_fn)
# 启动训练
runner.train([X_train, y_train], [X_dev, y_dev],num_epochs=1, log_epochs=None,save_path="best_model.pdparams",custom_print_log=custom_print_log)

class Model_MLP_L5(torch.nn.Module):def __init__(self, input_size, output_size, act='sigmoid',w_init=torch.nn.init.normal_(torch.rand(3,3),mean=0,std=0.01),b_init=torch.nn.init.constant_(torch.rand(3,3),val=1.0)):super(Model_MLP_L5, self).__init__()self.fc1 = torch.nn.Linear(input_size, 3)self.fc2 = torch.nn.Linear(3, 3)self.fc3 = torch.nn.Linear(3, 3)self.fc4 = torch.nn.Linear(3, 3)self.fc5 = torch.nn.Linear(3, output_size)# 定义网络使用的激活函数if act == 'sigmoid':self.act = torch.sigmoidelif act == 'relu':self.act = torch.reluelif act == 'lrelu':self.act = F.leaky_reluelse:raise ValueError("Please enter sigmoid relu or lrelu!")# 初始化线性层权重和偏置参数self.init_weights(w_init, b_init)# 初始化线性层权重和偏置参数def init_weights(self, w_init, b_init):# 使用'named_sublayers'遍历所有网络层for n, m in enumerate(self.modules()):# 如果是线性层，则使用指定方式进行参数初始化if isinstance(m, nn.Linear):torch.nn.init.normal_(w_init,mean=0,std=0.01)torch.nn.init.constant_(b_init,val=1.0)def forward(self, inputs):outputs = self.fc1(inputs)outputs = self.act(outputs)outputs = self.fc2(outputs)outputs = self.act(outputs)outputs = self.fc3(outputs)outputs = self.act(outputs)outputs = self.fc4(outputs)outputs = self.act(outputs)outputs = self.fc5(outputs)outputs = torch.sigmoid(outputs)return outputs

def print_grads(runner):# 打印每一层的权重的模print('The gradient of the Layers：')for item in runner.model.named_parameters():if len(item[1])==3:print(item[0],".gard:")print(torch.mean(item[1].grad))print("=============")

The gradient of the Layers：
fc1.weight .gard:
tensor(1.6457e-06)
=============
fc1.bias .gard:
tensor(2.0551e-06)
=============
fc2.weight .gard:
tensor(1.6275e-05)
=============
fc2.bias .gard:
tensor(3.2316e-05)
=============
fc3.weight .gard:
tensor(5.5536e-05)
=============
fc3.bias .gard:
tensor(9.8989e-05)
=============
fc4.weight .gard:
tensor(-0.0003)
=============
fc4.bias .gard:
tensor(-0.0006)
=============
[Evaluate] best accuracy performence has been updated: 0.00000 --> 0.46875Process finished with exit code 0

 使用lregu激活函数后：

The gradient of the Layers：
fc1.weight .gard:
tensor(-3.8817e-06)
=============
fc1.bias .gard:
tensor(-1.2626e-05)
=============
fc2.weight .gard:
tensor(2.3137e-05)
=============
fc2.bias .gard:
tensor(5.6947e-05)
=============
fc3.weight .gard:
tensor(-6.8904e-08)
=============
fc3.bias .gard:
tensor(-0.0001)
=============
fc4.weight .gard:
tensor(-2.3767e-06)
=============
fc4.bias .gard:
tensor(-6.4036e-06)
=============
[Evaluate] best accuracy performence has been updated: 0.00000 --> 0.46875

4.4.3 死亡ReLU问题

ReLU激活函数可以一定程度上改善梯度消失问题，但是ReLU函数在某些情况下容易出现死亡 ReLU问题，使得网络难以训练。

这是由于当x<0x<0时，ReLU函数的输出恒为0。在训练过程中，如果参数在一次不恰当的更新后，某个ReLU神经元在所有训练数据上都不能被激活（即输出为0），那么这个神经元自身参数的梯度永远都会是0，在以后的训练过程中永远都不能被激活。

一种简单有效的优化方式就是将激活函数更换为Leaky ReLU、ELU等ReLU的变种。

The gradient of the Layers：
fc1.weight .gard:
tensor(0.)
=============
fc1.bias .gard:
tensor(0.)
=============
fc2.weight .gard:
tensor(0.)
=============
fc2.bias .gard:
tensor(0.)
=============
fc3.weight .gard:
tensor(0.)
=============
fc3.bias .gard:
tensor(0.0014)
=============
fc4.weight .gard:
tensor(-0.0016)
=============
fc4.bias .gard:
tensor(-0.0194)
=============
[Evaluate] best accuracy performence has been updated: 0.00000 --> 0.46875

一些梯度为0 ，出现了死亡relu现象
使用lregu激活函数后

The gradient of the Layers：
fc1.weight .gard:
tensor(4.0675e-05)
=============
fc1.bias .gard:
tensor(6.5517e-05)
=============
fc2.weight .gard:
tensor(6.5789e-06)
=============
fc2.bias .gard:
tensor(1.5382e-06)
=============
fc3.weight .gard:
tensor(-8.0225e-05)
=============
fc3.bias .gard:
tensor(-6.3153e-06)
=============
fc4.weight .gard:
tensor(4.2280e-05)
=============
fc4.bias .gard:
tensor(-0.0008)
=============
[Evaluate] best accuracy performence has been updated: 0.00000 --> 0.45000

使用lrelu后，梯度全不为0，没有出现死亡relu问题。

总结：

这次实验掌握了自动梯度计算的方法，了解到了自动梯度计算的优势。以及激活函数的优化问题，权值的初始化选择。解决梯度消失，regu死亡的方法。