Gradient Vanishing / Exploding

• Gradient Vanishing : Sigmoid Activation Function과 같이, Gradient값이 Back propagation이 되면서 소멸하는 문제를 말한다.
• Gradient Exploding : Gradient Vanishing과 반대로 Gradient 값이 너무 커져서 발산하는 것을 말한다.(Nand와 같은것)

Solution

• Change Activation Function: Sigmoid Function을 ReLU function으로 바꾼것처럼 Activation 함수를 변경해서 문제를 해결하는 것을 말한다.
• Weight Initialization: He / Xavier Initializaion처럼 weight값을 섬세하게 초기화하여 문제의 발생을 막는 것을 말한다.
• Small Learning Rate : learning rate를 줄여서 exploding을 예방해준다.
• Batch Normalization : 아래에서 다룰 예정이다. 직접적인 해결방법으로, 학습 안정확, 속도 향상에도 영향을 준다.

원인 분석

Internal Covariate Shift

• 신경망 모델에서 학습을 하면서 각 layer에서 input과 output값의 distribution정도가 다른 현상을 Covariate Shift라고 부른다. Internal Covarite Shift는 이로 인해 각 layer의 최종 값의 분포값이 처음에 의도한 input값과 매우 다른 결과를 만들어 낼때를 의미한다.
  
  

Batch Normalizaion

• 각 layer마다 normalization을 해주는 것을 의미하는데, 각 layer의 batch들을 normalize를 하여 문제를 해결해준다. 아래는 모두를 위한 딥러닝에서 제공하는 필기의 일부이다.
  

• 코드 작성시 유의 사항 : bn=torch.nn.BatchNorm1d(number)와 같은 방식으로 layer들을 선언할 때 작성해준다. Train 모델일 때는model.train()을 test를 할때에는 model.eval()을 이용해준다. 그 이유는 배치마다 mean, variance값이 다른데, eval()을 이용해주면, 훈련데이터의 배치마다 mean과 variance를 normalize를 이용하여 변하지 않는 값 learning mean과 variance 값을 이용하기 때문에 꼭 선언해줘야한다.

# Lab 10 MNIST and softmax
import torch
import torchvision.datasets as dsets
import torchvision.transforms as transforms
import matplotlib.pylab as plt

device = 'cuda' if torch.cuda.is_available() else 'cpu'

# for reproducibility
torch.manual_seed(1)
if device == 'cuda':
    torch.cuda.manual_seed_all(1)
    
# parameters
learning_rate = 0.01
training_epochs = 10
batch_size = 32

# MNIST dataset
mnist_train = dsets.MNIST(root='MNIST_data/',
                          train=True,
                          transform=transforms.ToTensor(),
                          download=True)

mnist_test = dsets.MNIST(root='MNIST_data/',
                         train=False,
                         transform=transforms.ToTensor(),
                         download=True)
                         
# dataset loader
train_loader = torch.utils.data.DataLoader(dataset=mnist_train,
                                          batch_size=batch_size,
                                          shuffle=True,
                                          drop_last=True)

test_loader = torch.utils.data.DataLoader(dataset=mnist_test,
                                          batch_size=batch_size,
                                          shuffle=False,
                                          drop_last=True)
                                          
                                          # nn layers
linear1 = torch.nn.Linear(784, 32, bias=True)
linear2 = torch.nn.Linear(32, 32, bias=True)
linear3 = torch.nn.Linear(32, 10, bias=True)
relu = torch.nn.ReLU()
bn1 = torch.nn.BatchNorm1d(32)
bn2 = torch.nn.BatchNorm1d(32)

nn_linear1 = torch.nn.Linear(784, 32, bias=True)
nn_linear2 = torch.nn.Linear(32, 32, bias=True)
nn_linear3 = torch.nn.Linear(32, 10, bias=True)

# model
bn_model = torch.nn.Sequential(linear1, bn1, relu,
                            linear2, bn2, relu,
                            linear3).to(device)
nn_model = torch.nn.Sequential(nn_linear1, relu,
                               nn_linear2, relu,
                               nn_linear3).to(device)
                               
# define cost/loss & optimizer
criterion = torch.nn.CrossEntropyLoss().to(device)    # Softmax is internally computed.
bn_optimizer = torch.optim.Adam(bn_model.parameters(), lr=learning_rate)
nn_optimizer = torch.optim.Adam(nn_model.parameters(), lr=learning_rate)

# Save Losses and Accuracies every epoch
# We are going to plot them later
train_losses = []
train_accs = []

valid_losses = []
valid_accs = []

train_total_batch = len(train_loader)
test_total_batch = len(test_loader)
for epoch in range(training_epochs):
    bn_model.train()  # set the model to train mode

    for X, Y in train_loader:
        # reshape input image into [batch_size by 784]
        # label is not one-hot encoded
        X = X.view(-1, 28 * 28).to(device)
        Y = Y.to(device)

        bn_optimizer.zero_grad()
        bn_prediction = bn_model(X)
        bn_loss = criterion(bn_prediction, Y)
        bn_loss.backward()
        bn_optimizer.step()

        nn_optimizer.zero_grad()
        nn_prediction = nn_model(X)
        nn_loss = criterion(nn_prediction, Y)
        nn_loss.backward()
        nn_optimizer.step()

    with torch.no_grad():
        bn_model.eval()     # set the model to evaluation mode

        # Test the model using train sets
        bn_loss, nn_loss, bn_acc, nn_acc = 0, 0, 0, 0
        for i, (X, Y) in enumerate(train_loader):
            X = X.view(-1, 28 * 28).to(device)
            Y = Y.to(device)

            bn_prediction = bn_model(X)
            bn_correct_prediction = torch.argmax(bn_prediction, 1) == Y
            bn_loss += criterion(bn_prediction, Y)
            bn_acc += bn_correct_prediction.float().mean()

            nn_prediction = nn_model(X)
            nn_correct_prediction = torch.argmax(nn_prediction, 1) == Y
            nn_loss += criterion(nn_prediction, Y)
            nn_acc += nn_correct_prediction.float().mean()

        bn_loss, nn_loss, bn_acc, nn_acc = bn_loss / train_total_batch, nn_loss / train_total_batch, bn_acc / train_total_batch, nn_acc / train_total_batch

        # Save train losses/acc
        train_losses.append([bn_loss, nn_loss])
        train_accs.append([bn_acc, nn_acc])
        print(
            '[Epoch %d-TRAIN] Batchnorm Loss(Acc): bn_loss:%.5f(bn_acc:%.2f) vs No Batchnorm Loss(Acc): nn_loss:%.5f(nn_acc:%.2f)' % (
            (epoch + 1), bn_loss.item(), bn_acc.item(), nn_loss.item(), nn_acc.item()))
        # Test the model using test sets
        bn_loss, nn_loss, bn_acc, nn_acc = 0, 0, 0, 0
        for i, (X, Y) in enumerate(test_loader):
            X = X.view(-1, 28 * 28).to(device)
            Y = Y.to(device)

            bn_prediction = bn_model(X)
            bn_correct_prediction = torch.argmax(bn_prediction, 1) == Y
            bn_loss += criterion(bn_prediction, Y)
            bn_acc += bn_correct_prediction.float().mean()

            nn_prediction = nn_model(X)
            nn_correct_prediction = torch.argmax(nn_prediction, 1) == Y
            nn_loss += criterion(nn_prediction, Y)
            nn_acc += nn_correct_prediction.float().mean()

        bn_loss, nn_loss, bn_acc, nn_acc = bn_loss / test_total_batch, nn_loss / test_total_batch, bn_acc / test_total_batch, nn_acc / test_total_batch

        # Save valid losses/acc
        valid_losses.append([bn_loss, nn_loss])
        valid_accs.append([bn_acc, nn_acc])
        print(
            '[Epoch %d-VALID] Batchnorm Loss(Acc): bn_loss:%.5f(bn_acc:%.2f) vs No Batchnorm Loss(Acc): nn_loss:%.5f(nn_acc:%.2f)' % (
                (epoch + 1), bn_loss.item(), bn_acc.item(), nn_loss.item(), nn_acc.item()))
        print()

print('Learning finished')

def plot_compare(loss_list: list, ylim=None, title=None) -> None:
    bn = [i[0] for i in loss_list]
    nn = [i[1] for i in loss_list]

    plt.figure(figsize=(15, 10))
    plt.plot(bn, label='With BN')
    plt.plot(nn, label='Without BN')
    if ylim:
        plt.ylim(ylim)

    if title:
        plt.title(title)
    plt.legend()
    plt.grid('on')
    plt.show()
    
#그래프 비교
plot_compare(train_losses, title='Training Loss at Epoch')
plot_compare(train_accs, [0, 1.0], title='Training Acc at Epoch')
plot_compare(valid_losses, title='Validation Loss at Epoch')
plot_compare(valid_accs, [0, 1.0], title='Validation Acc at Epoch')