딥러닝 학습 방법론 완전 정복: 최적화부터 분산 학습까지

L(theta) = (1/N) * sum_{i=1}^{N} l(f(x_i; theta), y_i)

theta_{t+1} = theta_t - lr * grad_L(theta_t)

import torch
import torch.nn as nn
import numpy as np

# 간단한 선형 회귀로 경사 하강법 구현
class LinearRegression(nn.Module):
    def __init__(self, input_dim):
        super().__init__()
        self.linear = nn.Linear(input_dim, 1)

    def forward(self, x):
        return self.linear(x)

# 데이터 생성
torch.manual_seed(42)
X = torch.randn(1000, 10)
true_w = torch.randn(10, 1)
y = X @ true_w + 0.1 * torch.randn(1000, 1)

# 미니배치 경사 하강법 구현
def train_minibatch(model, X, y, batch_size=32, lr=0.01, epochs=100):
    optimizer = torch.optim.SGD(model.parameters(), lr=lr)
    criterion = nn.MSELoss()
    losses = []

    N = len(X)
    for epoch in range(epochs):
        # 셔플
        perm = torch.randperm(N)
        X_shuffled = X[perm]
        y_shuffled = y[perm]

        epoch_loss = 0
        for i in range(0, N, batch_size):
            x_batch = X_shuffled[i:i+batch_size]
            y_batch = y_shuffled[i:i+batch_size]

            optimizer.zero_grad()
            pred = model(x_batch)
            loss = criterion(pred, y_batch)
            loss.backward()
            optimizer.step()

            epoch_loss += loss.item()

        losses.append(epoch_loss / (N // batch_size))
        if epoch % 10 == 0:
            print(f"Epoch {epoch}: Loss = {losses[-1]:.4f}")

    return losses

model = LinearRegression(10)
losses = train_minibatch(model, X, y)

forward: x -> z1=W1*x -> a1=relu(z1) -> z2=W2*a1 -> output
loss: L = MSE(output, y)

backward (chain rule):
dL/dW2 = dL/d_output * d_output/dz2 * dz2/dW2
dL/dW1 = dL/d_output * ... * da1/dz1 * dz1/dW1

# NumPy로 직접 역전파 구현
import numpy as np

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def sigmoid_deriv(x):
    s = sigmoid(x)
    return s * (1 - s)

class SimpleNet:
    def __init__(self, input_dim, hidden_dim, output_dim):
        # He 초기화
        self.W1 = np.random.randn(input_dim, hidden_dim) * np.sqrt(2/input_dim)
        self.b1 = np.zeros(hidden_dim)
        self.W2 = np.random.randn(hidden_dim, output_dim) * np.sqrt(2/hidden_dim)
        self.b2 = np.zeros(output_dim)

    def forward(self, x):
        self.x = x
        self.z1 = x @ self.W1 + self.b1
        self.a1 = sigmoid(self.z1)
        self.z2 = self.a1 @ self.W2 + self.b2
        return self.z2

    def backward(self, y, lr=0.01):
        N = len(y)
        # 출력층 그래디언트 (MSE loss)
        dL_dz2 = 2 * (self.z2 - y.reshape(-1, 1)) / N

        # W2, b2 그래디언트
        dL_dW2 = self.a1.T @ dL_dz2
        dL_db2 = dL_dz2.sum(axis=0)

        # 은닉층으로 역전파
        dL_da1 = dL_dz2 @ self.W2.T
        dL_dz1 = dL_da1 * sigmoid_deriv(self.z1)

        # W1, b1 그래디언트
        dL_dW1 = self.x.T @ dL_dz1
        dL_db1 = dL_dz1.sum(axis=0)

        # 파라미터 업데이트
        self.W2 -= lr * dL_dW2
        self.b2 -= lr * dL_db2
        self.W1 -= lr * dL_dW1
        self.b1 -= lr * dL_db1

# 테스트
net = SimpleNet(10, 32, 1)
X_np = np.random.randn(100, 10)
y_np = np.random.randn(100)

for i in range(100):
    pred = net.forward(X_np)
    loss = np.mean((pred.flatten() - y_np) ** 2)
    net.backward(y_np)
    if i % 20 == 0:
        print(f"Step {i}: MSE = {loss:.4f}")

v_t = beta * v_{t-1} + (1 - beta) * grad_t
theta_{t+1} = theta_t - lr * v_t

import torch
import torch.nn as nn

# Momentum SGD
optimizer_momentum = torch.optim.SGD(
    model.parameters(),
    lr=0.01,
    momentum=0.9,
    nesterov=False  # Nesterov Momentum 사용 여부
)

# Nesterov Momentum (NAG) - 더 정확한 방향 예측
optimizer_nag = torch.optim.SGD(
    model.parameters(),
    lr=0.01,
    momentum=0.9,
    nesterov=True
)

G_t = G_{t-1} + grad_t^2
theta_{t+1} = theta_t - (lr / sqrt(G_t + epsilon)) * grad_t

optimizer_adagrad = torch.optim.Adagrad(
    model.parameters(),
    lr=0.01,
    eps=1e-8,
    weight_decay=0
)

E[g^2]_t = rho * E[g^2]_{t-1} + (1 - rho) * grad_t^2
theta_{t+1} = theta_t - (lr / sqrt(E[g^2]_t + epsilon)) * grad_t

optimizer_rmsprop = torch.optim.RMSprop(
    model.parameters(),
    lr=0.001,
    alpha=0.99,  # rho (decay factor)
    eps=1e-8,
    momentum=0,
    centered=False
)

m_t = beta1 * m_{t-1} + (1 - beta1) * g_t        # 1차 모멘트 (편향 보정 전)
v_t = beta2 * v_{t-1} + (1 - beta2) * g_t^2      # 2차 모멘트 (편향 보정 전)

m_hat = m_t / (1 - beta1^t)                        # 편향 보정
v_hat = v_t / (1 - beta2^t)                        # 편향 보정

theta_{t+1} = theta_t - lr * m_hat / (sqrt(v_hat) + epsilon)

optimizer_adam = torch.optim.Adam(
    model.parameters(),
    lr=1e-3,
    betas=(0.9, 0.999),
    eps=1e-8,
    weight_decay=0
)

theta_{t+1} = theta_t - lr * (m_hat / (sqrt(v_hat) + epsilon) + lambda * theta_t)

optimizer_adamw = torch.optim.AdamW(
    model.parameters(),
    lr=1e-4,
    betas=(0.9, 0.999),
    eps=1e-8,
    weight_decay=0.01  # L2 정규화 강도
)

LARS: lr_l = lr * ||w_l|| / (||g_l|| + lambda * ||w_l||)
LAMB: Adam 업데이트에 레이어별 신뢰 비율 적용

# pip install lars (또는 직접 구현)
# LAMB는 Hugging Face transformers에 포함
from transformers import optimization

# LAMB optimizer (transformers 라이브러리 활용)
# 또는 apex 라이브러리의 FusedLAMB 사용

class Lion(torch.optim.Optimizer):
    def __init__(self, params, lr=1e-4, betas=(0.9, 0.99), weight_decay=0.0):
        defaults = dict(lr=lr, betas=betas, weight_decay=weight_decay)
        super().__init__(params, defaults)

    def step(self, closure=None):
        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()

        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue

                grad = p.grad
                lr = group['lr']
                beta1, beta2 = group['betas']
                wd = group['weight_decay']

                state = self.state[p]
                if len(state) == 0:
                    state['exp_avg'] = torch.zeros_like(p)

                exp_avg = state['exp_avg']

                # Lion 업데이트
                update = exp_avg * beta1 + grad * (1 - beta1)
                p.data.mul_(1 - lr * wd)
                p.data.add_(update.sign_(), alpha=-lr)

                # 모멘텀 업데이트
                exp_avg.mul_(beta2).add_(grad, alpha=1 - beta2)

        return loss

import torch
import torch.nn as nn
import matplotlib.pyplot as plt

# 간단한 모델로 옵티마이저 비교
class MLP(nn.Module):
    def __init__(self):
        super().__init__()
        self.net = nn.Sequential(
            nn.Linear(2, 64),
            nn.ReLU(),
            nn.Linear(64, 64),
            nn.ReLU(),
            nn.Linear(64, 1)
        )

    def forward(self, x):
        return self.net(x)

def train_and_compare(optimizers_dict, X, y, epochs=200):
    results = {}

    for name, opt_fn in optimizers_dict.items():
        model = MLP()
        optimizer = opt_fn(model.parameters())
        criterion = nn.MSELoss()
        losses = []

        for epoch in range(epochs):
            optimizer.zero_grad()
            pred = model(X)
            loss = criterion(pred, y)
            loss.backward()
            optimizer.step()
            losses.append(loss.item())

        results[name] = losses
        print(f"{name}: Final Loss = {losses[-1]:.4f}")

    return results

# 데이터 생성
X = torch.randn(500, 2)
y = (X[:, 0] * 2 + X[:, 1] * 3 + torch.randn(500) * 0.1).unsqueeze(1)

optimizers = {
    'SGD': lambda p: torch.optim.SGD(p, lr=0.01),
    'SGD+Momentum': lambda p: torch.optim.SGD(p, lr=0.01, momentum=0.9),
    'Adam': lambda p: torch.optim.Adam(p, lr=0.001),
    'AdamW': lambda p: torch.optim.AdamW(p, lr=0.001, weight_decay=0.01),
    'RMSprop': lambda p: torch.optim.RMSprop(p, lr=0.001),
}

results = train_and_compare(optimizers, X, y)

import torch
import torch.optim as optim

model = MLP()
optimizer = optim.SGD(model.parameters(), lr=0.1)

# Step Decay: 일정 에폭마다 학습률을 gamma배로 감소
step_scheduler = optim.lr_scheduler.StepLR(
    optimizer,
    step_size=30,   # 30 에폭마다
    gamma=0.1       # 10배 감소
)

# MultiStep Decay: 지정된 에폭에서 감소
multistep_scheduler = optim.lr_scheduler.MultiStepLR(
    optimizer,
    milestones=[30, 60, 80],
    gamma=0.1
)

# Exponential Decay: 매 에폭마다 지수적으로 감소
exp_scheduler = optim.lr_scheduler.ExponentialLR(
    optimizer,
    gamma=0.95  # 매 에폭 5% 감소
)

# Cosine Annealing
cosine_scheduler = optim.lr_scheduler.CosineAnnealingLR(
    optimizer,
    T_max=100,      # 주기 (에폭 수)
    eta_min=1e-6    # 최소 학습률
)

# Cosine Annealing with Warm Restarts (SGDR)
cosine_restart = optim.lr_scheduler.CosineAnnealingWarmRestarts(
    optimizer,
    T_0=10,     # 초기 주기
    T_mult=2,   # 주기 배수
    eta_min=1e-6
)

import math
from torch.optim.lr_scheduler import LambdaLR

def get_cosine_schedule_with_warmup(optimizer, num_warmup_steps, num_training_steps, num_cycles=0.5):
    def lr_lambda(current_step):
        # Warmup 구간
        if current_step < num_warmup_steps:
            return float(current_step) / float(max(1, num_warmup_steps))

        # Cosine 감소 구간
        progress = float(current_step - num_warmup_steps) / float(
            max(1, num_training_steps - num_warmup_steps)
        )
        return max(0.0, 0.5 * (1.0 + math.cos(math.pi * float(num_cycles) * 2.0 * progress)))

    return LambdaLR(optimizer, lr_lambda)

# 사용 예시
optimizer = optim.AdamW(model.parameters(), lr=5e-5)
scheduler = get_cosine_schedule_with_warmup(
    optimizer,
    num_warmup_steps=1000,
    num_training_steps=10000
)

optimizer = optim.SGD(model.parameters(), lr=0.01)
scheduler = optim.lr_scheduler.OneCycleLR(
    optimizer,
    max_lr=0.1,
    steps_per_epoch=len(train_loader),
    epochs=10,
    pct_start=0.3,          # warmup 비율
    anneal_strategy='cos',  # 감소 방식
    div_factor=25.0,        # 초기 lr = max_lr / div_factor
    final_div_factor=1e4    # 최종 lr = max_lr / (div_factor * final_div_factor)
)

# 학습 루프
for epoch in range(10):
    for batch in train_loader:
        optimizer.zero_grad()
        loss = criterion(model(batch[0]), batch[1])
        loss.backward()
        optimizer.step()
        scheduler.step()  # OneCycleLR은 배치마다 호출

from torch_lr_finder import LRFinder

model = MLP()
optimizer = optim.SGD(model.parameters(), lr=1e-7, weight_decay=1e-2)
criterion = nn.MSELoss()

# LR Finder 실행
lr_finder = LRFinder(model, optimizer, criterion, device="cuda")
lr_finder.range_test(train_loader, end_lr=100, num_iter=100)
lr_finder.plot()  # 손실-학습률 그래프 표시
lr_finder.reset()  # 옵티마이저를 초기 상태로 복원

# 그래프에서 손실이 가장 가파르게 하락하는 지점의 학습률을 선택
# 일반적으로 최솟값의 1/10 ~ 1/3 정도를 사용

import torch
import torch.nn as nn
import torch.nn.functional as F

# MSE (Mean Squared Error) - 이상치에 민감
mse_loss = nn.MSELoss()

# MAE (Mean Absolute Error) - 이상치에 강건
mae_loss = nn.L1Loss()

# Huber Loss - MSE와 MAE의 절충점
# |y - y_hat| < delta: 0.5 * (y - y_hat)^2
# |y - y_hat| >= delta: delta * (|y - y_hat| - 0.5 * delta)
huber_loss = nn.HuberLoss(delta=1.0)

# 직접 구현
def huber_loss_manual(pred, target, delta=1.0):
    residual = torch.abs(pred - target)
    condition = residual < delta
    squared_loss = 0.5 * residual ** 2
    linear_loss = delta * residual - 0.5 * delta ** 2
    return torch.where(condition, squared_loss, linear_loss).mean()

# Cross-Entropy Loss (다중 분류)
ce_loss = nn.CrossEntropyLoss()

# Binary Cross-Entropy (이진 분류)
bce_loss = nn.BCEWithLogitsLoss()

# Label Smoothing Cross-Entropy (과적합 방지)
ce_smooth = nn.CrossEntropyLoss(label_smoothing=0.1)

# Focal Loss (클래스 불균형 해결)
class FocalLoss(nn.Module):
    def __init__(self, gamma=2.0, alpha=None, reduction='mean'):
        super().__init__()
        self.gamma = gamma
        self.alpha = alpha
        self.reduction = reduction

    def forward(self, inputs, targets):
        # inputs: (N, C) logits, targets: (N,) class indices
        ce_loss = F.cross_entropy(inputs, targets, reduction='none')
        pt = torch.exp(-ce_loss)  # p_t = 모델이 정답 클래스에 할당한 확률
        focal_loss = ((1 - pt) ** self.gamma) * ce_loss

        if self.alpha is not None:
            alpha_t = self.alpha[targets]
            focal_loss = alpha_t * focal_loss

        if self.reduction == 'mean':
            return focal_loss.mean()
        elif self.reduction == 'sum':
            return focal_loss.sum()
        return focal_loss

# BCE Loss for binary segmentation
def bce_loss(pred, target):
    return F.binary_cross_entropy_with_logits(pred, target)

# Dice Loss (클래스 불균형에 강건)
def dice_loss(pred, target, smooth=1.0):
    pred = torch.sigmoid(pred)
    pred_flat = pred.view(-1)
    target_flat = target.view(-1)

    intersection = (pred_flat * target_flat).sum()
    dice = (2. * intersection + smooth) / (pred_flat.sum() + target_flat.sum() + smooth)
    return 1 - dice

# BCE + Dice 결합 (세그멘테이션에서 자주 사용)
def bce_dice_loss(pred, target, bce_weight=0.5):
    bce = bce_loss(pred, target)
    dice = dice_loss(pred, target)
    return bce_weight * bce + (1 - bce_weight) * dice

# Contrastive Loss (유사한 샘플은 가깝게, 다른 샘플은 멀게)
class ContrastiveLoss(nn.Module):
    def __init__(self, margin=1.0):
        super().__init__()
        self.margin = margin

    def forward(self, output1, output2, label):
        # label=1: 같은 클래스, label=0: 다른 클래스
        euclidean_dist = F.pairwise_distance(output1, output2)
        loss = (label * euclidean_dist.pow(2) +
                (1 - label) * F.relu(self.margin - euclidean_dist).pow(2))
        return loss.mean()

# Triplet Loss (anchor, positive, negative)
class TripletLoss(nn.Module):
    def __init__(self, margin=0.3):
        super().__init__()
        self.margin = margin

    def forward(self, anchor, positive, negative):
        pos_dist = F.pairwise_distance(anchor, positive)
        neg_dist = F.pairwise_distance(anchor, negative)
        loss = F.relu(pos_dist - neg_dist + self.margin)
        return loss.mean()

# L2 Regularization (Weight Decay)
optimizer = torch.optim.Adam(model.parameters(), lr=1e-3, weight_decay=1e-4)

# L1 Regularization (직접 구현)
def l1_regularization(model, lambda_l1):
    l1_penalty = 0
    for param in model.parameters():
        l1_penalty += torch.abs(param).sum()
    return lambda_l1 * l1_penalty

# L1 + L2 (Elastic Net)
def elastic_net_loss(model, criterion, outputs, targets, lambda_l1=1e-5, lambda_l2=1e-4):
    # 기본 손실
    base_loss = criterion(outputs, targets)

    # L1 패널티
    l1_penalty = sum(torch.abs(p).sum() for p in model.parameters())

    # L2 패널티
    l2_penalty = sum((p ** 2).sum() for p in model.parameters())

    return base_loss + lambda_l1 * l1_penalty + lambda_l2 * l2_penalty

class ModelWithDropout(nn.Module):
    def __init__(self, dropout_rate=0.5):
        super().__init__()
        self.net = nn.Sequential(
            nn.Linear(784, 512),
            nn.ReLU(),
            nn.Dropout(p=dropout_rate),  # Inverted Dropout (PyTorch 기본)
            nn.Linear(512, 256),
            nn.ReLU(),
            nn.Dropout(p=dropout_rate),
            nn.Linear(256, 10)
        )

    def forward(self, x):
        return self.net(x)

# 학습 모드: dropout 활성화
model.train()

# 추론 모드: dropout 비활성화
model.eval()

# DropConnect (가중치를 무작위로 0으로 설정)
class DropConnect(nn.Module):
    def __init__(self, p=0.5):
        super().__init__()
        self.p = p

    def forward(self, x):
        if not self.training:
            return x
        # 가중치 마스킹은 nn.Linear 레이어 수준에서 적용
        mask = torch.bernoulli(torch.ones_like(x) * (1 - self.p))
        return x * mask / (1 - self.p)

from torchvision import transforms
import torchvision.transforms.functional as TF

# 기본 이미지 증강
train_transform = transforms.Compose([
    transforms.RandomHorizontalFlip(p=0.5),
    transforms.RandomCrop(32, padding=4),
    transforms.ColorJitter(brightness=0.2, contrast=0.2, saturation=0.2, hue=0.1),
    transforms.RandomRotation(degrees=15),
    transforms.ToTensor(),
    transforms.Normalize(mean=[0.485, 0.456, 0.406], std=[0.229, 0.224, 0.225])
])

# Mixup Augmentation
def mixup_data(x, y, alpha=1.0):
    if alpha > 0:
        lam = np.random.beta(alpha, alpha)
    else:
        lam = 1

    batch_size = x.size()[0]
    index = torch.randperm(batch_size)

    mixed_x = lam * x + (1 - lam) * x[index]
    y_a, y_b = y, y[index]
    return mixed_x, y_a, y_b, lam

def mixup_criterion(criterion, pred, y_a, y_b, lam):
    return lam * criterion(pred, y_a) + (1 - lam) * criterion(pred, y_b)

# CutMix Augmentation
def cutmix_data(x, y, alpha=1.0):
    lam = np.random.beta(alpha, alpha)
    batch_size, C, H, W = x.size()
    index = torch.randperm(batch_size)

    # 랜덤 박스 좌표 계산
    cut_ratio = np.sqrt(1. - lam)
    cut_w = int(W * cut_ratio)
    cut_h = int(H * cut_ratio)

    cx = np.random.randint(W)
    cy = np.random.randint(H)

    bbx1 = np.clip(cx - cut_w // 2, 0, W)
    bby1 = np.clip(cy - cut_h // 2, 0, H)
    bbx2 = np.clip(cx + cut_w // 2, 0, W)
    bby2 = np.clip(cy + cut_h // 2, 0, H)

    mixed_x = x.clone()
    mixed_x[:, :, bby1:bby2, bbx1:bbx2] = x[index, :, bby1:bby2, bbx1:bbx2]

    # 실제 박스 크기에 맞게 lambda 재계산
    lam = 1 - ((bbx2 - bbx1) * (bby2 - bby1) / (W * H))

    return mixed_x, y, y[index], lam

class EarlyStopping:
    def __init__(self, patience=10, min_delta=0.001, restore_best_weights=True):
        self.patience = patience
        self.min_delta = min_delta
        self.restore_best_weights = restore_best_weights
        self.counter = 0
        self.best_loss = None
        self.best_weights = None
        self.early_stop = False

    def __call__(self, val_loss, model):
        if self.best_loss is None:
            self.best_loss = val_loss
            self.best_weights = {k: v.clone() for k, v in model.state_dict().items()}
        elif val_loss > self.best_loss - self.min_delta:
            self.counter += 1
            print(f"EarlyStopping counter: {self.counter}/{self.patience}")
            if self.counter >= self.patience:
                self.early_stop = True
        else:
            self.best_loss = val_loss
            self.best_weights = {k: v.clone() for k, v in model.state_dict().items()}
            self.counter = 0

    def restore(self, model):
        if self.restore_best_weights and self.best_weights:
            model.load_state_dict(self.best_weights)
            print("Restored best model weights")

# 사용 예시
early_stopping = EarlyStopping(patience=10)

for epoch in range(max_epochs):
    train_loss = train_one_epoch(model, train_loader, optimizer)
    val_loss = evaluate(model, val_loader)

    early_stopping(val_loss, model)
    if early_stopping.early_stop:
        print("Early stopping triggered!")
        early_stopping.restore(model)
        break

1. 미니배치 평균: mu_B = (1/m) * sum(x_i)
2. 미니배치 분산: sigma_B^2 = (1/m) * sum((x_i - mu_B)^2)
3. 정규화: x_hat_i = (x_i - mu_B) / sqrt(sigma_B^2 + epsilon)
4. 스케일 및 이동: y_i = gamma * x_hat_i + beta

import torch
import torch.nn as nn

class BatchNormNet(nn.Module):
    def __init__(self):
        super().__init__()
        self.net = nn.Sequential(
            nn.Linear(784, 512),
            nn.BatchNorm1d(512),
            nn.ReLU(),
            nn.Linear(512, 256),
            nn.BatchNorm1d(256),
            nn.ReLU(),
            nn.Linear(256, 10)
        )

    def forward(self, x):
        return self.net(x)

# Conv 레이어에서 BatchNorm 사용
class ConvBNNet(nn.Module):
    def __init__(self):
        super().__init__()
        self.conv1 = nn.Conv2d(3, 64, 3, padding=1)
        self.bn1 = nn.BatchNorm2d(64)
        self.relu = nn.ReLU(inplace=True)

    def forward(self, x):
        return self.relu(self.bn1(self.conv1(x)))

# 직접 구현
class BatchNorm(nn.Module):
    def __init__(self, num_features, eps=1e-5, momentum=0.1):
        super().__init__()
        self.gamma = nn.Parameter(torch.ones(num_features))
        self.beta = nn.Parameter(torch.zeros(num_features))
        self.eps = eps
        self.momentum = momentum

        self.register_buffer('running_mean', torch.zeros(num_features))
        self.register_buffer('running_var', torch.ones(num_features))

    def forward(self, x):
        if self.training:
            mean = x.mean(dim=0)
            var = x.var(dim=0, unbiased=False)

            # 이동 평균 업데이트
            self.running_mean = (1 - self.momentum) * self.running_mean + self.momentum * mean
            self.running_var = (1 - self.momentum) * self.running_var + self.momentum * var
        else:
            mean = self.running_mean
            var = self.running_var

        x_norm = (x - mean) / torch.sqrt(var + self.eps)
        return self.gamma * x_norm + self.beta

class LayerNorm(nn.Module):
    def __init__(self, normalized_shape, eps=1e-5):
        super().__init__()
        if isinstance(normalized_shape, int):
            normalized_shape = (normalized_shape,)
        self.normalized_shape = normalized_shape
        self.gamma = nn.Parameter(torch.ones(normalized_shape))
        self.beta = nn.Parameter(torch.zeros(normalized_shape))
        self.eps = eps

    def forward(self, x):
        # 마지막 len(normalized_shape)개 차원에서 정규화
        mean = x.mean(dim=-1, keepdim=True)
        var = x.var(dim=-1, keepdim=True, unbiased=False)
        x_norm = (x - mean) / torch.sqrt(var + self.eps)
        return self.gamma * x_norm + self.beta

# PyTorch 내장 LayerNorm
layer_norm = nn.LayerNorm(512)

# Transformer 블록에서 사용
class TransformerBlock(nn.Module):
    def __init__(self, d_model, nhead, dim_feedforward):
        super().__init__()
        self.attention = nn.MultiheadAttention(d_model, nhead)
        self.norm1 = nn.LayerNorm(d_model)
        self.norm2 = nn.LayerNorm(d_model)
        self.ffn = nn.Sequential(
            nn.Linear(d_model, dim_feedforward),
            nn.GELU(),
            nn.Linear(dim_feedforward, d_model)
        )

    def forward(self, x):
        # Pre-LayerNorm (최신 GPT 스타일)
        attn_out, _ = self.attention(self.norm1(x), self.norm1(x), self.norm1(x))
        x = x + attn_out
        x = x + self.ffn(self.norm2(x))
        return x

# Instance Normalization (각 샘플, 각 채널 독립적으로 정규화)
# 스타일 전이(Style Transfer)에 효과적
instance_norm = nn.InstanceNorm2d(64)

# Group Normalization (채널을 그룹으로 나누어 정규화)
# 배치 크기가 작을 때 BN 대안
group_norm = nn.GroupNorm(num_groups=8, num_channels=64)

# RMS Normalization (LLaMA, T5에서 사용)
# LayerNorm에서 평균 제거, 학습 속도 향상
class RMSNorm(nn.Module):
    def __init__(self, dim, eps=1e-6):
        super().__init__()
        self.eps = eps
        self.weight = nn.Parameter(torch.ones(dim))

    def _norm(self, x):
        return x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps)

    def forward(self, x):
        return self.weight * self._norm(x.float()).type_as(x)

# 정규화 방법 비교 요약
# BatchNorm: 배치 차원 정규화, CNN에 적합, 배치 크기에 의존
# LayerNorm: 특성 차원 정규화, Transformer/RNN에 적합
# InstanceNorm: 채널별 정규화, 스타일 전이에 적합
# GroupNorm: 채널 그룹 정규화, 작은 배치에 적합
# RMSNorm: 경량화된 LayerNorm, LLM에 적합

import torch
import torch.nn as nn
import math

class WeightInitDemo(nn.Module):
    def __init__(self, init_method='xavier'):
        super().__init__()
        self.layers = nn.ModuleList([
            nn.Linear(256, 256) for _ in range(5)
        ])
        self.apply_init(init_method)

    def apply_init(self, method):
        for layer in self.layers:
            if method == 'zeros':
                nn.init.zeros_(layer.weight)  # 나쁜 초기화: 대칭성 문제
            elif method == 'random_small':
                nn.init.normal_(layer.weight, std=0.01)
            elif method == 'xavier_uniform':
                nn.init.xavier_uniform_(layer.weight)  # sigmoid/tanh 활성화에 적합
            elif method == 'xavier_normal':
                nn.init.xavier_normal_(layer.weight)
            elif method == 'kaiming_uniform':
                nn.init.kaiming_uniform_(layer.weight, mode='fan_in', nonlinearity='relu')
            elif method == 'kaiming_normal':
                nn.init.kaiming_normal_(layer.weight, mode='fan_out', nonlinearity='relu')  # ReLU에 적합
            nn.init.zeros_(layer.bias)

    def forward(self, x):
        for layer in self.layers:
            x = torch.relu(layer(x))
        return x

# 초기화 비교 실험
import matplotlib.pyplot as plt

def check_activations(model, x):
    activations = []
    hooks = []

    def hook(module, input, output):
        activations.append(output.detach())

    for layer in model.layers:
        hooks.append(layer.register_forward_hook(hook))

    with torch.no_grad():
        model(x)

    for hook in hooks:
        hook.remove()

    return activations

x = torch.randn(100, 256)
for method in ['zeros', 'random_small', 'xavier_uniform', 'kaiming_normal']:
    model = WeightInitDemo(method)
    acts = check_activations(model, x)
    print(f"{method}:")
    for i, act in enumerate(acts):
        print(f"  Layer {i+1}: mean={act.mean():.4f}, std={act.std():.4f}")

# Gradient Clipping
import torch.nn.utils as utils

# 방법 1: 기울기 노름(norm) 클리핑
max_norm = 1.0
total_norm = utils.clip_grad_norm_(model.parameters(), max_norm)
print(f"Gradient norm: {total_norm:.4f}")

# 방법 2: 기울기 값 클리핑
utils.clip_grad_value_(model.parameters(), clip_value=0.5)

# 학습 루프에서의 사용
optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)

for batch in train_loader:
    optimizer.zero_grad()
    loss = criterion(model(batch[0]), batch[1])
    loss.backward()

    # 역전파 후, 옵티마이저 step 전에 클리핑
    torch.nn.utils.clip_grad_norm_(model.parameters(), max_norm=1.0)

    optimizer.step()

class ResidualBlock(nn.Module):
    def __init__(self, in_channels, out_channels, stride=1):
        super().__init__()
        self.conv1 = nn.Conv2d(in_channels, out_channels, 3, stride=stride, padding=1, bias=False)
        self.bn1 = nn.BatchNorm2d(out_channels)
        self.relu = nn.ReLU(inplace=True)
        self.conv2 = nn.Conv2d(out_channels, out_channels, 3, padding=1, bias=False)
        self.bn2 = nn.BatchNorm2d(out_channels)

        # 차원이 다를 경우 shortcut
        self.shortcut = nn.Sequential()
        if stride != 1 or in_channels != out_channels:
            self.shortcut = nn.Sequential(
                nn.Conv2d(in_channels, out_channels, 1, stride=stride, bias=False),
                nn.BatchNorm2d(out_channels)
            )

    def forward(self, x):
        out = self.relu(self.bn1(self.conv1(x)))
        out = self.bn2(self.conv2(out))
        out += self.shortcut(x)  # Skip Connection
        out = self.relu(out)
        return out

from torch.utils.checkpoint import checkpoint, checkpoint_sequential

class DeepModel(nn.Module):
    def __init__(self):
        super().__init__()
        self.layers = nn.Sequential(*[
            nn.Sequential(nn.Linear(512, 512), nn.ReLU())
            for _ in range(20)
        ])

    def forward(self, x):
        # 일반: 모든 활성화 저장 (메모리 O(N))
        # return self.layers(x)

        # Gradient Checkpointing: 메모리 O(sqrt(N))
        return checkpoint_sequential(self.layers, segments=5, input=x)

import torchvision.models as models

# Feature Extraction: 사전학습 가중치 동결
def feature_extraction(num_classes):
    model = models.resnet50(pretrained=True)

    # 모든 파라미터 동결
    for param in model.parameters():
        param.requires_grad = False

    # 마지막 분류 레이어만 교체 (학습 가능)
    model.fc = nn.Linear(model.fc.in_features, num_classes)

    return model

# Fine-tuning: 일부 또는 전체 레이어 학습
def fine_tuning(num_classes, unfreeze_layers=None):
    model = models.resnet50(pretrained=True)

    # 처음에는 모두 동결
    for param in model.parameters():
        param.requires_grad = False

    # 마지막 레이어 교체 및 활성화
    model.fc = nn.Linear(model.fc.in_features, num_classes)

    # 지정된 레이어 활성화
    if unfreeze_layers:
        for name, param in model.named_parameters():
            for layer in unfreeze_layers:
                if layer in name:
                    param.requires_grad = True

    return model

def progressive_unfreezing_setup(model, base_lr=1e-4):
    # ResNet50의 레이어 그룹
    layer_groups = [
        list(model.layer1.parameters()),
        list(model.layer2.parameters()),
        list(model.layer3.parameters()),
        list(model.layer4.parameters()),
        list(model.fc.parameters())
    ]

    # 처음에는 fc만 학습
    for group in layer_groups[:-1]:
        for p in group:
            p.requires_grad = False

    return layer_groups

def discriminative_lr_optimizer(model, base_lr=1e-4, lr_multiplier=10):
    # 레이어별 다른 학습률 설정 (초기 레이어는 낮은 lr, 후기 레이어는 높은 lr)
    param_groups = [
        {'params': model.layer1.parameters(), 'lr': base_lr / (lr_multiplier**3)},
        {'params': model.layer2.parameters(), 'lr': base_lr / (lr_multiplier**2)},
        {'params': model.layer3.parameters(), 'lr': base_lr / lr_multiplier},
        {'params': model.layer4.parameters(), 'lr': base_lr},
        {'params': model.fc.parameters(), 'lr': base_lr * lr_multiplier},
    ]

    return torch.optim.Adam(param_groups)

import torch
import torch.nn as nn

class LoRALayer(nn.Module):
    def __init__(self, in_features, out_features, rank=4, alpha=1.0):
        super().__init__()
        self.rank = rank
        self.alpha = alpha
        self.scaling = alpha / rank

        # 원래 가중치 (동결)
        self.weight = nn.Parameter(
            torch.randn(out_features, in_features),
            requires_grad=False
        )

        # LoRA 행렬 A (랜덤 초기화)
        self.lora_A = nn.Parameter(torch.randn(rank, in_features) * 0.01)
        # LoRA 행렬 B (0으로 초기화 -> 학습 시작 시 원래 모델과 동일)
        self.lora_B = nn.Parameter(torch.zeros(out_features, rank))
        self.bias = nn.Parameter(torch.zeros(out_features))

    def forward(self, x):
        # 원래 출력 + LoRA 변화량
        base_output = nn.functional.linear(x, self.weight, self.bias)
        lora_output = (x @ self.lora_A.T @ self.lora_B.T) * self.scaling
        return base_output + lora_output

# HuggingFace PEFT 라이브러리 사용 (실제 LLM 파인튜닝)
from peft import get_peft_model, LoraConfig, TaskType

lora_config = LoraConfig(
    task_type=TaskType.CAUSAL_LM,
    r=8,                          # LoRA 랭크
    lora_alpha=32,                # 스케일링 팩터
    target_modules=["q_proj", "v_proj"],  # 적용할 모듈
    lora_dropout=0.05,
    bias="none"
)

# peft_model = get_peft_model(base_model, lora_config)
# peft_model.print_trainable_parameters()
# trainable params: 4,194,304 || all params: 6,742,609,920 || trainable%: 0.062

import optuna
import torch
import torch.nn as nn

def objective(trial):
    # 하이퍼파라미터 탐색 공간 정의
    lr = trial.suggest_float('lr', 1e-5, 1e-1, log=True)
    n_layers = trial.suggest_int('n_layers', 1, 5)
    n_units = trial.suggest_categorical('n_units', [64, 128, 256, 512])
    dropout_rate = trial.suggest_float('dropout', 0.0, 0.5)
    optimizer_name = trial.suggest_categorical('optimizer', ['Adam', 'AdamW', 'SGD'])

    # 모델 생성
    layers = []
    in_dim = 784
    for _ in range(n_layers):
        layers.extend([
            nn.Linear(in_dim, n_units),
            nn.ReLU(),
            nn.Dropout(dropout_rate)
        ])
        in_dim = n_units
    layers.append(nn.Linear(in_dim, 10))
    model = nn.Sequential(*layers)

    # 옵티마이저 선택
    if optimizer_name == 'Adam':
        optimizer = torch.optim.Adam(model.parameters(), lr=lr)
    elif optimizer_name == 'AdamW':
        optimizer = torch.optim.AdamW(model.parameters(), lr=lr, weight_decay=0.01)
    else:
        optimizer = torch.optim.SGD(model.parameters(), lr=lr, momentum=0.9)

    # 학습 및 검증
    # ... (학습 루프 생략)
    val_accuracy = 0.95  # 실제로는 학습 후 계산

    return val_accuracy

# Optuna 스터디 생성 및 실행
study = optuna.create_study(
    direction='maximize',
    sampler=optuna.samplers.TPESampler(),    # Tree-structured Parzen Estimator
    pruner=optuna.pruners.MedianPruner()     # 성능 나쁜 트라이얼 조기 종료
)

study.optimize(objective, n_trials=100, timeout=3600)

print(f"Best trial: {study.best_trial.value:.4f}")
print(f"Best params: {study.best_trial.params}")

# 결과 시각화
# optuna.visualization.plot_optimization_history(study)
# optuna.visualization.plot_param_importances(study)

import torch
from torch.cuda.amp import autocast, GradScaler

# GradScaler: FP16 언더플로우 방지를 위한 손실 스케일링
scaler = GradScaler()

model = MyModel().cuda()
optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)
criterion = nn.CrossEntropyLoss()

for epoch in range(num_epochs):
    for inputs, labels in train_loader:
        inputs, labels = inputs.cuda(), labels.cuda()

        optimizer.zero_grad()

        # autocast 컨텍스트에서 FP16 연산
        with autocast(dtype=torch.float16):
            outputs = model(inputs)
            loss = criterion(outputs, labels)

        # 손실 스케일링 후 역전파
        scaler.scale(loss).backward()

        # 그래디언트 클리핑 (스케일 조정 후)
        scaler.unscale_(optimizer)
        torch.nn.utils.clip_grad_norm_(model.parameters(), max_norm=1.0)

        # 옵티마이저 스텝 (NaN/Inf 그래디언트 자동 건너뜀)
        scaler.step(optimizer)
        scaler.update()

# BF16 사용 (더 안정적, Ampere 이상 GPU 필요)
with autocast(dtype=torch.bfloat16):
    outputs = model(inputs)
    loss = criterion(outputs, labels)

import torch
import torch.nn as nn
import torch.distributed as dist
from torch.nn.parallel import DistributedDataParallel as DDP
from torch.utils.data.distributed import DistributedSampler

def setup(rank, world_size):
    import os
    os.environ['MASTER_ADDR'] = 'localhost'
    os.environ['MASTER_PORT'] = '12355'
    dist.init_process_group('nccl', rank=rank, world_size=world_size)

def cleanup():
    dist.destroy_process_group()

def train_ddp(rank, world_size, model_class, dataset):
    setup(rank, world_size)

    # 각 프로세스가 자신의 GPU 사용
    device = torch.device(f'cuda:{rank}')
    model = model_class().to(device)

    # DDP로 감싸기
    model = DDP(model, device_ids=[rank])

    # DistributedSampler: 각 프로세스가 다른 데이터 샘플링
    sampler = DistributedSampler(
        dataset,
        num_replicas=world_size,
        rank=rank,
        shuffle=True
    )

    loader = torch.utils.data.DataLoader(
        dataset,
        batch_size=32,
        sampler=sampler,
        num_workers=4,
        pin_memory=True
    )

    optimizer = torch.optim.Adam(model.parameters(), lr=1e-3 * world_size)
    criterion = nn.CrossEntropyLoss()

    for epoch in range(num_epochs):
        sampler.set_epoch(epoch)  # 에폭마다 셔플 시드 변경

        for inputs, labels in loader:
            inputs, labels = inputs.to(device), labels.to(device)
            optimizer.zero_grad()

            with autocast():
                outputs = model(inputs)
                loss = criterion(outputs, labels)

            scaler.scale(loss).backward()
            scaler.step(optimizer)
            scaler.update()

        if rank == 0:
            print(f"Epoch {epoch}: Loss = {loss.item():.4f}")

    cleanup()

# 멀티프로세스 실행
import torch.multiprocessing as mp

if __name__ == '__main__':
    world_size = torch.cuda.device_count()
    mp.spawn(train_ddp, args=(world_size, MyModel, dataset), nprocs=world_size, join=True)

from torch.distributed.fsdp import FullyShardedDataParallel as FSDP
from torch.distributed.fsdp import ShardingStrategy, MixedPrecision
from torch.distributed.fsdp.wrap import transformer_auto_wrap_policy
import functools

# Mixed Precision 설정
bf16_policy = MixedPrecision(
    param_dtype=torch.bfloat16,
    reduce_dtype=torch.bfloat16,
    buffer_dtype=torch.bfloat16
)

# Transformer 레이어 자동 래핑 정책
auto_wrap_policy = functools.partial(
    transformer_auto_wrap_policy,
    transformer_layer_cls={TransformerBlock}
)

# FSDP 모델 생성
model = FSDP(
    model,
    sharding_strategy=ShardingStrategy.FULL_SHARD,    # 완전 분산
    mixed_precision=bf16_policy,
    auto_wrap_policy=auto_wrap_policy,
    device_id=rank
)

model = MyModel().cuda()
optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)
criterion = nn.CrossEntropyLoss()

# 유효 배치 크기 = micro_batch_size * accumulation_steps
micro_batch_size = 8
accumulation_steps = 8  # 유효 배치 크기: 64

optimizer.zero_grad()
for step, (inputs, labels) in enumerate(train_loader):
    inputs, labels = inputs.cuda(), labels.cuda()

    with autocast():
        outputs = model(inputs)
        loss = criterion(outputs, labels)
        # 손실을 accumulation_steps로 나눔 (평균 유지)
        loss = loss / accumulation_steps

    scaler.scale(loss).backward()

    if (step + 1) % accumulation_steps == 0:
        scaler.unscale_(optimizer)
        torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0)
        scaler.step(optimizer)
        scaler.update()
        optimizer.zero_grad()

# Instruction Tuning 데이터 포맷 예시
instruction_data = [
    {
        "instruction": "다음 텍스트의 감정을 분석하세요.",
        "input": "오늘 날씨가 너무 좋아서 기분이 최고예요!",
        "output": "긍정적인 감정입니다. 날씨에 대한 만족감과 행복감이 표현되어 있습니다."
    },
    {
        "instruction": "주어진 정보를 바탕으로 요약문을 작성하세요.",
        "input": "...(긴 텍스트)...",
        "output": "...(요약)..."
    }
]

# Alpaca 형식으로 프롬프트 구성
def format_instruction(sample):
    if sample.get('input'):
        return f"""### Instruction:
{sample['instruction']}

### Input:
{sample['input']}

### Response:
{sample['output']}"""
    else:
        return f"""### Instruction:
{sample['instruction']}

### Response:
{sample['output']}"""

# 단계 2: Reward Model (Bradley-Terry 모델)
class RewardModel(nn.Module):
    def __init__(self, base_model):
        super().__init__()
        self.base_model = base_model
        self.reward_head = nn.Linear(base_model.config.hidden_size, 1)

    def forward(self, input_ids, attention_mask):
        outputs = self.base_model(input_ids=input_ids, attention_mask=attention_mask)
        # 마지막 토큰의 hidden state 사용
        last_hidden = outputs.last_hidden_state[:, -1, :]
        reward = self.reward_head(last_hidden).squeeze(-1)
        return reward

# Reward Model 학습 (선호도 손실)
def preference_loss(reward_chosen, reward_rejected):
    # Bradley-Terry 모델: p(chosen > rejected) = sigmoid(r_chosen - r_rejected)
    return -torch.log(torch.sigmoid(reward_chosen - reward_rejected)).mean()

import torch
import torch.nn.functional as F

def dpo_loss(
    policy_chosen_logps,    # 정책 모델의 선호 응답 로그 확률
    policy_rejected_logps,  # 정책 모델의 비선호 응답 로그 확률
    reference_chosen_logps, # 참조 모델의 선호 응답 로그 확률
    reference_rejected_logps, # 참조 모델의 비선호 응답 로그 확률
    beta=0.1                # KL 페널티 강도
):
    # 정책과 참조 모델 간의 log ratio
    chosen_rewards = beta * (policy_chosen_logps - reference_chosen_logps)
    rejected_rewards = beta * (policy_rejected_logps - reference_rejected_logps)

    # DPO 손실: -log(sigmoid(chosen_rewards - rejected_rewards))
    loss = -F.logsigmoid(chosen_rewards - rejected_rewards).mean()

    # 로깅용 보상
    chosen_reward = chosen_rewards.detach().mean()
    rejected_reward = rejected_rewards.detach().mean()
    reward_accuracy = (chosen_rewards > rejected_rewards).float().mean()

    return loss, chosen_reward, rejected_reward, reward_accuracy

import torch
import torch.nn as nn
from torch.cuda.amp import autocast, GradScaler
import wandb  # 실험 추적

class Trainer:
    def __init__(
        self,
        model,
        train_loader,
        val_loader,
        optimizer,
        scheduler,
        criterion,
        device='cuda',
        use_amp=True,
        grad_clip=1.0,
        accumulation_steps=1,
        log_wandb=False
    ):
        self.model = model.to(device)
        self.train_loader = train_loader
        self.val_loader = val_loader
        self.optimizer = optimizer
        self.scheduler = scheduler
        self.criterion = criterion
        self.device = device
        self.use_amp = use_amp
        self.grad_clip = grad_clip
        self.accumulation_steps = accumulation_steps
        self.scaler = GradScaler() if use_amp else None
        self.log_wandb = log_wandb

        if log_wandb:
            wandb.watch(model, log='all', log_freq=100)

    def train_epoch(self):
        self.model.train()
        total_loss = 0
        self.optimizer.zero_grad()

        for step, (inputs, labels) in enumerate(self.train_loader):
            inputs, labels = inputs.to(self.device), labels.to(self.device)

            if self.use_amp:
                with autocast():
                    outputs = self.model(inputs)
                    loss = self.criterion(outputs, labels) / self.accumulation_steps
                self.scaler.scale(loss).backward()
            else:
                outputs = self.model(inputs)
                loss = self.criterion(outputs, labels) / self.accumulation_steps
                loss.backward()

            if (step + 1) % self.accumulation_steps == 0:
                if self.use_amp:
                    self.scaler.unscale_(self.optimizer)

                if self.grad_clip:
                    nn.utils.clip_grad_norm_(self.model.parameters(), self.grad_clip)

                if self.use_amp:
                    self.scaler.step(self.optimizer)
                    self.scaler.update()
                else:
                    self.optimizer.step()

                if self.scheduler:
                    self.scheduler.step()

                self.optimizer.zero_grad()

            total_loss += loss.item() * self.accumulation_steps

        return total_loss / len(self.train_loader)

    @torch.no_grad()
    def evaluate(self):
        self.model.eval()
        total_loss = 0
        correct = 0
        total = 0

        for inputs, labels in self.val_loader:
            inputs, labels = inputs.to(self.device), labels.to(self.device)

            with autocast() if self.use_amp else torch.no_grad():
                outputs = self.model(inputs)
                loss = self.criterion(outputs, labels)

            total_loss += loss.item()
            _, predicted = outputs.max(1)
            total += labels.size(0)
            correct += predicted.eq(labels).sum().item()

        return total_loss / len(self.val_loader), 100. * correct / total

    def fit(self, epochs, save_path=None):
        best_val_acc = 0
        early_stopping = EarlyStopping(patience=10)

        for epoch in range(epochs):
            train_loss = self.train_epoch()
            val_loss, val_acc = self.evaluate()

            print(f"Epoch {epoch+1}/{epochs}: "
                  f"Train Loss: {train_loss:.4f}, "
                  f"Val Loss: {val_loss:.4f}, "
                  f"Val Acc: {val_acc:.2f}%")

            if self.log_wandb:
                wandb.log({
                    'train_loss': train_loss,
                    'val_loss': val_loss,
                    'val_acc': val_acc,
                    'lr': self.optimizer.param_groups[0]['lr']
                })

            if val_acc > best_val_acc:
                best_val_acc = val_acc
                if save_path:
                    torch.save(self.model.state_dict(), save_path)

            early_stopping(val_loss, self.model)
            if early_stopping.early_stop:
                print("Early stopping!")
                break

        return best_val_acc