refactor(topics): 멀티 에이전트용 지식 재편 — _Common(공통 기본기) + Domain_* 구조

에이전트 8종(대화형/프로그래머 C·S/디자이너/설계자/기획자/QA/PD/PM)에게 [공통 기본 능력 + 롤별 Specialty] 2층으로 지식을 주입하기 위한 재분류. 문서 내용·포맷은 무수정, 폴더 이동만 (6,372개 문서 수 보존 확인). - Topic_Programming → Domain_Programming (내부 구조 보존) - Topic_Graphic → Domain_Design - Topic_Business → Domain_Product - Topic_General → Domain_General - _Common 신설: Math(구 Topic_Math_Specialty), Reasoning(구 General/From_Thinking & Reasoning), Reasoning_Creativity(구 General/From_창의성), Communication(Poetic_Blog_Writing + From_writing) - 타 도메인의 From_* 폴더는 유지 (출처 표기일 뿐, 이미 도메인에 맞게 분류된 문서) - 빈 폴더 정리 (memory/procedures) - 에이전트→폴더 매핑은 workspace의 .astra/agent-knowledge-map.json (9개 에이전트) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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+---
+id: wiki-2026-0508-variational-autoencoders-vae
+title: Variational Autoencoders (VAE)
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [VAE, Variational Autoencoder, β-VAE]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.9
+verification_status: applied
+tags: [generative-model, deep-learning, latent-variable, variational-inference]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: Python
+  framework: PyTorch 2.x
+---
+
+# Variational Autoencoders (VAE)
+
+## 매 한 줄
+> **"매 encoder 가 input 의 latent distribution (μ, σ) 의 produce → reparameterization trick 으로 sample → decoder 의 reconstruct. 매 ELBO = reconstruction loss + KL(q(z|x) || p(z))"**. 매 Kingma & Welling 2013 (Auto-Encoding Variational Bayes). 매 2026 의 modern role: standalone generation 의 X (diffusion 의 우위) BUT 매 Stable Diffusion / FLUX / Sora 의 latent space 의 backbone — 매 image 의 8× downsampled latent 의 work.
+
+## 매 핵심
+
+### 매 수학 (ELBO)
+- **Goal**: maximize log p(x). 매 intractable.
+- **Trick**: variational posterior q_φ(z|x) ≈ p(z|x). 매 ELBO 의 lower bound.
+- **ELBO** = E_{z~q}[log p_θ(x|z)] − D_KL(q_φ(z|x) || p(z))
+  - 1번 term: reconstruction (decoder).
+  - 2번 term: regularize latent 의 prior (보통 N(0,I)) 에 가깝게.
+- **Reparameterization**: z = μ + σ ⊙ ε, ε~N(0,I) — 매 backprop through stochastic sampling.
+
+### 매 vs 다른 generative
+- **GAN**: sharp, no likelihood, mode collapse. VAE: blurry, likelihood, stable training.
+- **Diffusion**: state-of-art quality. VAE: faster inference (single forward).
+- **2026 dominant role**: latent diffusion 의 frontend — 매 VAE 가 pixel space → latent space 압축, diffusion 이 latent 의 denoise.
+
+### 매 변종
+- **β-VAE**: KL term 에 β 곱 → β>1 의 disentangled latent.
+- **VQ-VAE**: continuous latent → discrete codebook (Vector Quantization). 매 DALL-E, Sora 의 핵심.
+- **Hierarchical VAE / NVAE**: multi-scale latents.
+- **Conditional VAE (CVAE)**: conditional generation p(x|c).
+
+### 매 응용
+1. Latent diffusion (Stable Diffusion / FLUX / Sora) — 매 8×8 patch → 4-ch latent.
+2. Anomaly detection — high reconstruction error = anomaly.
+3. Molecular generation — 매 chemistry latent space exploration.
+
+## 💻 패턴
+
+### Vanilla VAE (PyTorch 2.x)
+```python
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+
+class VAE(nn.Module):
+    def __init__(self, in_dim=784, hidden=400, z_dim=20):
+        super().__init__()
+        self.fc1 = nn.Linear(in_dim, hidden)
+        self.fc_mu = nn.Linear(hidden, z_dim)
+        self.fc_logvar = nn.Linear(hidden, z_dim)
+        self.fc2 = nn.Linear(z_dim, hidden)
+        self.fc3 = nn.Linear(hidden, in_dim)
+
+    def encode(self, x):
+        h = F.relu(self.fc1(x))
+        return self.fc_mu(h), self.fc_logvar(h)
+
+    def reparameterize(self, mu, logvar):
+        std = torch.exp(0.5 * logvar)
+        eps = torch.randn_like(std)
+        return mu + eps * std
+
+    def decode(self, z):
+        return torch.sigmoid(self.fc3(F.relu(self.fc2(z))))
+
+    def forward(self, x):
+        mu, logvar = self.encode(x)
+        z = self.reparameterize(mu, logvar)
+        return self.decode(z), mu, logvar
+
+def vae_loss(recon, x, mu, logvar):
+    bce = F.binary_cross_entropy(recon, x, reduction='sum')
+    kld = -0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp())
+    return bce + kld
+```
+
+### Training loop
+```python
+model = VAE().cuda()
+opt = torch.optim.AdamW(model.parameters(), lr=1e-3)
+for epoch in range(50):
+    for x, _ in loader:
+        x = x.view(-1, 784).cuda()
+        recon, mu, logvar = model(x)
+        loss = vae_loss(recon, x, mu, logvar)
+        opt.zero_grad(); loss.backward(); opt.step()
+```
+
+### β-VAE (disentanglement)
+```python
+def beta_vae_loss(recon, x, mu, logvar, beta=4.0):
+    bce = F.binary_cross_entropy(recon, x, reduction='sum')
+    kld = -0.5 * torch.sum(1 + logvar - mu.pow(2) - logvar.exp())
+    return bce + beta * kld
+```
+
+### VQ-VAE (vector quantization)
+```python
+class VectorQuantizer(nn.Module):
+    def __init__(self, num_embeddings=512, embedding_dim=64, commitment=0.25):
+        super().__init__()
+        self.embed = nn.Embedding(num_embeddings, embedding_dim)
+        self.embed.weight.data.uniform_(-1.0 / num_embeddings, 1.0 / num_embeddings)
+        self.commitment = commitment
+
+    def forward(self, z_e):  # z_e: (B, C, H, W)
+        z_e_perm = z_e.permute(0, 2, 3, 1).contiguous()
+        flat = z_e_perm.view(-1, z_e_perm.size(-1))
+        # Nearest codebook vector
+        d = (flat.pow(2).sum(1, keepdim=True)
+             - 2 * flat @ self.embed.weight.t()
+             + self.embed.weight.pow(2).sum(1))
+        idx = d.argmin(1)
+        z_q = self.embed(idx).view(z_e_perm.shape).permute(0, 3, 1, 2)
+        # Straight-through estimator
+        loss = F.mse_loss(z_q.detach(), z_e) + self.commitment * F.mse_loss(z_q, z_e.detach())
+        z_q = z_e + (z_q - z_e).detach()
+        return z_q, loss, idx
+```
+
+### Sample / generate
+```python
+model.eval()
+with torch.no_grad():
+    z = torch.randn(64, 20).cuda()
+    samples = model.decode(z).view(-1, 1, 28, 28).cpu()
+```
+
+### Latent diffusion VAE (SD-style — using diffusers)
+```python
+from diffusers import AutoencoderKL
+import torch
+
+vae = AutoencoderKL.from_pretrained('stabilityai/sd-vae-ft-mse').cuda()
+# Encode 512x512 image → 4-ch 64x64 latent
+img = torch.randn(1, 3, 512, 512).cuda()
+latent = vae.encode(img).latent_dist.sample() * vae.config.scaling_factor
+# Diffusion happens in latent space, then decode
+recon = vae.decode(latent / vae.config.scaling_factor).sample
+```
+
+## 매 결정 기준
+| 목적 | Choice |
+|---|---|
+| 2026 SOTA 이미지 생성 | Diffusion (FLUX, Stable Diffusion 3.5) — 매 VAE 의 frontend 만 |
+| Disentangled representation 연구 | β-VAE |
+| Discrete latent (LLM tokenize 유사) | VQ-VAE / VQ-GAN |
+| Anomaly detection | Vanilla VAE — reconstruction error |
+| Latent diffusion 학습 | Pre-trained KL-regularized VAE (e.g. SD VAE) reuse |
+| Molecular / structured generation | VAE (continuous latent) — 매 still competitive |
+
+**기본값**: 매 image generation 의 directly 의 X — 매 latent diffusion 안 의 VAE 로 사용. 매 disentanglement / anomaly 의 standalone VAE.
+
+## 🔗 Graph
+- 부모: [[Variational Inference]]
+- 변형: [[β-VAE]]
+- 응용: [[Stable Diffusion]] · [[FLUX]]
+- Adjacent: [[Diffusion Models]] · [[Generative-Adversarial-Networks|GAN]]
+
+## 🤖 LLM 활용
+**언제**: 매 latent diffusion 의 VAE component 설명, 매 anomaly detection baseline 작성, 매 ELBO 수학 의 derivation, 매 reparameterization trick 의 implementation.
+**언제 X**: 매 standalone SOTA image generation (diffusion 우선), 매 sharp output 필수 (GAN/diffusion).
+
+## ❌ 안티패턴
+- **Posterior collapse**: q(z|x) → p(z) 의 무시 → KL=0, decoder 의 z 의 ignore. 매 KL annealing / β scheduling 필요.
+- **Pixel-space VAE 의 high-res 직접**: 매 blurry, 매 8× downsample latent + diffusion 으로 decouple.
+- **σ 의 직접 output**: 매 negative 가능. 매 logvar 의 output → σ = exp(0.5 * logvar).
+- **KL 의 mean reduction**: 매 batch mean 의 reconstruction 의 sum 과 mismatch — 매 두 term 의 same reduction.
+
+## 🧪 검증 / 중복
+- Verified (Kingma & Welling 2013 ICLR, Stable Diffusion paper, NVIDIA NVAE, DeepMind β-VAE).
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — full VAE with ELBO, β-VAE, VQ-VAE, latent diffusion role, 6 patterns |