---
id: wiki-2026-0508-boltzmann-machines
title: Boltzmann Machines
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [볼츠만 머신, RBM, restricted Boltzmann machine, deep belief network, energy-based model, contrastive divergence]
duplicate_of: none
source_trust_level: A
confidence_score: 0.88
verification_status: applied
tags: [boltzmann-machine, rbm, energy-based-model, deep-learning-history, hinton, contrastive-divergence]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: PyTorch / scikit-learn
---

# Boltzmann Machines

## 📌 한 줄 통찰
> **"매 data distribution 의 energy 의 model"**. 매 stat mech 의 Boltzmann distribution 의 inspire. 매 deep learning 의 spark (Hinton 2006 RBM pre-training). 매 modern: 매 energy-based model (EBM) 의 의 base + 매 score matching + 매 diffusion 의 connection.

## 📖 핵심

### 매 history
- 1985: Hinton & Sejnowski의 Boltzmann Machine.
- 2002: Hinton의 Contrastive Divergence (CD) 학습.
- 2006: Hinton's "A Fast Learning Algorithm for Deep Belief Networks" — 매 deep learning 의 부활.
- 2007-2012: 매 pre-training 의 ImageNet 의 unleash.
- 2010s: 매 backprop + ReLU + dropout 의 supersede.
- 2020s: 매 energy-based model 의 revival (Du, LeCun).

### 매 architecture

#### Vanilla Boltzmann Machine
- 매 모든 매 unit 가 connected.
- 매 visible + hidden.
- 매 train 어려움 (intractable).

#### RBM (Restricted)
- 매 same-layer connection X.
- 매 visible ↔ hidden 만.
- 매 efficient sampling.

#### DBN (Deep Belief Network)
- 매 RBM 의 stack.
- 매 layer-wise pre-training.

#### DBM (Deep Boltzmann Machine)
- 매 모든 layer 의 bidirectional.
- 매 train 매 hard.

### 매 energy formulation
$$E(v, h) = -\sum_i a_i v_i - \sum_j b_j h_j - \sum_{i,j} v_i W_{ij} h_j$$

$$P(v, h) = \frac{e^{-E(v, h)}}{Z}$$

- 매 Z = partition function (intractable).

### 매 학습: Contrastive Divergence (CD-k)
1. 매 data v0.
2. 매 sample h0 from P(h | v0).
3. 매 sample v1 from P(v | h0). [k step 의 Gibbs]
4. 매 update: ΔW = lr * (v0 h0^T - v1 h1^T).

### 매 modern relevance
- **Energy-Based Model (EBM)**: 매 LeCun 의 advocate.
- **Score matching**: 매 gradient 의 학습 — 매 diffusion model 의 base.
- **Diffusion model** (DDPM): 매 EBM 의 변형.
- **GAN**: 매 implicit EBM.
- **JEM** (Joint Energy Model): 매 classifier 의 EBM 의 reframe.

### 매 modern application
- **Anomaly detection**: 매 low energy = normal.
- **Generative model** (legacy): 매 collaborative filtering.
- **Recommender** (Netflix prize 의 RBM).
- **Pre-training** (legacy, mostly replaced).
- **Quantum Boltzmann** (quantum computing).

### 매 vs modern alternative
| 측면 | RBM | Modern |
|---|---|---|
| Density estimation | weak | Diffusion / Flow |
| Pre-training | weak | Self-supervised |
| Generation | OK | GAN / Diffusion |
| Tractability | hard | tractable (specific) |

→ 매 historical importance > 매 current usage.

## 💻 패턴

### RBM (scikit-learn)
```python
from sklearn.neural_network import BernoulliRBM
from sklearn.datasets import load_digits

X = load_digits().data / 16.0  # 매 normalize

rbm = BernoulliRBM(n_components=64, learning_rate=0.06, n_iter=20)
rbm.fit(X)

# 매 reconstruction
import numpy as np
hidden = rbm.transform(X[:1])  # 매 hidden activations
print(hidden.shape)  # (1, 64)
```

### RBM (PyTorch from scratch)
```python
import torch
import torch.nn as nn

class RBM(nn.Module):
    def __init__(self, n_visible, n_hidden):
        super().__init__()
        self.W = nn.Parameter(torch.randn(n_hidden, n_visible) * 0.01)
        self.v_bias = nn.Parameter(torch.zeros(n_visible))
        self.h_bias = nn.Parameter(torch.zeros(n_hidden))
    
    def sample_h(self, v):
        p_h = torch.sigmoid(F.linear(v, self.W, self.h_bias))
        return p_h, torch.bernoulli(p_h)
    
    def sample_v(self, h):
        p_v = torch.sigmoid(F.linear(h, self.W.t(), self.v_bias))
        return p_v, torch.bernoulli(p_v)
    
    def free_energy(self, v):
        wx_b = F.linear(v, self.W, self.h_bias)
        return -torch.sum(F.softplus(wx_b), dim=1) - v @ self.v_bias

def cd_k(rbm, v0, k=1, lr=0.01):
    """매 Contrastive Divergence."""
    p_h0, h0 = rbm.sample_h(v0)
    
    vk = v0
    for _ in range(k):
        p_h, h = rbm.sample_h(vk)
        p_v, vk = rbm.sample_v(h)
    
    p_hk, hk = rbm.sample_h(vk)
    
    # 매 gradient
    rbm.W.grad = -((p_h0.t() @ v0 - p_hk.t() @ vk) / v0.size(0))
    rbm.v_bias.grad = -((v0 - vk).mean(0))
    rbm.h_bias.grad = -((p_h0 - p_hk).mean(0))
```

### Energy-Based Model (modern)
```python
class EBM(nn.Module):
    """매 energy F(x) = MLP."""
    def __init__(self, dim):
        super().__init__()
        self.net = nn.Sequential(
            nn.Linear(dim, 256), nn.ReLU(),
            nn.Linear(256, 256), nn.ReLU(),
            nn.Linear(256, 1),
        )
    
    def energy(self, x):
        return self.net(x).squeeze(-1)

def langevin_sample(ebm, x, n_steps=100, step_size=0.1, noise=0.01):
    """매 Langevin dynamics 의 EBM 의 sample."""
    x = x.detach().requires_grad_()
    for _ in range(n_steps):
        e = ebm.energy(x).sum()
        grad = torch.autograd.grad(e, x)[0]
        x = x - step_size * grad + noise * torch.randn_like(x)
        x = x.detach().requires_grad_()
    return x
```

### Diffusion model (related EBM)
```python
# 매 DDPM 의 sketch — 매 noise 의 add + reverse
def diffusion_train(model, x0, T=1000):
    t = torch.randint(0, T, (x0.size(0),))
    noise = torch.randn_like(x0)
    alpha_bar = noise_schedule[t]
    xt = torch.sqrt(alpha_bar) * x0 + torch.sqrt(1 - alpha_bar) * noise
    
    pred_noise = model(xt, t)
    return F.mse_loss(pred_noise, noise)
```

### Anomaly detection (EBM)
```python
def is_anomaly(ebm, x, threshold):
    """매 high energy = 매 unusual."""
    return ebm.energy(x).item() > threshold
```

## 🤔 결정 기준
| 상황 | Approach |
|---|---|
| Modern generative | Diffusion / GAN |
| Anomaly detection | EBM / Autoencoder |
| Historical study | RBM / DBN |
| Quantum | Quantum Boltzmann |
| Pre-training | Self-supervised (BERT, MAE) |
| Sparse coding | Sparse autoencoder |

**기본값**: 매 historical 의 understand 가, 매 production 의 모더 매 alternative.

## 🔗 Graph
- 부모: [[Energy-Based-Models]] · [[Generative-Models]] · [[Statistical-Mechanics]]
- 변형: [[RBM]] · [[DBN]] · [[DBM]] · [[Helmholtz-Machine]]
- 응용: [[Diffusion-Model]] · [[Score-Matching]] · [[GAN]] · [[Anomaly-Detection]]
- Adjacent: [[Hinton]] · [[Contrastive-Divergence]] · [[Auto-Encoding]] · [[Bayesian-Brain-Hypothesis]]

## 🤖 LLM 활용
**언제**: 매 deep learning history. 매 EBM 의 understand. 매 anomaly detection. 매 diffusion 의 connection.
**언제 X**: 매 production generative (use diffusion). 매 production pre-train (use SSL).

## ❌ 안티패턴
- **RBM 의 production 의 expect**: 매 outdated.
- **Pre-training 의 RBM 으로 의 modern (BERT 의 era)**: 매 use SSL.
- **Z (partition) 의 compute attempt**: 매 intractable.
- **Single-step CD**: 매 biased estimator.
- **Continuous data 의 binary RBM**: 매 wrong.

## 🧪 검증 / 중복
- Verified (Hinton 2002 CD, 2006 DBN paper).
- 신뢰도 A.
- Related: [[Diffusion-Model]] · [[Energy-Based-Models]] · [[Auto-Encoding]] · [[Self-Supervised-Learning]].

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — RBM + EBM + diffusion connection + 매 PyTorch / sklearn code |
