2nd/10_Wiki/Topics/AI_and_ML/Perceptrons-Foundations.md

---
id: wiki-2026-0508-perceptrons-foundations
title: Perceptrons-Foundations
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Perceptron, Rosenblatt Perceptron, MLP]
duplicate_of: none
source_trust_level: A
confidence_score: 0.95
verification_status: applied
tags: [perceptron, neural-network, mlp, history, foundations]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: python
  framework: pytorch, numpy
---

# Perceptrons-Foundations

## 매 한 줄
> **"매 weighted sum + threshold = NN의 atom"**. Rosenblatt 1957 perceptron — 매 first trainable neuron model. Single-layer 의 XOR fail (Minsky 1969) → AI winter. MLP + backprop (1986) 의 revival. 매 modern transformer 도 결국 stacked perceptron.

## 매 핵심

### 매 history
- 1943: McCulloch-Pitts neuron (binary, no learning).
- 1957: Rosenblatt perceptron — 매 hardware Mark I, learnable weights.
- 1969: Minsky & Papert "Perceptrons" — 매 XOR limit proven → first AI winter.
- 1986: Rumelhart, Hinton, Williams — 매 backprop revives MLP.
- 2012: AlexNet — 매 deep MLP/CNN era 시작.

### 매 perceptron 수학
- `y = step(w·x + b)` where step(z) = 1 if z ≥ 0 else 0.
- Update rule (Rosenblatt): `w ← w + η(y_true - y_pred)x`.
- Convergence theorem: 매 linearly separable data 에 한해 finite steps 수렴.
- Limit: 매 XOR (non-linearly separable) 학습 불가.

### 매 multi-layer (MLP)
- Hidden layer + nonlinearity (sigmoid → ReLU → GELU).
- Universal approximation theorem (Cybenko 1989, Hornik 1991): 매 single hidden layer with enough units 가 매 continuous function 근사 가능.
- Training: backprop (chain rule으로 gradient 계산).

### 매 modern lens
- Transformer FFN block = 2-layer MLP per token.
- ViT, MLP-Mixer 등 매 pure-MLP 의 vision SOTA 도전.
- 매 every "neural network" 의 atomic unit — perceptron.

### 매 응용
1. Pedagogical (NN intro).
2. Linear classifier (single perceptron).
3. Building block (MLP in transformer).
4. Mixture-of-Experts: each expert = MLP.

## 💻 패턴

### Perceptron from scratch
```python
import numpy as np

class Perceptron:
    def __init__(self, n_features, lr=0.1):
        self.w = np.zeros(n_features)
        self.b = 0.0
        self.lr = lr

    def predict(self, x):
        return 1 if x @ self.w + self.b >= 0 else 0

    def fit(self, X, y, epochs=100):
        for _ in range(epochs):
            for xi, yi in zip(X, y):
                pred = self.predict(xi)
                err = yi - pred
                self.w += self.lr * err * xi
                self.b += self.lr * err
```

### XOR fails for single perceptron
```python
X = np.array([[0,0],[0,1],[1,0],[1,1]])
y = np.array([0, 1, 1, 0])  # XOR
p = Perceptron(2)
p.fit(X, y, epochs=1000)
# Will NOT converge — XOR is not linearly separable
```

### MLP solves XOR
```python
import torch.nn as nn
mlp = nn.Sequential(
    nn.Linear(2, 4), nn.ReLU(),
    nn.Linear(4, 1), nn.Sigmoid(),
)
# Train with BCELoss + Adam — converges in <1000 steps
```

### Transformer FFN = MLP per token
```python
class FFN(nn.Module):
    def __init__(self, dim, hidden):
        super().__init__()
        self.up = nn.Linear(dim, hidden)
        self.down = nn.Linear(hidden, dim)
    def forward(self, x):
        return self.down(nn.functional.gelu(self.up(x)))
```

### MLP-Mixer style (pure MLP vision)
```python
class MixerBlock(nn.Module):
    def __init__(self, n_patches, dim):
        super().__init__()
        self.token_mix = nn.Sequential(nn.Linear(n_patches, n_patches*4),
                                        nn.GELU(), nn.Linear(n_patches*4, n_patches))
        self.channel_mix = nn.Sequential(nn.Linear(dim, dim*4),
                                          nn.GELU(), nn.Linear(dim*4, dim))
    def forward(self, x):  # (B, N, D)
        x = x + self.token_mix(x.transpose(1,2)).transpose(1,2)
        x = x + self.channel_mix(x)
        return x
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Linearly separable | Single perceptron OK |
| Non-linear pattern | MLP (>=1 hidden layer) |
| Tabular data | Tree models (XGBoost) usually beat MLP |
| Image | CNN or ViT (still MLP-based) |
| Sequence | Transformer (MLP + attention) |
| Pedagogical | Start with perceptron history |

**기본값**: 매 modern model 의 building block 으로 MLP 이해.

## 🔗 Graph
- 변형: [[MLP]]
- 응용: [[MoE]]
- Adjacent: [[데이터_사이언스_및_ML_엔지니어링|Backpropagation]]

## 🤖 LLM 활용
**언제**: 매 NN fundamentals, debugging gradient flow, designing custom architectures.
**언제 X**: 매 production tabular tasks (use GBDT instead).

## ❌ 안티패턴
- **Linear activation only**: 매 multi-layer linear = single linear (collapses). 매 nonlinearity 필수.
- **Step function in modern NN**: 매 non-differentiable → backprop fail. 매 ReLU/GELU 사용.
- **Too wide, too shallow**: 매 universal approximation 가능해도 deep 가 sample-efficient.
- **Forgetting bias**: 매 b=0 forced → cannot shift decision boundary off origin.

## 🧪 검증 / 중복
- Verified (Rosenblatt 1958, Minsky-Papert 1969, Rumelhart et al. 1986).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — perceptron history, XOR limit, MLP modern lens |