---
id: wiki-2026-0508-inductive-bias
title: Inductive Bias
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [inductive bias, prior, model assumption, no free lunch]
duplicate_of: none
source_trust_level: A
confidence_score: 0.94
verification_status: applied
tags: [machine-learning, inductive-bias, prior, no-free-lunch, deep-learning]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: ML Theory
  applicable_to: [Model Design, Architecture]
---

# Inductive Bias

## 매 한 줄
> **"매 model 의 의 의 의 의 assumption 의 의 의 generalize"**. 매 No Free Lunch theorem (Wolpert): 매 매 algorithm 의 model 의 의 의 매 task 의 best. 매 modern: 매 transformer 의 inductive bias 의 의 의 weak — 매 scale 의 의 의 의 compensate.

## 매 핵심

### 매 examples
- **CNN**: 매 translation invariance, locality.
- **RNN**: 매 sequence, temporal.
- **Transformer**: 매 weak — 매 매 sufficient data 의 의 의 learn.
- **GNN**: 매 graph structure, permutation invariance.
- **Tree**: 매 axis-aligned splits.
- **kNN**: 매 local smoothness.

### 매 trade-off
- **Strong bias**: 매 small data 의 효율, 매 wrong domain 매 fail.
- **Weak bias** (transformer): 매 large data 매 win, 매 small data 매 lose.

### 매 No Free Lunch
- 매 average performance over 매 모든 problems 의 same.
- 매 매 task 의 의 의 의 best algorithm.
- 매 → 매 inductive bias 매 critical.

### 매 응용
1. **Architecture choice**.
2. **Transfer learning**.
3. **Few-shot learning**.
4. **Domain adaptation**.

## 💻 패턴

### CNN inductive bias (translation)
```python
import torch.nn as nn
# 매 same kernel 의 매 location 의 적용
conv = nn.Conv2d(3, 64, kernel_size=3, padding=1)
# 매 translation invariance + locality
```

### Transformer (weak bias)
```python
# 매 매 token pair 의 attention — 매 specific structure 의 X
# 매 → 매 large pretrain data 의 의 의 compensate
class Attention(nn.Module):
    def __init__(self, dim):
        super().__init__()
        self.q = nn.Linear(dim, dim)
        self.k = nn.Linear(dim, dim)
        self.v = nn.Linear(dim, dim)
    
    def forward(self, x):
        return torch.softmax(self.q(x) @ self.k(x).T, -1) @ self.v(x)
```

### GNN (graph + permutation invariance)
```python
# 매 message passing — 매 node order independent
class GNNLayer:
    def forward(self, x, edge_index):
        # 매 매 node 의 매 neighbor 의 aggregate (sum/mean)
        return aggregate_neighbors(x, edge_index)
```

### Strong vs weak bias (data regime)
```python
def model_for_data_size(n):
    if n < 1000:
        return 'tree-based'  # 매 strong inductive bias
    if n < 100000:
        return 'classical ML or small CNN'
    if n < 10_000_000:
        return 'CNN / RNN'
    return 'transformer'  # 매 매 weak bias 의 의 의 의 의 의 win
```

### Transfer learning (use pretrained bias)
```python
from torchvision.models import resnet50
model = resnet50(pretrained=True)
# 매 freeze backbone (use ImageNet bias)
for p in model.parameters(): p.requires_grad = False
# 매 fine-tune classifier
model.fc = nn.Linear(2048, n_classes)
```

### Encode bias as constraint
```python
# 매 monotonic prediction (e.g., income ↑ → spend ↑)
class MonotonicNN(nn.Module):
    def __init__(self):
        super().__init__()
        self.weights = nn.Parameter(torch.randn(...))
    
    def forward(self, x):
        # 매 abs of weights → 매 monotonic
        return x @ torch.abs(self.weights)
```

### Symmetry-aware network
```python
# 매 E(n)-equivariant for molecule
class EGNN(nn.Module):
    def forward(self, x, pos, edge_index):
        # 매 rotation / translation invariance built in
        ...
```

### Probing inductive bias
```python
def small_data_eval(model, train_sizes=[100, 1000, 10000]):
    """매 small data 의 의 의 model 의 generalize?"""
    perf = {}
    for n in train_sizes:
        m = train(model, X_train[:n], y_train[:n])
        perf[n] = evaluate(m, X_test, y_test)
    return perf  # 매 strong bias model 매 small n 의 win
```

### Architecture search (inductive bias picker)
```python
def pick_architecture(data_features):
    if data_features['has_spatial_structure']: return 'CNN'
    if data_features['is_graph']: return 'GNN'
    if data_features['is_sequence_long']: return 'Transformer'
    if data_features['is_tabular']: return 'XGBoost'
```

### Synthetic + real (mix biases)
```python
def hybrid_train(synthetic_data, real_data):
    """매 synthetic data 매 strong bias, 매 real data 매 fine-tune."""
    pretrain(model, synthetic_data)
    finetune(model, real_data)
```

## 매 결정 기준
| 상황 | Bias |
|---|---|
| Small data | Strong (tree, kNN) |
| Image | CNN (translation) |
| Sequence | RNN / Transformer |
| Graph | GNN |
| Tabular | Tree |
| Big data + flexible | Transformer |
| Symmetry-aware | Equivariant NN |

**기본값**: 매 task structure 의 match 의 inductive bias + 매 large data 의 의 의 weak bias 의 OK + 매 small data 의 의 strong bias 의 critical.

## 🔗 Graph
- 부모: [[Machine-Learning-Theory]]
- 변형: [[Strong-Bias]] · [[Weak-Bias]] · [[No-Free-Lunch]]
- 응용: [[Transfer-Learning]] · [[Architecture-Selection]]
- Adjacent: [[Generalization-in-AI]] · [[Equivariant-NN]] · [[Foundation-Models]]

## 🤖 LLM 활용
**언제**: 매 model design. 매 small data. 매 transfer.
**언제 X**: 매 toy.

## ❌ 안티패턴
- **Wrong bias for task**: 매 image 매 dense MLP.
- **Always weak bias**: 매 small data 의 fail.
- **Ignore symmetry**: 매 sample efficiency lose.
- **No transfer for small data**: 매 reinvent.

## 🧪 검증 / 중복
- Verified (Wolpert NFL, Mitchell ML).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — bias + 매 CNN/Transformer/GNN / NFL / arch picker code |
