---
id: wiki-2026-0508-predictive-coding
title: Predictive Coding
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Predictive Coding Networks, PCN, Hierarchical Predictive Coding]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [neuroscience, computational-neuroscience, free-energy, brain-models]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: PyTorch / JAX
---

# Predictive Coding

## 매 한 줄
> **"매 brain = prediction machine — top-down predictions vs bottom-up errors 의 hierarchical loop"**. Rao & Ballard (1999) 의 visual cortex model 에서 시작, Friston 의 free-energy principle 로 generalized, 2020s 부터 backprop alternative 로 deep learning 에서 재조명. Each layer predicts activity below; only prediction errors propagate up.

## 매 핵심

### 매 Rao-Ballard (1999)
- Hierarchical generative model: layer L predicts layer L-1 activity.
- Prediction error e_L = r_{L-1} - W_L * r_L.
- Errors drive higher representations; representations drive top-down predictions.
- Endstop neurons, surround suppression 매 emergent properties.

### 매 free-energy principle (Friston)
- Brain minimizes variational free energy = surprise upper bound.
- Active inference: action selection also minimizes expected free energy.
- Unifies perception, action, learning under one objective.

### 매 modern PC neural networks
- **PCN as backprop alternative**: local Hebbian-like updates only.
- **Equilibrium propagation** (Scellier-Bengio): related fixed-point training.
- **Z-IL (Zero-divergence Inference Learning)**: PC equivalent to BP at convergence (Song 2020).
- 2024-2026 work: scaling PC to ImageNet, transformer-PC hybrids.

### 매 advantages over backprop
1. Local plasticity (biologically plausible).
2. No need to store activations for backward pass.
3. Natural for online / continual learning.
4. Robust to weight transport problem.

## 💻 패턴

### Minimal PC layer (PyTorch)
```python
import torch, torch.nn as nn

class PCLayer(nn.Module):
    def __init__(self, dim_below, dim_above):
        super().__init__()
        self.W = nn.Parameter(torch.randn(dim_above, dim_below) * 0.1)
        self.r = None  # state, set per batch

    def init_state(self, batch_size, device):
        self.r = torch.zeros(batch_size, self.W.shape[0], device=device, requires_grad=True)

    def predict(self):
        return self.r @ self.W  # top-down prediction of layer below

    def error(self, below):
        return below - self.predict()
```

### Inference loop (energy minimization)
```python
def pc_inference(layers, x, n_steps=20, lr_r=0.1):
    # x: input at bottom
    for L in layers: L.init_state(x.size(0), x.device)
    activity = [x] + [L.r for L in layers]

    for _ in range(n_steps):
        # compute errors at each level
        errors = []
        for i, L in enumerate(layers):
            errors.append(activity[i] - L.predict())
        # update r via gradient descent on free energy
        for i, L in enumerate(layers):
            grad = -errors[i] @ L.W.T
            if i + 1 < len(layers):
                grad = grad + errors[i + 1]
            L.r = (L.r - lr_r * grad).detach().requires_grad_(True)
            activity[i + 1] = L.r
    return errors
```

### Weight update (local Hebbian)
```python
def pc_weight_update(layers, errors, activity, lr_w=0.01):
    with torch.no_grad():
        for i, L in enumerate(layers):
            # dW ∝ r_above^T * error_below
            dW = L.r.T @ errors[i] / errors[i].size(0)
            L.W += lr_w * dW
```

### Active inference (action selection)
```python
def select_action(model, state, candidate_actions):
    """Pick action minimizing expected free energy G = epistemic + pragmatic."""
    G = []
    for a in candidate_actions:
        next_belief = model.transition(state, a)
        ambiguity = model.entropy(next_belief)
        risk = model.kl_to_preferred(next_belief)
        G.append(ambiguity + risk)
    return candidate_actions[torch.argmin(torch.tensor(G))]
```

### Z-IL (PC ≡ BP at convergence)
```python
# Song et al 2020: at the equilibrium of PC inference,
# weight updates equal those produced by BP.
# Critical detail: feedback weights = transpose of forward weights (tied).
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Biological plausibility required | Predictive coding |
| Energy efficiency on neuromorphic HW | PC / spiking PC |
| SOTA accuracy on ImageNet | Backprop CNN/ViT (still wins) |
| Continual learning | PC w/ uncertainty-weighted errors |
| Interpretation of cortical hierarchy | PC as theory |

**기본값**: BP for engineering; PC for neuroscience modeling 또는 neuromorphic deployment.

## 🔗 Graph
- 부모: [[Computational-Neuroscience-RL|Computational-Neuroscience]] · [[Free-Energy-Principle]]
- 변형: [[Active-Inference]]
- 응용: [[Bayesian-Brain]] · [[Neuromorphic-Computing]]
- Adjacent: [[데이터 사이언스 및 ML 엔지니어링|Backpropagation]] · [[Variational-Inference]]

## 🤖 LLM 활용
**언제**: brain-inspired model design, biologically-plausible learning, continual learning, neuromorphic chips.
**언제 X**: pure engineering goals — backprop is faster and more accurate.

## ❌ 안티패턴
- **PC as drop-in BP replacement**: still slower and less accurate at scale.
- **Confusing inference vs learning**: PC has nested loops (fast inference, slow weights).
- **Ignoring weight symmetry**: untied feedback breaks BP equivalence.
- **Free-energy hand-wave**: equation must be operationalized concretely.

## 🧪 검증 / 중복
- Verified (Rao & Ballard 1999 Nat Neurosci, Friston 2010, Song et al 2020 NeurIPS).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — full PC theory + modern PC NN code |