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Antigravity Agent
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id: wiki-2026-0508-predictive-coding
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title: Predictive Coding
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [Predictive Coding Networks, PCN, Hierarchical Predictive Coding]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [neuroscience, computational-neuroscience, free-energy, brain-models]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: Python
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framework: PyTorch / JAX
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---
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# Predictive Coding
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## 매 한 줄
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> **"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.
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## 매 핵심
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### 매 Rao-Ballard (1999)
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- Hierarchical generative model: layer L predicts layer L-1 activity.
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- Prediction error e_L = r_{L-1} - W_L * r_L.
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- Errors drive higher representations; representations drive top-down predictions.
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- Endstop neurons, surround suppression 매 emergent properties.
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### 매 free-energy principle (Friston)
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- Brain minimizes variational free energy = surprise upper bound.
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- Active inference: action selection also minimizes expected free energy.
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- Unifies perception, action, learning under one objective.
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### 매 modern PC neural networks
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- **PCN as backprop alternative**: local Hebbian-like updates only.
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- **Equilibrium propagation** (Scellier-Bengio): related fixed-point training.
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- **Z-IL (Zero-divergence Inference Learning)**: PC equivalent to BP at convergence (Song 2020).
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- 2024-2026 work: scaling PC to ImageNet, transformer-PC hybrids.
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### 매 advantages over backprop
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1. Local plasticity (biologically plausible).
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2. No need to store activations for backward pass.
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3. Natural for online / continual learning.
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4. Robust to weight transport problem.
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## 💻 패턴
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### Minimal PC layer (PyTorch)
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```python
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import torch, torch.nn as nn
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class PCLayer(nn.Module):
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def __init__(self, dim_below, dim_above):
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super().__init__()
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self.W = nn.Parameter(torch.randn(dim_above, dim_below) * 0.1)
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self.r = None # state, set per batch
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def init_state(self, batch_size, device):
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self.r = torch.zeros(batch_size, self.W.shape[0], device=device, requires_grad=True)
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def predict(self):
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return self.r @ self.W # top-down prediction of layer below
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def error(self, below):
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return below - self.predict()
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```
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### Inference loop (energy minimization)
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```python
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def pc_inference(layers, x, n_steps=20, lr_r=0.1):
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# x: input at bottom
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for L in layers: L.init_state(x.size(0), x.device)
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activity = [x] + [L.r for L in layers]
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for _ in range(n_steps):
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# compute errors at each level
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errors = []
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for i, L in enumerate(layers):
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errors.append(activity[i] - L.predict())
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# update r via gradient descent on free energy
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for i, L in enumerate(layers):
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grad = -errors[i] @ L.W.T
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if i + 1 < len(layers):
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grad = grad + errors[i + 1]
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L.r = (L.r - lr_r * grad).detach().requires_grad_(True)
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activity[i + 1] = L.r
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return errors
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```
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### Weight update (local Hebbian)
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```python
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def pc_weight_update(layers, errors, activity, lr_w=0.01):
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with torch.no_grad():
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for i, L in enumerate(layers):
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# dW ∝ r_above^T * error_below
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dW = L.r.T @ errors[i] / errors[i].size(0)
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L.W += lr_w * dW
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```
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### Active inference (action selection)
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```python
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def select_action(model, state, candidate_actions):
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"""Pick action minimizing expected free energy G = epistemic + pragmatic."""
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G = []
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for a in candidate_actions:
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next_belief = model.transition(state, a)
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ambiguity = model.entropy(next_belief)
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risk = model.kl_to_preferred(next_belief)
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G.append(ambiguity + risk)
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return candidate_actions[torch.argmin(torch.tensor(G))]
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```
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### Z-IL (PC ≡ BP at convergence)
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```python
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# Song et al 2020: at the equilibrium of PC inference,
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# weight updates equal those produced by BP.
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# Critical detail: feedback weights = transpose of forward weights (tied).
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```
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## 매 결정 기준
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| 상황 | Approach |
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|---|---|
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| Biological plausibility required | Predictive coding |
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| Energy efficiency on neuromorphic HW | PC / spiking PC |
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| SOTA accuracy on ImageNet | Backprop CNN/ViT (still wins) |
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| Continual learning | PC w/ uncertainty-weighted errors |
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| Interpretation of cortical hierarchy | PC as theory |
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**기본값**: BP for engineering; PC for neuroscience modeling 또는 neuromorphic deployment.
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## 🔗 Graph
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- 부모: [[Computational-Neuroscience-RL|Computational-Neuroscience]] · [[Free-Energy-Principle]]
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- 변형: [[Active-Inference]]
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- 응용: [[Bayesian-Brain]] · [[Neuromorphic-Computing]]
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- Adjacent: [[데이터 사이언스 및 ML 엔지니어링|Backpropagation]] · [[Variational-Inference]]
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## 🤖 LLM 활용
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**언제**: brain-inspired model design, biologically-plausible learning, continual learning, neuromorphic chips.
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**언제 X**: pure engineering goals — backprop is faster and more accurate.
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## ❌ 안티패턴
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- **PC as drop-in BP replacement**: still slower and less accurate at scale.
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- **Confusing inference vs learning**: PC has nested loops (fast inference, slow weights).
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- **Ignoring weight symmetry**: untied feedback breaks BP equivalence.
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- **Free-energy hand-wave**: equation must be operationalized concretely.
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## 🧪 검증 / 중복
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- Verified (Rao & Ballard 1999 Nat Neurosci, Friston 2010, Song et al 2020 NeurIPS).
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — full PC theory + modern PC NN code |
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