2nd/10_Wiki/Topics/Domain_Programming/AI_and_ML/Predictive-Coding.md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

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

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)

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)

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)

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)

# 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 · Free-Energy-Principle
• 변형: Active-Inference
• 응용: Bayesian-Brain · Neuromorphic-Computing
• Adjacent: 데이터 사이언스 및 ML 엔지니어링 · 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