2nd/10_Wiki/Topics/Other/Feedback-Loops.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-feedback-loops	Feedback Loops	10_Wiki/Topics	verified	self	Feedback Control Closed Loop Cybernetic Feedback	none	A	0.9	applied	systems control-theory cybernetics dynamics		2026-05-10	pending	language framework python control-systems

Feedback Loops

매 한 줄

"매 system output 의 input 의 re-entry — 매 stability 또는 amplification 의 결정". 매 1948 Wiener 의 Cybernetics 가 unifying frame. 매 2026 의 RLHF, autoscaling, climate tipping points, social media engagement loop 의 modern instances.

매 핵심

매 2 polarities

• Negative (balancing): 매 deviation 의 dampen — 매 thermostat, homeostasis, PID controller.
• Positive (reinforcing): 매 deviation 의 amplify — 매 viral growth, asset bubble, ice-albedo feedback, runaway selection.

매 5 archetypes (Senge)

• Limits to growth: 매 reinforcing + balancing — 매 S-curve.
• Shifting the burden: 매 quick fix 의 underlying issue 의 weaken.
• Tragedy of the commons: 매 individual reinforcing → collective collapse.
• Fixes that fail: 매 short-term fix 의 long-term backfire.
• Success to the successful: 매 winner-take-all reinforcing.

매 stability concepts

• Gain: 매 output/input ratio.
• Phase margin: 매 stability buffer (>45° robust).
• Time delay: 매 instability driver (Bode-Nyquist).
• Setpoint vs. error: 매 target — actual.

매 응용

1. PID controller (industrial process).
2. RLHF (LLM 의 preference loop).
3. Autoscaling (Kubernetes HPA, target CPU).
4. Insulin-glucose homeostasis.
5. Market price discovery.

💻 패턴

PID controller

class PID:
    def __init__(self, kp: float, ki: float, kd: float, setpoint: float):
        self.kp, self.ki, self.kd = kp, ki, kd
        self.setpoint = setpoint
        self.integral = 0.0
        self.prev_error = 0.0

    def step(self, measurement: float, dt: float) -> float:
        error = self.setpoint - measurement
        self.integral += error * dt
        derivative = (error - self.prev_error) / dt if dt > 0 else 0
        self.prev_error = error
        return self.kp * error + self.ki * self.integral + self.kd * derivative

Logistic growth (limits-to-growth archetype)

import numpy as np
from scipy.integrate import odeint

def logistic(N, t, r, K):
    return r * N * (1 - N / K)

t = np.linspace(0, 50, 500)
N = odeint(logistic, y0=1, t=t, args=(0.3, 1000))
# Reinforcing (rN) + balancing ((1 - N/K))

Autoscaling reactive loop

def autoscale_step(current_replicas: int, cpu_utilization: float,
                   target: float = 0.7, max_replicas: int = 100) -> int:
    desired = int(current_replicas * cpu_utilization / target)
    return max(1, min(desired, max_replicas))

Reinforcement learning (RLHF reward model loop)

def rlhf_iteration(policy, reward_model, prompts, ppo_optimizer):
    rollouts = [policy.generate(p) for p in prompts]
    rewards = [reward_model.score(p, r) for p, r in zip(prompts, rollouts)]
    advantages = compute_advantages(rewards)
    ppo_optimizer.step(policy, rollouts, advantages)
    # Loop closes: policy → output → reward → policy update

Stability check (root locus)

import numpy as np
from scipy.signal import TransferFunction, bode

# Open-loop transfer function
sys = TransferFunction([1], [1, 2, 3, 1])  # 3rd order
w, mag, phase = bode(sys)
# Phase margin: phase at gain crossover + 180°

Detect runaway positive feedback

def detect_runaway(time_series: list[float], window: int = 10, threshold: float = 1.5) -> bool:
    """Exponential growth detector — log-linear fit slope."""
    import numpy as np
    if len(time_series) < window:
        return False
    y = np.log(np.maximum(time_series[-window:], 1e-9))
    slope = np.polyfit(range(window), y, 1)[0]
    return slope > np.log(threshold) / window

매 결정 기준

상황	Approach
Process regulation, setpoint tracking	PID (negative feedback)
Growth modeling	logistic / Gompertz (mixed)
Cascading failure prevention	rate limiters + circuit breakers
Slow process w/ delay	feed-forward + smith predictor
ML training	RLHF / GRPO with KL regularization

기본값: 매 negative feedback 의 default for stability. 매 positive feedback 의 explicit guard (rate limit, kill switch).

🔗 Graph

• 부모: Cybernetics Foundations · Control Theory · Systems_Thinking
• 응용: RLHF · Homeostasis (항상성)

🤖 LLM 활용

언제: 매 archetype identification, 매 PID gain initial estimation, 매 system dynamics diagram 의 stock-flow conversion. 언제 X: 매 safety-critical control gain tuning — 매 hardware-in-the-loop testing, 매 actual phase margin verification 필수.

❌ 안티패턴

• Ignoring delay: 매 time-delay 의 PID 의 instability — 매 dead-time compensation 필요.
• High gain assumption = better tracking: 매 oscillation, 매 noise amplification.
• Open-loop control for safety-critical: 매 disturbance rejection X — 매 closed-loop 필수.
• Reinforcing loop 의 무방어 deploy: 매 viral metric 의 optimization — 매 social harm runaway (engagement maximization → polarization).

🧪 검증 / 중복

• Verified (Wiener "Cybernetics" 1948, Åström & Murray "Feedback Systems" 2nd ed, Sterman "Business Dynamics" 2000, Senge "Fifth Discipline" rev. ed).
• 신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — PID, Senge archetypes, RLHF/autoscaling 추가