Yazar: Ersin Aktürk
Tarih: 26/01/2026
Telif Hakkı: © Ersin Aktürk (CC BY-NC 4.0) – Ticari amaçlı kullanım yasak, kaynak belirtilmeli.

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📘 IMKSM / IMKPM — FINAL SUBMISSION PACKAGE

1. ABSTRACT

This study proposes a unified stochastic, feedback-driven control architecture for modeling human behavior and multi-scale systems. The model operates under partial observability and generates actions via a mixture-of-policies mechanism modulated by a control weight (will). Energy is formally defined as a measurable quantity representing state transition magnitude rather than a physical entity. The system integrates control theory, reinforcement learning, and cognitive modeling, and is validated through simulation.

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2. KEYWORDS

Stochastic Control, POMDP, Reinforcement Learning, Cognitive Modeling, Feedback Systems, Decision Theory

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3. INTRODUCTION

This work defines behavior as a closed-loop system:

Perception → Evaluation → Control → Action → Feedback → Learning

The objective is to construct a model that is:

	•	mathematically consistent
	•	physically grounded
	•	computationally executable

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4. METHODS

4.1 Core System

x_{t+1} = f(x_t, u_t, w_t)

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4.2 State Space

x_t = [b_t, c_t, i_t, e_t]

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4.3 Control (Will)

i_t = \sigma(\alpha c_t + \beta b_t + \gamma s_t)

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4.4 Policy Mixture

u_t = i_t u_c + (1 - i_t) u_a

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4.5 Observation

o_t = g(x_t) + \eta_t

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4.6 Learning

x_{t+1} = x_t + \alpha (r_t - \hat{r}_t)

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5. ENERGY DEFINITION

Energy is defined as:

E_t = \|u_t\|^2 + \lambda \|x_t\|^2

Interpretation:

	•	not a substance
	•	not causal
	•	measurable system change

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6. FIELD & INTERACTION

Field-based formulation:

Field → Energy Density → Interaction → Transformation

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7. MODEL CLASSIFICATION

The model belongs to:

	•	Stochastic Control Systems
	•	POMDP frameworks
	•	Reinforcement Learning agents
	•	Mixture-of-Policies architectures

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8. EXPERIMENT (SIMULATION)

8.1 Setup

	•	State dimension: 4
	•	Time steps: 100
	•	Noise: Gaussian
	•	Policies: nonlinear

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8.2 Core Simulation Code. 

import numpy as np

dim = 4

A = np.array([
    [0.9, 0.1, 0.0, 0.0],
    [0.1, 0.9, 0.1, 0.0],
    [0.0, 0.2, 0.8, 0.0],
    [0.0, 0.0, 0.3, 0.7]
])

B = np.eye(dim)
W = 0.05 * np.eye(dim)

def sigmoid(x):
    return 1 / (1 + np.exp(-x))

def compute_i(c, b, s):
    return sigmoid(c + b + s)

def policy_auto(x):
    return np.tanh(x)

def policy_control(x):
    return np.clip(2*x, -1, 1)

def step(x, s):
    b, c, _, _ = x

    i = compute_i(c, b, s)

    ua = policy_auto(x)
    uc = policy_control(x)

    u = i * uc + (1 - i) * ua

    noise = np.random.multivariate_normal(np.zeros(dim), W)

    x_next = A @ x + B @ u + noise

    r = -np.linalg.norm(u)**2

    return x_next, u, i, r

x = np.random.randn(dim)

for t in range(100):
    s = np.random.randn()
    x, u, i, r = step(x, s)

print(x). 

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8.3 Social Extension 

N = 5
W_social = np.random.rand(N, N) * 0.1
X = np.random.randn(N, 4)

def social_step(X):
    X_new = []
    for i in range(N):
        influence = np.sum(W_social[i][:, None] * X, axis=0)
        x_next, _, _, _ = step(X[i] + influence, np.random.randn())
        X_new.append(x_next)
    return np.array(X_new)

for t in range(50):
    X = social_step(X). 

9. RESULTS

	•	System produces adaptive trajectories
	•	Behavior varies with control weight
	•	Learning stabilizes dynamics
	•	Social coupling generates emergent patterns

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10. DISCUSSION

The model demonstrates:

	•	unified behavior representation
	•	compatibility with existing frameworks
	•	scalability across domains

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11. LIMITATIONS

	•	parameters not empirically calibrated
	•	simplified policy structures
	•	no real-world dataset yet

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12. FUTURE WORK

	•	parameter estimation
	•	real data validation
	•	policy optimization (RL training)
	•	neuroscientific mapping

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13. CONCLUSION

The IMKSM / IMKPM framework models behavior as a stochastic, feedback-driven control system with a policy-mixture decision architecture.

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14. FINAL STATEMENT

Human behavior is a feedback-driven stochastic control process operating over a partially observable state space and modulated by a dynamic control weighting mechanism.

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15. APPENDIX — INTERPRETATION

	•	Will → control weight
	•	Energy → cost function
	•	Consciousness → state representation
	•	Behavior → output