Recursion

1. https://link.springer.com/10.1007/s10462-022-10149-w
2. https://bmcgeriatr.biomedcentral.com/articles/10.1186/s12877-024-05148-1
3. https://www.semanticscholar.org/paper/21755d181d0818f89005b2a5c88646a06249dbcb
4. https://www.semanticscholar.org/paper/30f177f4cfee537cd570b50036dca4dac837bd0d
5. https://ojs.ehu.eus/index.php/THEORIA/article/view/784
6. https://www.nature.com/articles/s41598-025-90459-5
7. https://ieeexplore.ieee.org/document/9035446/
8. https://besjournals.onlinelibrary.wiley.com/doi/10.1111/j.1365-2656.2008.01390.x
9. https://www.mdpi.com/2072-6694/15/3/625
10. https://ojs.sciencesforce.com/index.php/scin/article/view/267
11. https://arxiv.org/pdf/2307.00337.pdf
12. http://arxiv.org/pdf/1312.6192.pdf
13. https://academic.oup.com/pnasnexus/advance-article-pdf/doi/10.1093/pnasnexus/pgad337/52137329/pgad337.pdf
14. http://arxiv.org/pdf/2410.12375v1.pdf
15. http://arxiv.org/pdf/1901.09216.pdf
16. https://arxiv.org/pdf/1604.05557.pdf
17. https://www.mdpi.com/2227-7390/11/20/4309/pdf?version=1697451358
18. https://arxiv.org/pdf/2306.10196.pdf

Appendix  A:

Medical industry:

import numpy as np

class RecursiveAGIModel:
    def __init__(self, feature_names):
        # Initialize model state: feature importance weights, recursive states
        self.features = feature_names
        self.state = np.ones(len(self.features))  # initial uniform weights
        self.history = []

    def pattern_find(self, feature_values):
        # Normalizes feature values into a probability vector
        total = sum(feature_values)
        if total == 0:
            return np.zeros(len(feature_values))
        return np.array(feature_values) / total

    def recursive_update(self, input_features, learning_rate=0.1):
        # Update model state recursively with new input, incorporating pattern recognition
        pattern = self.pattern_find(input_features)
        # Simple weight update resembling Hebbian learning
        self.state = (1 - learning_rate) * self.state + learning_rate * pattern
        self.history.append(self.state.copy())
        return self.state

    def predict_condition(self, input_features, condition_templates):
        # Compares input pattern to known condition templates (pattern matching)
        pattern = self.pattern_find(input_features)
        similarities = {}
        for condition, template in condition_templates.items():
            # Cosine similarity or dot product
            similarity = np.dot(pattern, template) / (np.linalg.norm(pattern) * np.linalg.norm(template) + 1e-6)
            similarities[condition] = similarity
        # Return most similar condition
        predicted = max(similarities, key=similarities.get)
        confidence = similarities[predicted]
        return predicted, confidence

# Example usage in medical diagnostics setting:

# Patient features: medical signs/symptoms quantified scores
patient_data = [
    [3, 2, 5, 1, 0],  # Sample 1
    [4, 1, 6, 0, 1],  # Sample 2 etc.
    [2, 0, 7, 1, 2],
]

# Known condition templates (normalized patterns)
condition_templates = {
    'ConditionA': np.array([0.3, 0.2, 0.4, 0.05, 0.05]),
    'ConditionB': np.array([0.1, 0.1, 0.6, 0.1, 0.1]),
    'ConditionC': np.array([0.25, 0.25, 0.25, 0.15, 0.1])
}

model = RecursiveAGIModel(feature_names=['fever', 'cough', 'fatigue', 'headache', 'rash'])

for sample in patient_data:
    updated_state = model.recursive_update(sample)
    prediction, conf = model.predict_condition(sample, condition_templates)
    print(f"Predicted Condition: {prediction} with confidence {conf:.2f}")
    print(f"Updated internal state weights: {updated_state}")

Appendix B:

Financial Industry:

import numpy as np

class RecursiveAGIFinancialModel:
    def __init__(self, feature_names):
        # Initialize model state: feature importance weights, recursive states
        self.features = feature_names
        self.state = np.ones(len(self.features))  # initial uniform weights
        self.history = []

    def pattern_find(self, feature_values):
        # Normalize financial indicators into a probability vector
        total = sum(feature_values)
        if total == 0:
            return np.zeros(len(feature_values))
        return np.array(feature_values) / total

    def recursive_update(self, input_features, learning_rate=0.1):
        # Update model state recursively with new input, incorporating pattern recognition
        pattern = self.pattern_find(input_features)
        # Update weights resembling Hebbian learning adapted for financial signals
        self.state = (1 - learning_rate) * self.state + learning_rate * pattern
        self.history.append(self.state.copy())
        return self.state

    def predict_financial_state(self, input_features, financial_templates):
        # Compare input pattern to known financial patterns/templates (risk profiles, market states)
        pattern = self.pattern_find(input_features)
        similarities = {}
        for state, template in financial_templates.items():
            similarity = np.dot(pattern, template) / (np.linalg.norm(pattern) * np.linalg.norm(template) + 1e-6)
            similarities[state] = similarity
        predicted = max(similarities, key=similarities.get)
        confidence = similarities[predicted]
        return predicted, confidence

# Example usage in finance setting:

# Financial features: indicators like volatility, momentum, liquidity, leverage, sentiment scores
financial_data = [
    [0.4, 0.3, 0.1, 0.1, 0.1],  # Sample 1
    [0.1, 0.5, 0.2, 0.1, 0.1],  # Sample 2
    [0.3, 0.2, 0.3, 0.1, 0.1],  # Sample 3
]

# Known financial state templates (normalized risk or market states)
financial_templates = {
    'Bull Market': np.array([0.5, 0.3, 0.1, 0.05, 0.05]),
    'Bear Market': np.array([0.2, 0.2, 0.4, 0.1, 0.1]),
    'Volatile Market': np.array([0.3, 0.3, 0.2, 0.1, 0.1])
}

model = RecursiveAGIFinancialModel(feature_names=['volatility', 'momentum', 'liquidity', 'leverage', 'sentiment'])

for sample in financial_data:
    updated_state = model.recursive_update(sample)
    prediction, conf = model.predict_financial_state(sample, financial_templates)
    print(f"Predicted Market State: {prediction} with confidence {conf:.2f}")
    print(f"Updated internal state weights: {updated_state}")

Appendix C:

Grid Telco/Energy:

import numpy as np

class RecursiveAGIEnergyGridModel:
    def __init__(self, feature_names):
        # Initialize model state: feature importance weights, recursive states
        self.features = feature_names
        self.state = np.ones(len(self.features))  # initial uniform weights
        self.history = []

    def pattern_find(self, feature_values):
        # Normalize grid indicators into a probability vector
        total = sum(feature_values)
        if total == 0:
            return np.zeros(len(feature_values))
        return np.array(feature_values) / total

    def recursive_update(self, input_features, learning_rate=0.1):
        # Update model state recursively with new input, incorporating pattern recognition
        pattern = self.pattern_find(input_features)
        # Update weights resembling Hebbian learning adapted for energy system signals
        self.state = (1 - learning_rate) * self.state + learning_rate * pattern
        self.history.append(self.state.copy())
        return self.state

    def predict_grid_status(self, input_features, grid_status_templates):
        # Compare input pattern to known grid states (e.g., stable, overloaded, fault)
        pattern = self.pattern_find(input_features)
        similarities = {}
        for status, template in grid_status_templates.items():
            similarity = np.dot(pattern, template) / (np.linalg.norm(pattern) * np.linalg.norm(template) + 1e-6)
            similarities[status] = similarity
        predicted = max(similarities, key=similarities.get)
        confidence = similarities[predicted]
        return predicted, confidence

# Example usage in telecommunication energy grid management:

# Grid features: real-time indicators like load, voltage stability, frequency deviation, fault counts, renewable input ratio
grid_data = [
    [0.7, 0.8, 0.1, 0.0, 0.4],  # Sample 1
    [0.4, 0.6, 0.3, 0.2, 0.5],  # Sample 2
    [0.2, 0.7, 0.5, 0.3, 0.3],  # Sample 3
]

# Known grid status templates (normalized patterns)
grid_status_templates = {
    'Stable': np.array([0.6, 0.8, 0.05, 0.02, 0.4]),
    'Overloaded': np.array([0.3, 0.5, 0.4, 0.3, 0.2]),
    'Faulty': np.array([0.1, 0.2, 0.8, 0.6, 0.1])
}

model = RecursiveAGIEnergyGridModel(
    feature_names=['load', 'voltage_stability', 'frequency_deviation', 'fault_counts', 'renewable_input_ratio']
)

for sample in grid_data:
    updated_state = model.recursive_update(sample)
    prediction, conf = model.predict_grid_status(sample, grid_status_templates)
    print(f"Predicted Grid Status: {prediction} with confidence {conf:.2f}")
    print(f"Updated internal state weights: {updated_state}")

Appendix D:

Education System:

import numpy as np

class RecursiveAGIEducationModel:
    def __init__(self, feature_names):
        # Initialize model state: feature importance weights, recursive states
        self.features = feature_names
        self.state = np.ones(len(self.features))  # initial uniform weights
        self.history = []

    def pattern_find(self, feature_values):
        # Normalize educational indicators into a probability vector
        total = sum(feature_values)
        if total == 0:
            return np.zeros(len(feature_values))
        return np.array(feature_values) / total

    def recursive_update(self, input_features, learning_rate=0.1):
        # Update model state recursively with new input, incorporating pattern recognition
        pattern = self.pattern_find(input_features)
        # Update weights resembling Hebbian learning adapted for educational signals
        self.state = (1 - learning_rate) * self.state + learning_rate * pattern
        self.history.append(self.state.copy())
        return self.state

    def predict_learning_style(self, input_features, learning_style_templates):
        # Compare input pattern to known learning style templates (e.g., visual, auditory, kinesthetic)
        pattern = self.pattern_find(input_features)
        similarities = {}
        for style, template in learning_style_templates.items():
            similarity = np.dot(pattern, template) / (np.linalg.norm(pattern) * np.linalg.norm(template) + 1e-6)
            similarities[style] = similarity
        predicted = max(similarities, key=similarities.get)
        confidence = similarities[predicted]
        return predicted, confidence

# Example usage in educational setting:

# Student features: indicators like engagement, homework_completion, quiz_scores, participation, interest_level
student_data = [
    [0.6, 0.8, 0.7, 0.9, 0.5],  # Sample Student 1
    [0.3, 0.5, 0.6, 0.4, 0.7],  # Sample Student 2
    [0.7, 0.9, 0.8, 0.7, 0.6],  # Sample Student 3
]

# Known learning style templates (normalized patterns)
learning_style_templates = {
    'Visual': np.array([0.5, 0.3, 0.1, 0.05, 0.05]),
    'Auditory': np.array([0.2, 0.4, 0.3, 0.1, 0.0]),
    'Kinesthetic': np.array([0.3, 0.2, 0.4, 0.05, 0.05])
}

model = RecursiveAGIEducationModel(feature_names=['engagement', 'homework_completion', 'quiz_scores', 'participation', 'interest_level'])

for sample in student_data:
    updated_state = model.recursive_update(sample)
    prediction, conf = model.predict_learning_style(sample, learning_style_templates)
    print(f"Predicted Learning Style: {prediction} with confidence {conf:.2f}")
    print(f"Updated internal state weights: {updated_state}")