import numpy as np

class MathematicalNativeAGI:
    def __init__(self):
        self.knowledge_base = {}  # Dictionary to store learned mathematical functions and their rules
        self.learned_operations = set()  # Set to track which operations have been learned
        self.current_operation = None
    
    def learn(self, operation, inputs, output):
        """Learn a new mathematical operation."""
        if operation not in self.knowledge_base:
            self.knowledge_base[operation] = {'inputs': [], 'outputs': []}
        
        self.knowledge_base[operation]['inputs'].append(inputs)
        self.knowledge_base[operation]['outputs'].append(output)
        self.learned_operations.add(operation)

    def get_knowledge(self, operation):
        """Get the knowledge of a specific mathematical operation."""
        if operation in self.knowledge_base:
            return self.knowledge_base[operation]
        else:
            raise ValueError(f"No knowledge available for {operation}")

    def recognize_pattern(self, inputs):
        """Recognize patterns based on known operations and their inputs/outputs."""
        pattern_found = False
        best_match_operation = None
        min_distance = float('inf')
        
        for operation in self.learned_operations:
            stored_inputs = np.array(self.get_knowledge(operation)['inputs'])
            if len(stored_inputs) == 0:  # No knowledge on this operation yet.
                continue
            
            distance = np.linalg.norm(inputs - stored_inputs, axis=1).min()
            
            if distance < min_distance:
                pattern_found = True
                best_match_operation = operation
                min_distance = distance
        
        return best_match_operation, min_distance
    
    def perform_task(self, task):
        """Perform a given mathematical task based on learned knowledge."""
        self.current_operation = task.operation
        inputs = task.inputs

        if self.current_operation in self.learned_operations:
            # Perform the learned operation directly.
            output = self.get_knowledge(task.operation)['outputs'][-1]  # Use last stored output as initial guess
            for input_data, known_output in zip(self.get_knowledge(task.operation)['inputs'], self.get_knowledge(task.operation)['outputs']):
                if np.all(input_data == inputs):
                    return known_output
        else:
            # Recognize patterns and attempt to generalize.
            best_match_operation, _ = self.recognize_pattern(inputs)
            
            if best_match_operation is None:
                raise ValueError("No pattern recognized for the given inputs.")
            
            output = self.get_knowledge(best_match_operation)['outputs'][-1]
        
        return output
    
    def refine(self):
        """Refine knowledge based on feedback and new tasks."""
        # This function could involve more sophisticated techniques like machine learning,
        # but here we just add a simple rule-based approach.
        for operation, knowledge in self.knowledge_base.items():
            if len(knowledge['inputs']) > 1:
                avg_input = np.mean(np.array(knowledge['inputs']), axis=0)
                avg_output = np.mean(np.array(knowledge['outputs']))
                self.learn(operation, avg_input, avg_output)

class Task:
    def __init__(self, operation, inputs):
        self.operation = operation
        self.inputs = inputs

# Example usage:

agi_system = MathematicalNativeAGI()

# Learning some operations.
agi_system.learn('add', [1, 2], 3)
agi_system.learn('subtract', [5, 3], 2)
agi_system.learn('multiply', [4, 6], 24)

# Performing tasks
task_addition = Task(operation='add', inputs=[7, 3])
result_addition = agi_system.perform_task(task_addition)
print(f"Result of addition: {result_addition}")

task_subtraction = Task(operation='subtract', inputs=[8, 5])
result_subtraction = agi_system.perform_task(task_subtraction)
print(f"Result of subtraction: {result_subtraction}")

# Refining knowledge
agi_system.refine()