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Addressing Hallucinations in Large Language Models.md

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Addressing Hallucinations in Large Language Models

Slide 1: Understanding Intrinsic Hallucinations in LLMs

Neural networks often exhibit intrinsic hallucinations due to knowledge gaps in their training data. We can simulate this behavior by creating a simplified neural network that demonstrates how confidence scores may not correlate with factual accuracy.

import numpy as np

class SimpleHallucinationDetector:
    def __init__(self, knowledge_base):
        self.knowledge = knowledge_base
        self.confidence_threshold = 0.8
    
    def query(self, input_query):
        # Simulate knowledge retrieval with random confidence
        confidence = np.random.random()
        
        if input_query in self.knowledge:
            response = self.knowledge[input_query]
            is_hallucination = False
        else:
            # Generate synthetic response for unknown queries
            response = f"Synthetic answer for {input_query}"
            is_hallucination = True
            
        return {
            'response': response,
            'confidence': confidence,
            'is_hallucination': is_hallucination
        }

# Example usage
knowledge_base = {
    'capital of France': 'Paris',
    'largest planet': 'Jupiter'
}

detector = SimpleHallucinationDetector(knowledge_base)
print(detector.query('capital of France'))
print(detector.query('unknown topic'))

Slide 2: Extrinsic Hallucination Detection System

This implementation demonstrates how external hallucinations occur when models misinterpret input prompts. The system uses pattern matching and semantic similarity to identify potential hallucinations in model responses.

import numpy as np
from sklearn.feature_extraction.text import TfidfVectorizer
from sklearn.metrics.pairwise import cosine_similarity

class ExtrinsicHallucinationDetector:
    def __init__(self):
        self.vectorizer = TfidfVectorizer()
        self.context_vectors = None
        
    def train(self, context_documents):
        self.context_vectors = self.vectorizer.fit_transform(context_documents)
    
    def check_hallucination(self, response, threshold=0.3):
        response_vector = self.vectorizer.transform([response])
        similarities = cosine_similarity(response_vector, self.context_vectors)
        max_similarity = np.max(similarities)
        
        return {
            'is_hallucination': max_similarity < threshold,
            'confidence_score': max_similarity,
            'response': response
        }

# Example usage
context = [
    "AI models process data using neural networks",
    "Machine learning requires training data",
    "Deep learning uses multiple layers"
]

detector = ExtrinsicHallucinationDetector()
detector.train(context)

test_response = "AI models use quantum computing for training"
print(detector.check_hallucination(test_response))

Slide 3: Amalgamated Hallucination Analysis

To detect amalgamated hallucinations, we implement a system that tracks fact consistency across multiple knowledge sources and identifies incorrect combinations of otherwise valid information.

from typing import Dict, List, Tuple
import numpy as np

class AmalgamatedHallucinationAnalyzer:
    def __init__(self, fact_database: Dict[str, List[str]]):
        self.facts = fact_database
        self.connection_matrix = {}
        self._build_connections()
    
    def _build_connections(self):
        for topic, facts in self.facts.items():
            self.connection_matrix[topic] = {
                fact: self._calculate_fact_validity(fact, facts)
                for fact in facts
            }
    
    def _calculate_fact_validity(self, fact: str, related_facts: List[str]) -> float:
        # Simulate fact validation using random weights
        return np.random.random()
    
    def analyze_statement(self, statement: str) -> Dict:
        # Simplified analysis of combined facts
        validity_score = np.random.random()
        is_amalgamated = validity_score < 0.5
        
        return {
            'statement': statement,
            'validity_score': validity_score,
            'is_amalgamated_hallucination': is_amalgamated,
            'confidence': 1 - validity_score if is_amalgamated else validity_score
        }

# Example usage
facts_db = {
    'AI': ['processes data', 'uses algorithms'],
    'ML': ['requires training', 'needs validation']
}

analyzer = AmalgamatedHallucinationAnalyzer(facts_db)
result = analyzer.analyze_statement("AI processes validation using training algorithms")
print(result)

Slide 4: Non-Factual Hallucination Detection

The implementation focuses on identifying contradictions between model outputs and established knowledge bases, using semantic analysis and contradiction detection algorithms.

from dataclasses import dataclass
from typing import List, Set
import numpy as np

@dataclass
class KnowledgeItem:
    fact: str
    confidence: float
    sources: Set[str]

class NonFactualHallucinationDetector:
    def __init__(self, knowledge_base: List[KnowledgeItem]):
        self.knowledge = knowledge_base
        self.contradiction_threshold = 0.7
        
    def detect_contradictions(self, statement: str) -> Dict:
        # Simulate contradiction detection
        contradictions = []
        overall_confidence = 1.0
        
        for item in self.knowledge:
            contradiction_score = self._calculate_contradiction(statement, item)
            if contradiction_score > self.contradiction_threshold:
                contradictions.append({
                    'known_fact': item.fact,
                    'contradiction_score': contradiction_score
                })
                overall_confidence *= (1 - contradiction_score)
        
        return {
            'statement': statement,
            'is_contradictory': len(contradictions) > 0,
            'contradictions': contradictions,
            'confidence': overall_confidence
        }
    
    def _calculate_contradiction(self, statement: str, knowledge_item: KnowledgeItem) -> float:
        return np.random.random()

# Example usage
knowledge_base = [
    KnowledgeItem("Earth is spherical", 0.99, {"NASA", "Geography"}),
    KnowledgeItem("Gravity attracts objects", 0.99, {"Physics"})
]

detector = NonFactualHallucinationDetector(knowledge_base)
result = detector.detect_contradictions("Earth is flat and gravity repels objects")
print(result)

Slide 5: Knowledge Overshadowing Implementation

Knowledge overshadowing occurs when dominant concepts override relevant but less prominent information. This implementation demonstrates how to detect and quantify this phenomenon using attention weights and concept dominance scores.

import numpy as np
from typing import List, Dict, Tuple

class KnowledgeOvershadowingDetector:
    def __init__(self, concept_weights: Dict[str, float]):
        self.concept_weights = concept_weights
        self.attention_threshold = 0.6
        
    def analyze_attention_distribution(self, 
                                    input_concepts: List[str], 
                                    attention_scores: List[float]) -> Dict:
        dominant_concepts = []
        overshadowed_concepts = []
        
        # Calculate normalized attention distribution
        total_attention = sum(attention_scores)
        normalized_scores = [score/total_attention for score in attention_scores]
        
        for concept, score in zip(input_concepts, normalized_scores):
            if score > self.attention_threshold:
                dominant_concepts.append((concept, score))
            else:
                overshadowed_concepts.append((concept, score))
                
        return {
            'dominant_concepts': dominant_concepts,
            'overshadowed_concepts': overshadowed_concepts,
            'overshadowing_ratio': len(dominant_concepts) / len(input_concepts)
        }
    
    def detect_overshadowing(self, input_text: str) -> Dict:
        # Simulate attention scores for concepts
        concepts = input_text.split()
        attention_scores = [
            self.concept_weights.get(concept, np.random.random())
            for concept in concepts
        ]
        
        return self.analyze_attention_distribution(concepts, attention_scores)

# Example usage
concept_weights = {
    'neural': 0.9,
    'network': 0.8,
    'training': 0.7,
    'optimization': 0.3
}

detector = KnowledgeOvershadowingDetector(concept_weights)
result = detector.detect_overshadowing("neural network training optimization")
print(result)

Slide 6: Insufficient Knowledge Representation Analysis

A critical implementation for detecting knowledge gaps in deep learning models through layer-wise analysis. This system evaluates the depth and completeness of knowledge representation across neural network layers.

import numpy as np
from typing import List, Dict, Optional

class KnowledgeRepresentationAnalyzer:
    def __init__(self, num_layers: int, knowledge_dim: int):
        self.num_layers = num_layers
        self.knowledge_dim = knowledge_dim
        self.layer_matrices = self._initialize_layers()
        
    def _initialize_layers(self) -> List[np.ndarray]:
        return [
            np.random.random((self.knowledge_dim, self.knowledge_dim))
            for _ in range(self.num_layers)
        ]
    
    def compute_knowledge_coverage(self, 
                                 input_vector: np.ndarray,
                                 layer_idx: Optional[int] = None) -> Dict:
        if layer_idx is not None:
            coverage = self._single_layer_coverage(input_vector, layer_idx)
        else:
            coverage = self._full_network_coverage(input_vector)
            
        return {
            'coverage_score': float(coverage.mean()),
            'coverage_std': float(coverage.std()),
            'knowledge_gaps': np.where(coverage < 0.5)[0].tolist()
        }
    
    def _single_layer_coverage(self, 
                             input_vector: np.ndarray, 
                             layer_idx: int) -> np.ndarray:
        return np.dot(input_vector, self.layer_matrices[layer_idx])
    
    def _full_network_coverage(self, input_vector: np.ndarray) -> np.ndarray:
        current_vector = input_vector
        for layer_matrix in self.layer_matrices:
            current_vector = np.dot(current_vector, layer_matrix)
        return current_vector

# Example usage
analyzer = KnowledgeRepresentationAnalyzer(num_layers=3, knowledge_dim=5)
input_vector = np.random.random(5)
layer_result = analyzer.compute_knowledge_coverage(input_vector, layer_idx=1)
full_result = analyzer.compute_knowledge_coverage(input_vector)
print("Layer analysis:", layer_result)
print("Full network analysis:", full_result)

Slide 7: Information Extraction Error Detection

This implementation focuses on identifying and quantifying errors in the information extraction process, using pattern matching and semantic validation to detect potential extraction failures.

from dataclasses import dataclass
from typing import List, Dict, Set, Optional
import numpy as np

@dataclass
class ExtractedInfo:
    text: str
    confidence: float
    source_span: Tuple[int, int]
    validation_score: float

class InformationExtractionValidator:
    def __init__(self, validation_patterns: Dict[str, List[str]]):
        self.patterns = validation_patterns
        self.min_confidence = 0.7
        
    def validate_extraction(self, 
                          extracted_info: ExtractedInfo,
                          context: str) -> Dict:
        # Validate extraction against patterns
        pattern_matches = self._check_patterns(extracted_info.text)
        context_validity = self._validate_context(extracted_info, context)
        
        combined_score = (pattern_matches + context_validity) / 2
        
        return {
            'extracted_text': extracted_info.text,
            'is_valid': combined_score >= self.min_confidence,
            'confidence': extracted_info.confidence,
            'validation_score': combined_score,
            'error_analysis': {
                'pattern_match_score': pattern_matches,
                'context_validity': context_validity
            }
        }
    
    def _check_patterns(self, text: str) -> float:
        # Simulate pattern matching
        return np.random.random()
    
    def _validate_context(self, 
                         info: ExtractedInfo, 
                         context: str) -> float:
        # Simulate context validation
        return np.random.random()

# Example usage
patterns = {
    'date': [r'\d{4}-\d{2}-\d{2}', r'\d{2}/\d{2}/\d{4}'],
    'email': [r'[\w\.-]+@[\w\.-]+\.\w+']
}

validator = InformationExtractionValidator(patterns)
extracted = ExtractedInfo(
    text="[email protected]",
    confidence=0.85,
    source_span=(0, 15),
    validation_score=0.9
)

result = validator.validate_extraction(extracted, "Contact at [email protected]")
print(result)

Slide 8: Contextual Misalignment Detection System

This implementation provides a sophisticated approach to detecting contextual misalignments in LLM responses by analyzing semantic coherence and context relevance through vector space comparisons.

import numpy as np
from typing import List, Dict, Tuple
from scipy.spatial.distance import cosine

class ContextualMisalignmentDetector:
    def __init__(self, context_window_size: int = 5):
        self.window_size = context_window_size
        self.semantic_threshold = 0.75
        
    def create_context_embeddings(self, text_sequence: List[str]) -> np.ndarray:
        # Simulate word embeddings (In practice, use proper embeddings)
        return np.random.random((len(text_sequence), 300))
    
    def detect_misalignment(self, 
                          context: List[str],
                          response: str) -> Dict[str, float]:
        context_embeddings = self.create_context_embeddings(context)
        response_embedding = self.create_context_embeddings([response])[0]
        
        window_scores = []
        for i in range(len(context) - self.window_size + 1):
            window = context_embeddings[i:i + self.window_size]
            window_centroid = np.mean(window, axis=0)
            alignment_score = 1 - cosine(window_centroid, response_embedding)
            window_scores.append(alignment_score)
        
        max_alignment = max(window_scores)
        
        return {
            'alignment_score': max_alignment,
            'is_misaligned': max_alignment < self.semantic_threshold,
            'confidence': max_alignment,
            'window_scores': window_scores
        }
    
    def analyze_semantic_flow(self, text_sequence: List[str]) -> Dict:
        embeddings = self.create_context_embeddings(text_sequence)
        flow_scores = []
        
        for i in range(len(embeddings) - 1):
            coherence = 1 - cosine(embeddings[i], embeddings[i + 1])
            flow_scores.append(coherence)
            
        return {
            'semantic_coherence': np.mean(flow_scores),
            'coherence_std': np.std(flow_scores),
            'flow_breaks': [i for i, score in enumerate(flow_scores) 
                          if score < self.semantic_threshold]
        }

# Example usage
detector = ContextualMisalignmentDetector()
context = ["AI", "models", "process", "data", "efficiently"]
response = "quantum computing algorithms"

misalignment = detector.detect_misalignment(context, response)
flow_analysis = detector.analyze_semantic_flow(context)

print("Misalignment Analysis:", misalignment)
print("Semantic Flow Analysis:", flow_analysis)

Slide 9: Semantic Entropy Measurement

The implementation quantifies knowledge degradation and semantic drift in LLM responses by measuring entropy increase across multiple inference steps and knowledge transformations.

import numpy as np
from scipy.stats import entropy
from typing import List, Dict, Tuple

class SemanticEntropyAnalyzer:
    def __init__(self, base_entropy_threshold: float = 0.5):
        self.threshold = base_entropy_threshold
        self.concept_distribution = {}
        
    def compute_semantic_entropy(self, 
                               text_segments: List[str],
                               reference_distribution: Dict[str, float]) -> Dict:
        # Calculate probability distributions
        observed_dist = self._calculate_distribution(text_segments)
        reference_dist = np.array(list(reference_distribution.values()))
        observed_dist_array = np.array(list(observed_dist.values()))
        
        # Calculate KL divergence
        kl_div = entropy(observed_dist_array, reference_dist)
        
        # Compute semantic coherence
        coherence_score = np.exp(-kl_div)
        
        return {
            'entropy_score': float(kl_div),
            'coherence_score': float(coherence_score),
            'distribution_difference': self._distribution_difference(
                observed_dist, reference_distribution
            ),
            'is_degraded': kl_div > self.threshold
        }
    
    def _calculate_distribution(self, segments: List[str]) -> Dict[str, float]:
        # Simulate probability distribution calculation
        total_len = len(segments)
        distribution = {}
        
        for segment in segments:
            if segment not in distribution:
                distribution[segment] = 1
            else:
                distribution[segment] += 1
                
        return {k: v/total_len for k, v in distribution.items()}
    
    def _distribution_difference(self, 
                               dist1: Dict[str, float],
                               dist2: Dict[str, float]) -> Dict[str, float]:
        all_keys = set(dist1.keys()) | set(dist2.keys())
        return {
            k: abs(dist1.get(k, 0) - dist2.get(k, 0))
            for k in all_keys
        }
    
    def track_entropy_evolution(self, 
                              sequence: List[str],
                              window_size: int = 3) -> Dict:
        entropy_trajectory = []
        
        for i in range(len(sequence) - window_size + 1):
            window = sequence[i:i + window_size]
            window_dist = self._calculate_distribution(window)
            window_entropy = entropy(list(window_dist.values()))
            entropy_trajectory.append(float(window_entropy))
            
        return {
            'entropy_trajectory': entropy_trajectory,
            'mean_entropy': np.mean(entropy_trajectory),
            'entropy_increase': entropy_trajectory[-1] - entropy_trajectory[0]
        }

# Example usage
analyzer = SemanticEntropyAnalyzer()
reference_dist = {'AI': 0.3, 'ML': 0.3, 'DL': 0.4}
sequence = ['AI', 'ML', 'DL', 'quantum', 'computing']

entropy_analysis = analyzer.compute_semantic_entropy(sequence, reference_dist)
evolution_analysis = analyzer.track_entropy_evolution(sequence)

print("Entropy Analysis:", entropy_analysis)
print("Evolution Analysis:", evolution_analysis)

Slide 10: Training Data Quality Assessment

This implementation provides a comprehensive system for evaluating training data quality and its impact on hallucination reduction through statistical analysis and content validation mechanisms.

import numpy as np
from typing import List, Dict, Tuple
from dataclasses import dataclass
from sklearn.feature_extraction.text import TfidfVectorizer

@dataclass
class DataQualityMetrics:
    diversity_score: float
    consistency_score: float
    completeness_score: float
    accuracy_score: float

class TrainingDataQualityAnalyzer:
    def __init__(self, min_quality_threshold: float = 0.7):
        self.threshold = min_quality_threshold
        self.vectorizer = TfidfVectorizer()
        
    def analyze_dataset_quality(self, 
                              training_samples: List[str],
                              reference_data: List[str] = None) -> DataQualityMetrics:
        # Vectorize the training samples
        vectors = self.vectorizer.fit_transform(training_samples)
        
        # Calculate quality metrics
        diversity = self._calculate_diversity(vectors)
        consistency = self._measure_consistency(training_samples)
        completeness = self._assess_completeness(training_samples)
        accuracy = self._evaluate_accuracy(training_samples, reference_data)
        
        return DataQualityMetrics(
            diversity_score=diversity,
            consistency_score=consistency,
            completeness_score=completeness,
            accuracy_score=accuracy
        )
    
    def _calculate_diversity(self, vectors) -> float:
        # Simulate diversity calculation using vector distances
        return float(np.random.random())
    
    def _measure_consistency(self, samples: List[str]) -> float:
        # Simulate consistency measurement
        return float(np.random.random())
    
    def _assess_completeness(self, samples: List[str]) -> float:
        # Simulate completeness assessment
        return float(np.random.random())
    
    def _evaluate_accuracy(self, 
                         samples: List[str],
                         reference: List[str] = None) -> float:
        if reference is None:
            return float(np.random.random())
        # Simulate accuracy evaluation against reference
        return float(np.random.random())
    
    def generate_quality_report(self, metrics: DataQualityMetrics) -> Dict:
        overall_quality = np.mean([
            metrics.diversity_score,
            metrics.consistency_score,
            metrics.completeness_score,
            metrics.accuracy_score
        ])
        
        return {
            'metrics': metrics.__dict__,
            'overall_quality': float(overall_quality),
            'meets_threshold': overall_quality >= self.threshold,
            'improvement_areas': self._identify_improvement_areas(metrics)
        }
    
    def _identify_improvement_areas(self, metrics: DataQualityMetrics) -> List[str]:
        improvements = []
        for metric_name, value in metrics.__dict__.items():
            if value < self.threshold:
                improvements.append(f"Improve {metric_name.replace('_score', '')}")
        return improvements

# Example usage
analyzer = TrainingDataQualityAnalyzer()
training_data = [
    "AI models process information",
    "Neural networks learn patterns",
    "Deep learning requires data"
]
reference_data = [
    "AI systems analyze data",
    "Neural networks identify patterns"
]

metrics = analyzer.analyze_dataset_quality(training_data, reference_data)
report = analyzer.generate_quality_report(metrics)
print("Quality Report:", report)

Slide 11: Model Architecture Optimization

This implementation demonstrates how to optimize model architecture to minimize hallucination tendencies through dynamic layer adjustment and attention mechanism refinement.

import numpy as np
from typing import List, Dict, Optional, Tuple

class ModelArchitectureOptimizer:
    def __init__(self, 
                 initial_layers: int,
                 attention_heads: int):
        self.num_layers = initial_layers
        self.attention_heads = attention_heads
        self.optimization_history = []
        
    def optimize_architecture(self,
                            performance_metrics: Dict[str, float],
                            hallucination_rate: float) -> Dict:
        # Calculate optimal architecture parameters
        optimal_layers = self._optimize_layer_count(
            performance_metrics['accuracy'],
            hallucination_rate
        )
        
        optimal_heads = self._optimize_attention_heads(
            performance_metrics['attention_score'],
            hallucination_rate
        )
        
        architecture_changes = {
            'layer_adjustment': optimal_layers - self.num_layers,
            'head_adjustment': optimal_heads - self.attention_heads
        }
        
        self._update_architecture(optimal_layers, optimal_heads)
        
        return {
            'optimized_layers': optimal_layers,
            'optimized_heads': optimal_heads,
            'architecture_changes': architecture_changes,
            'expected_improvement': self._calculate_improvement(
                performance_metrics,
                architecture_changes
            )
        }
    
    def _optimize_layer_count(self,
                            accuracy: float,
                            hallucination_rate: float) -> int:
        # Simulate layer optimization
        base_adjustment = int(np.ceil(
            (1 - accuracy) * 5 + hallucination_rate * 3
        ))
        return max(2, self.num_layers + base_adjustment)
    
    def _optimize_attention_heads(self,
                                attention_score: float,
                                hallucination_rate: float) -> int:
        # Simulate attention head optimization
        base_adjustment = int(np.ceil(
            (1 - attention_score) * 4 + hallucination_rate * 2
        ))
        return max(1, self.attention_heads + base_adjustment)
    
    def _update_architecture(self,
                           new_layers: int,
                           new_heads: int):
        self.optimization_history.append({
            'previous_layers': self.num_layers,
            'previous_heads': self.attention_heads,
            'new_layers': new_layers,
            'new_heads': new_heads
        })
        
        self.num_layers = new_layers
        self.attention_heads = new_heads
    
    def _calculate_improvement(self,
                             metrics: Dict[str, float],
                             changes: Dict[str, int]) -> Dict[str, float]:
        # Simulate improvement calculations
        layer_impact = changes['layer_adjustment'] * 0.05
        head_impact = changes['head_adjustment'] * 0.03
        
        return {
            'accuracy_improvement': max(0, min(1, metrics['accuracy'] + layer_impact)),
            'hallucination_reduction': max(0, min(0.5, abs(head_impact)))
        }

# Example usage
optimizer = ModelArchitectureOptimizer(initial_layers=6, attention_heads=8)
current_metrics = {
    'accuracy': 0.85,
    'attention_score': 0.78,
    'hallucination_rate': 0.15
}

optimization_result = optimizer.optimize_architecture(
    current_metrics,
    hallucination_rate=0.15
)
print("Optimization Result:", optimization_result)

Slide 12: Task Complexity Reduction Engine

This implementation provides a systematic approach to decomposing complex tasks into simpler subtasks, reducing the likelihood of hallucinations through granular processing and validation.

import numpy as np
from typing import List, Dict, Set
from dataclasses import dataclass

@dataclass
class SubTask:
    id: str
    description: str
    complexity_score: float
    dependencies: Set[str]

class TaskComplexityReducer:
    def __init__(self, complexity_threshold: float = 0.7):
        self.threshold = complexity_threshold
        self.subtasks = {}
        
    def decompose_task(self, task: str, context: Dict) -> Dict:
        # Generate subtasks with complexity analysis
        raw_subtasks = self._generate_subtasks(task, context)
        complexity_graph = self._build_dependency_graph(raw_subtasks)
        
        optimized_sequence = self._optimize_execution_sequence(complexity_graph)
        
        return {
            'original_complexity': self._measure_complexity(task),
            'subtasks': optimized_sequence,
            'reduced_complexity': np.mean([
                st.complexity_score for st in optimized_sequence
            ]),
            'optimization_ratio': len(optimized_sequence) / len(raw_subtasks)
        }
    
    def _generate_subtasks(self, task: str, context: Dict) -> List[SubTask]:
        # Simulate subtask generation
        subtask_count = np.random.randint(3, 7)
        subtasks = []
        
        for i in range(subtask_count):
            subtask = SubTask(
                id=f"task_{i}",
                description=f"Subtask {i} for {task[:20]}...",
                complexity_score=np.random.random(),
                dependencies=set(
                    [f"task_{j}" for j in range(i) 
                     if np.random.random() > 0.7]
                )
            )
            subtasks.append(subtask)
            
        return subtasks
    
    def _build_dependency_graph(self, 
                              subtasks: List[SubTask]) -> Dict[str, Set[str]]:
        dependency_graph = {}
        for subtask in subtasks:
            dependency_graph[subtask.id] = subtask.dependencies
        return dependency_graph
    
    def _optimize_execution_sequence(self, 
                                  graph: Dict[str, Set[str]]) -> List[SubTask]:
        # Topological sort with complexity optimization
        visited = set()
        sequence = []
        
        def visit(task_id):
            if task_id in visited:
                return
            visited.add(task_id)
            for dep in graph[task_id]:
                visit(dep)
            sequence.append(self.subtasks.get(task_id))
            
        for task_id in graph:
            if task_id not in visited:
                visit(task_id)
                
        return sequence
    
    def _measure_complexity(self, task: str) -> float:
        # Simulate complexity measurement
        length_factor = len(task.split()) / 100
        return min(1.0, length_factor + np.random.random() * 0.5)
    
    def validate_reduction(self, 
                         original_task: str,
                         subtasks: List[SubTask]) -> Dict:
        original_complexity = self._measure_complexity(original_task)
        reduced_complexities = [st.complexity_score for st in subtasks]
        
        return {
            'is_valid': max(reduced_complexities) < original_complexity,
            'complexity_reduction': original_complexity - np.mean(reduced_complexities),
            'subtask_distribution': {
                'mean': float(np.mean(reduced_complexities)),
                'std': float(np.std(reduced_complexities)),
                'max': float(max(reduced_complexities))
            }
        }

# Example usage
reducer = TaskComplexityReducer()
complex_task = "Analyze the impact of neural network architecture on hallucination rates in large language models"
context = {'domain': 'AI', 'complexity_level': 'high'}

decomposition = reducer.decompose_task(complex_task, context)
validation = reducer.validate_reduction(
    complex_task,
    decomposition['subtasks']
)

print("Task Decomposition:", decomposition)
print("Validation Results:", validation)

Slide 13: Dynamic Reasoning Implementation

This implementation focuses on building a dynamic reasoning system that continuously evolves its error detection capabilities through feedback loops and pattern recognition.

import numpy as np
from typing import List, Dict, Tuple, Optional
from dataclasses import dataclass
import time

@dataclass
class ReasoningStep:
    step_id: str
    description: str
    confidence: float
    evidence: List[str]
    timestamp: float

class DynamicReasoningEngine:
    def __init__(self, learning_rate: float = 0.1):
        self.learning_rate = learning_rate
        self.reasoning_history = []
        self.pattern_weights = {}
        
    def evolve_reasoning(self, 
                        input_data: Dict,
                        feedback: Optional[Dict] = None) -> Dict:
        # Generate reasoning steps
        steps = self._generate_reasoning_steps(input_data)
        
        # Update weights based on feedback
        if feedback:
            self._update_weights(feedback)
        
        # Apply current patterns
        reasoned_output = self._apply_reasoning_patterns(steps)
        
        return {
            'reasoning_steps': steps,
            'confidence_scores': self._calculate_confidence(steps),
            'pattern_influence': self._measure_pattern_influence(reasoned_output),
            'evolution_metrics': self._compute_evolution_metrics()
        }
    
    def _generate_reasoning_steps(self, 
                                input_data: Dict) -> List[ReasoningStep]:
        steps = []
        for i in range(np.random.randint(3, 6)):
            step = ReasoningStep(
                step_id=f"step_{i}",
                description=f"Reasoning step {i}",
                confidence=np.random.random(),
                evidence=[f"evidence_{j}" for j in range(2)],
                timestamp=time.time()
            )
            steps.append(step)
        return steps
    
    def _update_weights(self, feedback: Dict):
        for pattern, impact in feedback.items():
            if pattern in self.pattern_weights:
                self.pattern_weights[pattern] += self.learning_rate * impact
            else:
                self.pattern_weights[pattern] = self.learning_rate * impact
    
    def _apply_reasoning_patterns(self, 
                                steps: List[ReasoningStep]) -> Dict:
        applied_patterns = {}
        for step in steps:
            patterns = self._identify_patterns(step)
            applied_patterns[step.step_id] = patterns
        return applied_patterns
    
    def _identify_patterns(self, step: ReasoningStep) -> List[str]:
        # Simulate pattern identification
        return [f"pattern_{i}" for i in range(2) 
                if np.random.random() > 0.5]
    
    def _calculate_confidence(self, 
                            steps: List[ReasoningStep]) -> Dict[str, float]:
        return {
            step.step_id: step.confidence * 
            sum(self.pattern_weights.get(p, 0.1) 
                for p in self._identify_patterns(step))
            for step in steps
        }
    
    def _measure_pattern_influence(self, 
                                 applied_patterns: Dict) -> Dict[str, float]:
        influence_scores = {}
        for patterns in applied_patterns.values():
            for pattern in patterns:
                if pattern in influence_scores:
                    influence_scores[pattern] += 1
                else:
                    influence_scores[pattern] = 1
        return influence_scores
    
    def _compute_evolution_metrics(self) -> Dict:
        return {
            'pattern_diversity': len(self.pattern_weights),
            'weight_distribution': {
                'mean': float(np.mean(list(self.pattern_weights.values()))),
                'std': float(np.std(list(self.pattern_weights.values())))
            },
            'evolution_rate': self.learning_rate * len(self.reasoning_history)
        }

# Example usage
engine = DynamicReasoningEngine()
input_data = {
    'context': 'LLM hallucination analysis',
    'complexity': 'high'
}
feedback = {
    'pattern_1': 0.8,
    'pattern_2': -0.3
}

evolution_result = engine.evolve_reasoning(input_data, feedback)
print("Evolution Result:", evolution_result)

Slide 14: Grounding Techniques Implementation

This implementation demonstrates advanced grounding techniques for LLMs, incorporating external knowledge validation and semantic consistency checking to reduce hallucinations.

import numpy as np
from typing import List, Dict, Set, Optional
from dataclasses import dataclass
from datetime import datetime

@dataclass
class GroundingEvidence:
    source: str
    confidence: float
    timestamp: datetime
    content: str
    validation_score: float

class GroundingEngine:
    def __init__(self, confidence_threshold: float = 0.8):
        self.threshold = confidence_threshold
        self.evidence_cache = {}
        self.validation_history = []
        
    def ground_statement(self, 
                        statement: str,
                        context: Optional[Dict] = None) -> Dict:
        # Collect and validate evidence
        evidence = self._collect_evidence(statement)
        validation_result = self._validate_evidence(evidence)
        
        # Ground the statement
        grounded_output = self._apply_grounding(statement, evidence)
        
        return {
            'original_statement': statement,
            'grounded_statement': grounded_output['text'],
            'grounding_confidence': grounded_output['confidence'],
            'evidence_support': validation_result,
            'semantic_consistency': self._check_semantic_consistency(
                statement,
                grounded_output['text']
            )
        }
    
    def _collect_evidence(self, statement: str) -> List[GroundingEvidence]:
        # Simulate evidence collection
        evidence_count = np.random.randint(2, 5)
        evidence_list = []
        
        for i in range(evidence_count):
            evidence = GroundingEvidence(
                source=f"source_{i}",
                confidence=np.random.random(),
                timestamp=datetime.now(),
                content=f"Evidence {i} for: {statement[:30]}...",
                validation_score=np.random.random()
            )
            evidence_list.append(evidence)
            
        return evidence_list
    
    def _validate_evidence(self, 
                         evidence: List[GroundingEvidence]) -> Dict:
        validation_scores = [e.validation_score for e in evidence]
        
        return {
            'mean_confidence': float(np.mean(validation_scores)),
            'evidence_count': len(evidence),
            'strong_evidence': len([
                s for s in validation_scores if s >= self.threshold
            ]),
            'evidence_distribution': {
                'min': float(min(validation_scores)),
                'max': float(max(validation_scores)),
                'std': float(np.std(validation_scores))
            }
        }
    
    def _apply_grounding(self, 
                        statement: str,
                        evidence: List[GroundingEvidence]) -> Dict:
        # Simulate grounding application
        confidence_boost = np.mean([e.confidence for e in evidence])
        
        return {
            'text': self._modify_statement(statement, evidence),
            'confidence': min(1.0, confidence_boost * 1.2)
        }
    
    def _modify_statement(self, 
                         statement: str,
                         evidence: List[GroundingEvidence]) -> str:
        # Simulate statement modification based on evidence
        if np.mean([e.confidence for e in evidence]) > self.threshold:
            return statement  # Strong evidence supports original statement
        return f"{statement} (with {len(evidence)} supporting references)"
    
    def _check_semantic_consistency(self, 
                                  original: str,
                                  grounded: str) -> Dict:
        # Simulate semantic consistency check
        consistency_score = np.random.random()
        
        return {
            'consistency_score': float(consistency_score),
            'is_consistent': consistency_score >= self.threshold,
            'modification_degree': len(grounded) / len(original)
        }
    
    def update_grounding_history(self, 
                               grounding_result: Dict) -> None:
        self.validation_history.append({
            'timestamp': datetime.now(),
            'confidence': grounding_result['grounding_confidence'],
            'evidence_count': grounding_result['evidence_support']['evidence_count']
        })
    
    def get_grounding_statistics(self) -> Dict:
        if not self.validation_history:
            return {'error': 'No grounding history available'}
            
        confidences = [h['confidence'] for h in self.validation_history]
        evidence_counts = [h['evidence_count'] for h in self.validation_history]
        
        return {
            'total_groundings': len(self.validation_history),
            'average_confidence': float(np.mean(confidences)),
            'average_evidence_count': float(np.mean(evidence_counts)),
            'confidence_trend': float(np.polyfit(
                range(len(confidences)),
                confidences,
                1
            )[0])
        }

# Example usage
engine = GroundingEngine()
statement = "Neural networks can process complex patterns in data through hierarchical feature extraction"
context = {'domain': 'machine_learning', 'confidence_required': 'high'}

grounding_result = engine.ground_statement(statement, context)
engine.update_grounding_history(grounding_result)
statistics = engine.get_grounding_statistics()

print("Grounding Result:", grounding_result)
print("Grounding Statistics:", statistics)

Slide 15: Additional Resources

Note: Since my knowledge cutoff date precedes these papers, please verify the URLs and availability of these resources.