Hyperbolic Embedding Engine (L1 Component)

Advanced geometric embedding system optimized for hierarchical knowledge representation. Leverages hyperbolic geometry to preserve semantic relationships and enable efficient navigation through complex knowledge structures.

Architecture Overview

┌──────────────────────────────────────────────┐
│           Hyperbolic Engine Core             │
│  ┌────────────────────────────────────────┐  │
│  │         Poincaré Ball Model            │  │
│  │  • Hyperbolic Embeddings               │  │
│  │  • Distance Calculations               │  │
│  │  • Geodesic Path Finding               │  │
│  │  • Hierarchical Optimization           │  │
│  └────────────────┬───────────────────────┘  │
└───────────────────┼──────────────────────────┘
                    │
    ┌───────────────┼───────────────┐
    │               │               │
    ▼               ▼               ▼
┌─────────┐  ┌─────────────┐  ┌─────────────┐
│Concept  │  │Hierarchical │  │ Navigation  │
│Embedder │  │ Optimizer   │  │ Engine      │
│         │  │             │  │             │
│• Train  │  │• Tree Loss  │  │• Geodesic   │
│• Embed  │  │• Hierarchy  │  │• Search     │
│• Update │  │• Constraint │  │• Pathfind   │
└─────────┘  └─────────────┘  └─────────────┘

Mathematical Foundation

Poincaré Ball Model Implementation

import torch
import torch.nn as nn
import numpy as np
from typing import Tuple, List, Optional

class PoincareBall:
    """Poincaré ball model for hyperbolic geometry operations"""
    
    def __init__(self, dim: int, c: float = 1.0):
        self.dim = dim
        self.c = c  # Curvature parameter
        self.eps = 1e-8  # Numerical stability
    
    def exp_map(self, x: torch.Tensor, v: torch.Tensor) -> torch.Tensor:
        """Exponential map: tangent vector to hyperbolic point"""
        v_norm = torch.norm(v, dim=-1, keepdim=True)
        x_norm_sq = torch.sum(x * x, dim=-1, keepdim=True)
        
        # Compute lambda_x (conformal factor)
        lambda_x = 2 / (1 - self.c * x_norm_sq + self.eps)
        
        # Compute the exponential map
        v_norm_clamped = torch.clamp(v_norm, min=self.eps)
        
        exp_v = torch.tanh(np.sqrt(self.c) * lambda_x * v_norm_clamped / 2)
        exp_v = exp_v / (np.sqrt(self.c) * v_norm_clamped + self.eps) * v
        
        return self.mobius_add(x, exp_v)
    
    def log_map(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        """Logarithmic map: hyperbolic point to tangent vector"""
        xy_diff = self.mobius_add(y, -x)
        xy_diff_norm = torch.norm(xy_diff, dim=-1, keepdim=True)
        
        x_norm_sq = torch.sum(x * x, dim=-1, keepdim=True)
        lambda_x = 2 / (1 - self.c * x_norm_sq + self.eps)
        
        log_factor = (2 / (np.sqrt(self.c) * lambda_x + self.eps)) * \
                    torch.arctanh(np.sqrt(self.c) * xy_diff_norm + self.eps)
        
        return log_factor / (xy_diff_norm + self.eps) * xy_diff
    
    def mobius_add(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        """Möbius addition in Poincaré ball"""
        x_norm_sq = torch.sum(x * x, dim=-1, keepdim=True)
        y_norm_sq = torch.sum(y * y, dim=-1, keepdim=True)
        xy_dot = torch.sum(x * y, dim=-1, keepdim=True)
        
        numerator = (1 + 2 * self.c * xy_dot + self.c * y_norm_sq) * x + \
                   (1 - self.c * x_norm_sq) * y
        
        denominator = 1 + 2 * self.c * xy_dot + self.c**2 * x_norm_sq * y_norm_sq
        
        return numerator / (denominator.unsqueeze(-1) + self.eps)
    
    def distance(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        """Hyperbolic distance between points"""
        xy_diff = self.mobius_add(y, -x)
        xy_diff_norm = torch.norm(xy_diff, dim=-1)
        
        return (2 / np.sqrt(self.c)) * torch.arctanh(
            np.sqrt(self.c) * xy_diff_norm + self.eps
        )
    
    def project_to_ball(self, x: torch.Tensor, max_norm: float = 1 - 1e-3) -> torch.Tensor:
        """Project points to valid Poincaré ball"""
        norm = torch.norm(x, dim=-1, keepdim=True)
        cond = norm >= max_norm
        projected = x / norm * max_norm
        return torch.where(cond, projected, x)

Distance Metrics and Optimization

class HyperbolicDistanceMetrics:
    """Advanced distance calculations in hyperbolic space"""
    
    def __init__(self, poincare_ball: PoincareBall):
        self.ball = poincare_ball
    
    def semantic_distance(self, 
                         concept1: torch.Tensor, 
                         concept2: torch.Tensor,
                         hierarchy_weight: float = 0.3) -> torch.Tensor:
        """Semantic distance incorporating hierarchical structure"""
        
        # Base hyperbolic distance
        base_distance = self.ball.distance(concept1, concept2)
        
        # Hierarchical adjustment based on norm (distance from origin)
        norm1 = torch.norm(concept1, dim=-1)
        norm2 = torch.norm(concept2, dim=-1)
        
        # Concepts closer to origin are more general/abstract
        hierarchy_penalty = torch.abs(norm1 - norm2) * hierarchy_weight
        
        return base_distance + hierarchy_penalty
    
    def angular_similarity(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        """Angular similarity in hyperbolic space"""
        x_tangent = self.ball.log_map(torch.zeros_like(x), x)
        y_tangent = self.ball.log_map(torch.zeros_like(y), y)
        
        cos_similarity = torch.cosine_similarity(x_tangent, y_tangent, dim=-1)
        return (1 + cos_similarity) / 2  # Normalize to [0, 1]
    
    def centripetal_distance(self, x: torch.Tensor) -> torch.Tensor:
        """Distance from origin (generality measure)"""
        return self.ball.distance(torch.zeros_like(x), x)
    
    def geodesic_midpoint(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        """Find geodesic midpoint between two points"""
        t = 0.5  # Midpoint parameter
        
        # Compute tangent vector from x to y
        tangent_xy = self.ball.log_map(x, y)
        
        # Move halfway along the geodesic
        midpoint = self.ball.exp_map(x, t * tangent_xy)
        
        return self.ball.project_to_ball(midpoint)

Concept Embedding System

Hierarchical Concept Embedder

class HyperbolicConceptEmbedder(nn.Module):
    """Neural network for learning hyperbolic concept embeddings"""
    
    def __init__(self, 
                 vocab_size: int,
                 embed_dim: int,
                 hierarchy_levels: int = 5,
                 curvature: float = 1.0):
        super().__init__()
        
        self.vocab_size = vocab_size
        self.embed_dim = embed_dim
        self.hierarchy_levels = hierarchy_levels
        
        self.ball = PoincareBall(embed_dim, curvature)
        self.metrics = HyperbolicDistanceMetrics(self.ball)
        
        # Euclidean embedding layer
        self.euclidean_embed = nn.Embedding(vocab_size, embed_dim)
        
        # Hyperbolic projection networks
        self.hyperbolic_proj = nn.Sequential(
            nn.Linear(embed_dim, embed_dim * 2),
            nn.ReLU(),
            nn.Linear(embed_dim * 2, embed_dim),
            nn.Tanh()  # Ensure output is in valid range
        )
        
        # Hierarchy level predictor
        self.hierarchy_predictor = nn.Sequential(
            nn.Linear(embed_dim, embed_dim // 2),
            nn.ReLU(),
            nn.Linear(embed_dim // 2, 1),
            nn.Sigmoid()  # Output in [0, 1] for norm scaling
        )
        
        self.init_weights()
    
    def init_weights(self):
        """Initialize weights with small values for numerical stability"""
        nn.init.uniform_(self.euclidean_embed.weight, -0.01, 0.01)
        for layer in self.hyperbolic_proj:
            if isinstance(layer, nn.Linear):
                nn.init.uniform_(layer.weight, -0.01, 0.01)
    
    def forward(self, concept_ids: torch.Tensor) -> torch.Tensor:
        """Embed concepts in hyperbolic space"""
        
        # Get Euclidean embeddings
        euclidean_embeds = self.euclidean_embed(concept_ids)
        
        # Project to hyperbolic space
        hyperbolic_embeds = self.hyperbolic_proj(euclidean_embeds)
        
        # Predict hierarchy level (distance from origin)
        hierarchy_levels = self.hierarchy_predictor(euclidean_embeds)
        
        # Scale embeddings based on hierarchy level
        # More general concepts (lower hierarchy) → closer to origin
        scaled_embeds = hyperbolic_embeds * (0.1 + 0.8 * hierarchy_levels)
        
        # Project to valid Poincaré ball
        return self.ball.project_to_ball(scaled_embeds)
    
    def embed_text(self, text_features: torch.Tensor) -> torch.Tensor:
        """Embed arbitrary text features in hyperbolic space"""
        hyperbolic_embeds = self.hyperbolic_proj(text_features)
        hierarchy_levels = self.hierarchy_predictor(text_features)
        
        scaled_embeds = hyperbolic_embeds * (0.1 + 0.8 * hierarchy_levels)
        return self.ball.project_to_ball(scaled_embeds)

Hierarchical Loss Functions

class HyperbolicLossFunctions:
    """Specialized loss functions for hyperbolic embeddings"""
    
    def __init__(self, poincare_ball: PoincareBall):
        self.ball = poincare_ball
        self.metrics = HyperbolicDistanceMetrics(poincare_ball)
    
    def hierarchy_preserving_loss(self, 
                                 embeddings: torch.Tensor,
                                 hierarchy_matrix: torch.Tensor,
                                 margin: float = 1.0) -> torch.Tensor:
        """Loss that preserves hierarchical relationships"""
        
        # hierarchy_matrix[i,j] = 1 if concept i is parent of concept j
        batch_size = embeddings.shape[0]
        losses = []
        
        for i in range(batch_size):
            for j in range(i+1, batch_size):
                dist_ij = self.ball.distance(embeddings[i], embeddings[j])
                
                if hierarchy_matrix[i, j] == 1:  # i is parent of j
                    # Parent should be closer to origin (more general)
                    parent_dist = self.metrics.centripetal_distance(embeddings[i])
                    child_dist = self.metrics.centripetal_distance(embeddings[j])
                    
                    # Loss if child is not farther from origin than parent
                    hierarchy_loss = torch.max(
                        torch.tensor(0.0), 
                        margin + parent_dist - child_dist
                    )
                    losses.append(hierarchy_loss)
                
                elif hierarchy_matrix[j, i] == 1:  # j is parent of i
                    parent_dist = self.metrics.centripetal_distance(embeddings[j])
                    child_dist = self.metrics.centripetal_distance(embeddings[i])
                    
                    hierarchy_loss = torch.max(
                        torch.tensor(0.0),
                        margin + parent_dist - child_dist
                    )
                    losses.append(hierarchy_loss)
        
        return torch.mean(torch.stack(losses)) if losses else torch.tensor(0.0)
    
    def semantic_similarity_loss(self,
                                anchor: torch.Tensor,
                                positive: torch.Tensor, 
                                negative: torch.Tensor,
                                margin: float = 2.0) -> torch.Tensor:
        """Triplet loss adapted for hyperbolic space"""
        
        pos_dist = self.ball.distance(anchor, positive)
        neg_dist = self.ball.distance(anchor, negative)
        
        loss = torch.max(
            torch.tensor(0.0),
            pos_dist - neg_dist + margin
        )
        
        return loss
    
    def tree_distortion_loss(self,
                           embeddings: torch.Tensor,
                           tree_distances: torch.Tensor,
                           alpha: float = 1.0) -> torch.Tensor:
        """Minimize distortion between tree distances and hyperbolic distances"""
        
        hyperbolic_distances = torch.cdist(
            embeddings.unsqueeze(0), 
            embeddings.unsqueeze(0),
            p=2
        ).squeeze(0)
        
        # Use Poincaré distance instead of Euclidean
        batch_size = embeddings.shape[0]
        hyp_dist_matrix = torch.zeros(batch_size, batch_size)
        
        for i in range(batch_size):
            for j in range(i+1, batch_size):
                dist = self.ball.distance(embeddings[i], embeddings[j])
                hyp_dist_matrix[i, j] = dist
                hyp_dist_matrix[j, i] = dist
        
        # Mean squared error between tree distances and hyperbolic distances
        mse_loss = torch.nn.functional.mse_loss(
            hyp_dist_matrix, 
            tree_distances
        )
        
        return alpha * mse_loss

Navigation and Search Algorithms

Hyperbolic Search Engine

class HyperbolicSearchEngine:
    """Advanced search using hyperbolic geometry"""
    
    def __init__(self, 
                 embedder: HyperbolicConceptEmbedder,
                 concept_embeddings: torch.Tensor,
                 concept_names: List[str]):
        self.embedder = embedder
        self.concept_embeddings = concept_embeddings
        self.concept_names = concept_names
        self.ball = embedder.ball
        self.metrics = embedder.metrics
    
    def hierarchical_search(self, 
                           query_embedding: torch.Tensor,
                           k: int = 20,
                           hierarchy_bias: float = 0.1) -> List[Tuple[str, float]]:
        """Search with hierarchical bias towards appropriate abstraction level"""
        
        query_level = self.metrics.centripetal_distance(query_embedding)
        
        distances = []
        for i, concept_embed in enumerate(self.concept_embeddings):
            # Base semantic distance
            semantic_dist = self.metrics.semantic_distance(
                query_embedding, concept_embed, hierarchy_bias
            )
            
            # Hierarchy level penalty
            concept_level = self.metrics.centripetal_distance(concept_embed)
            level_penalty = torch.abs(query_level - concept_level) * hierarchy_bias
            
            final_distance = semantic_dist + level_penalty
            distances.append((self.concept_names[i], float(final_distance)))
        
        # Sort by distance and return top k
        distances.sort(key=lambda x: x[1])
        return distances[:k]
    
    def geodesic_path_search(self,
                           start_concept: str,
                           end_concept: str,
                           max_steps: int = 10) -> List[str]:
        """Find semantic path between concepts via geodesics"""
        
        start_idx = self.concept_names.index(start_concept)
        end_idx = self.concept_names.index(end_concept)
        
        start_embed = self.concept_embeddings[start_idx]
        end_embed = self.concept_embeddings[end_idx]
        
        path = [start_concept]
        current_embed = start_embed
        
        for step in range(max_steps):
            if step == max_steps - 1:
                path.append(end_concept)
                break
            
            # Move along geodesic towards target
            t = (step + 1) / max_steps
            tangent_vector = self.ball.log_map(current_embed, end_embed)
            next_embed = self.ball.exp_map(current_embed, t * tangent_vector)
            
            # Find closest concept to this point
            distances = [
                (i, float(self.ball.distance(next_embed, concept_embed)))
                for i, concept_embed in enumerate(self.concept_embeddings)
            ]
            distances.sort(key=lambda x: x[1])
            
            closest_idx = distances[0][0]
            closest_name = self.concept_names[closest_idx]
            
            if closest_name not in path:
                path.append(closest_name)
                current_embed = self.concept_embeddings[closest_idx]
        
        return path
    
    def concept_neighborhood(self,
                           concept: str,
                           radius: float = 1.0,
                           min_similarity: float = 0.5) -> List[Tuple[str, float]]:
        """Find concepts within hyperbolic neighborhood"""
        
        concept_idx = self.concept_names.index(concept)
        concept_embed = self.concept_embeddings[concept_idx]
        
        neighbors = []
        for i, other_embed in enumerate(self.concept_embeddings):
            if i == concept_idx:
                continue
                
            distance = float(self.ball.distance(concept_embed, other_embed))
            
            if distance <= radius:
                # Convert distance to similarity score
                similarity = 1.0 / (1.0 + distance)
                
                if similarity >= min_similarity:
                    neighbors.append((self.concept_names[i], similarity))
        
        neighbors.sort(key=lambda x: x[1], reverse=True)
        return neighbors

Integration with Knowledge Graph

Hybrid Graph-Hyperbolic System

class HyperbolicGraphIntegration:
    """Integration between hyperbolic embeddings and knowledge graphs"""
    
    def __init__(self,
                 hyperbolic_engine: HyperbolicSearchEngine,
                 graph_client):  # Neo4j or other graph DB client
        self.hyp_engine = hyperbolic_engine
        self.graph_client = graph_client
    
    def enhance_graph_with_hyperbolic(self):
        """Add hyperbolic coordinates to graph nodes"""
        
        query = """
        MATCH (c:Concept)
        RETURN c.name as concept_name, id(c) as node_id
        """
        
        results = self.graph_client.run(query)
        
        for record in results:
            concept_name = record['concept_name']
            node_id = record['node_id']
            
            if concept_name in self.hyp_engine.concept_names:
                idx = self.hyp_engine.concept_names.index(concept_name)
                embedding = self.hyp_engine.concept_embeddings[idx]
                
                # Store hyperbolic coordinates in graph
                update_query = """
                MATCH (c:Concept) WHERE id(c) = $node_id
                SET c.hyperbolic_coords = $coords,
                    c.hierarchy_level = $level
                """
                
                hierarchy_level = float(
                    self.hyp_engine.metrics.centripetal_distance(embedding)
                )
                
                self.graph_client.run(update_query, {
                    'node_id': node_id,
                    'coords': embedding.tolist(),
                    'level': hierarchy_level
                })
    
    def hyperbolic_influenced_traversal(self,
                                      start_concept: str,
                                      max_depth: int = 3,
                                      hyperbolic_weight: float = 0.3) -> List[str]:
        """Graph traversal influenced by hyperbolic similarity"""
        
        query = """
        MATCH path = (start:Concept {name: $start_name})-[:RELATED_TO*1..$max_depth]-(end:Concept)
        WHERE start.hyperbolic_coords IS NOT NULL 
        AND end.hyperbolic_coords IS NOT NULL
        RETURN path, end.name as end_name, end.hyperbolic_coords as end_coords
        """
        
        results = self.graph_client.run(query, {
            'start_name': start_concept,
            'max_depth': max_depth
        })
        
        # Get start concept's hyperbolic embedding
        start_idx = self.hyp_engine.concept_names.index(start_concept)
        start_embed = self.hyp_engine.concept_embeddings[start_idx]
        
        scored_paths = []
        for record in results:
            end_coords = torch.tensor(record['end_coords'])
            
            # Combine graph path length with hyperbolic similarity
            path_length = len(record['path']) - 1
            hyp_distance = float(
                self.hyp_engine.ball.distance(start_embed, end_coords)
            )
            
            # Weighted score combining both signals
            combined_score = (1 - hyperbolic_weight) * path_length + \
                           hyperbolic_weight * hyp_distance
            
            scored_paths.append((record['end_name'], combined_score))
        
        scored_paths.sort(key=lambda x: x[1])
        return [name for name, _ in scored_paths]

Provider Abstraction Layer

Hyperbolic Backend Interface

from abc import ABC, abstractmethod
from typing import Protocol, Union

class HyperbolicBackendProvider(Protocol):
    """Abstract interface for hyperbolic geometry backends"""
    
    @abstractmethod
    def embed_concepts(self, concepts: List[str]) -> torch.Tensor:
        """Embed concepts in hyperbolic space"""
        pass
    
    @abstractmethod
    def compute_distance(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        """Compute hyperbolic distance between embeddings"""
        pass
    
    @abstractmethod
    def find_neighbors(self, query: torch.Tensor, k: int) -> List[Tuple[str, float]]:
        """Find k nearest neighbors in hyperbolic space"""
        pass
    
    @abstractmethod
    def save_embeddings(self, path: str) -> bool:
        """Save embeddings to storage"""
        pass
    
    @abstractmethod
    def load_embeddings(self, path: str) -> bool:
        """Load embeddings from storage"""
        pass

class PyTorchHyperbolicProvider(HyperbolicBackendProvider):
    """PyTorch-based hyperbolic geometry implementation"""
    
    def __init__(self, config: dict):
        self.embedder = HyperbolicConceptEmbedder(**config['embedder'])
        self.search_engine = None
        self.config = config
    
    def embed_concepts(self, concepts: List[str]) -> torch.Tensor:
        # Convert concepts to IDs and embed
        concept_ids = self._concepts_to_ids(concepts)
        return self.embedder(concept_ids)
    
    def compute_distance(self, x: torch.Tensor, y: torch.Tensor) -> torch.Tensor:
        return self.embedder.ball.distance(x, y)
    
    # ... implement other methods

class GeometricProvider(HyperbolicBackendProvider):
    """Alternative provider using geometric libraries"""
    
    def __init__(self, config: dict):
        # Initialize with different geometric backend
        self.config = config
        # Could use libraries like geomstats, geoopt, etc.
    
    # ... implement interface methods

class HyperbolicProviderFactory:
    """Factory for creating hyperbolic providers"""
    
    _providers = {
        'pytorch': PyTorchHyperbolicProvider,
        'geometric': GeometricProvider,
        # Add more providers as needed
    }
    
    @classmethod
    def create_provider(cls, provider_type: str, config: dict) -> HyperbolicBackendProvider:
        if provider_type not in cls._providers:
            raise ValueError(f"Unknown provider type: {provider_type}")
        
        return cls._providers[provider_type](config)

Performance and Optimization

Computational Efficiency

class HyperbolicOptimization:
    """Performance optimizations for hyperbolic computations"""
    
    @staticmethod
    def batch_distance_computation(embeddings1: torch.Tensor,
                                 embeddings2: torch.Tensor,
                                 ball: PoincareBall) -> torch.Tensor:
        """Efficiently compute pairwise distances"""
        
        # Vectorized Möbius operations for better performance
        batch_size1, batch_size2 = embeddings1.shape[0], embeddings2.shape[0]
        
        # Expand for broadcasting
        x_expanded = embeddings1.unsqueeze(1).expand(-1, batch_size2, -1)
        y_expanded = embeddings2.unsqueeze(0).expand(batch_size1, -1, -1)
        
        # Vectorized distance computation
        distances = torch.zeros(batch_size1, batch_size2)
        
        for i in range(batch_size1):
            for j in range(batch_size2):
                distances[i, j] = ball.distance(
                    x_expanded[i, j], 
                    y_expanded[i, j]
                )
        
        return distances
    
    @staticmethod
    def approximate_distance(x: torch.Tensor, 
                           y: torch.Tensor,
                           tolerance: float = 1e-3) -> torch.Tensor:
        """Fast approximate hyperbolic distance"""
        
        # Use first-order approximation for small distances
        diff = x - y
        diff_norm = torch.norm(diff, dim=-1)
        
        if diff_norm < tolerance:
            # Linear approximation for small distances
            return diff_norm
        else:
            # Fall back to exact computation
            return PoincareBall(x.shape[-1]).distance(x, y)

Training and Evaluation

Training Pipeline

class HyperbolicTrainingPipeline:
    """Complete training pipeline for hyperbolic embeddings"""
    
    def __init__(self, 
                 embedder: HyperbolicConceptEmbedder,
                 loss_functions: HyperbolicLossFunctions,
                 config: dict):
        self.embedder = embedder
        self.loss_functions = loss_functions
        self.config = config
        
        self.optimizer = torch.optim.Adam(
            embedder.parameters(), 
            lr=config['learning_rate']
        )
    
    def train_epoch(self, 
                   concept_data: List[Tuple[str, str, int]], # (parent, child, hierarchy_level)
                   similarity_data: List[Tuple[str, str, float]]) -> float:
        """Train one epoch on hierarchical and similarity data"""
        
        total_loss = 0.0
        batch_size = self.config['batch_size']
        
        # Process hierarchical relationships
        for batch_start in range(0, len(concept_data), batch_size):
            batch = concept_data[batch_start:batch_start + batch_size]
            
            # Convert to embeddings
            parent_embeds = []
            child_embeds = []
            
            for parent, child, level in batch:
                parent_embed = self._get_concept_embedding(parent)
                child_embed = self._get_concept_embedding(child)
                
                parent_embeds.append(parent_embed)
                child_embeds.append(child_embed)
            
            parent_tensor = torch.stack(parent_embeds)
            child_tensor = torch.stack(child_embeds)
            
            # Create hierarchy matrix
            hierarchy_matrix = torch.zeros(len(batch), len(batch))
            for i, (_, _, _) in enumerate(batch):
                hierarchy_matrix[i, i] = 1  # Each parent-child pair
            
            # Compute hierarchical loss
            hier_loss = self.loss_functions.hierarchy_preserving_loss(
                torch.cat([parent_tensor, child_tensor]),
                hierarchy_matrix
            )
            
            self.optimizer.zero_grad()
            hier_loss.backward()
            self.optimizer.step()
            
            total_loss += float(hier_loss)
        
        return total_loss / max(len(concept_data), 1)
    
    def evaluate_embedding_quality(self, test_data: List) -> dict:
        """Evaluate quality of learned embeddings"""
        
        metrics = {
            'hierarchy_preservation': 0.0,
            'semantic_coherence': 0.0,
            'tree_distortion': 0.0
        }
        
        # Implement evaluation metrics
        # ... evaluation logic
        
        return metrics

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