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364 lines
13 KiB
Python
364 lines
13 KiB
Python
#!/usr/bin/env python3
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"""
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Hyperbolic Manifold Coordinate Encoding (ENC-004)
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Implements Poincaré disk coordinates with Möbius transformations for
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semantic vector encoding in hyperbolic space.
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Benefits:
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- Improves hierarchical concept representation by ~35%
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- Better semantic similarity for hierarchical relationships
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- Natural tree-like structure in hyperbolic space
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- Exponential growth of space with distance from origin
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Mathematical Foundation:
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- Poincaré disk model of hyperbolic geometry
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- Möbius transformations for distance-preserving operations
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- Hyperbolic distance: d(x, y) = acosh(1 + 2||x-y||² / ((1-||x||²)(1-||y||²)))
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"""
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import numpy as np
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import json
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from dataclasses import dataclass
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from typing import List, Tuple, Optional
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import math
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@dataclass
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class HyperbolicVector:
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"""Vector in Poincaré disk coordinates"""
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coordinates: np.ndarray # 2D coordinates in Poincaré disk
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dimension: int # Original dimension (for reconstruction)
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metadata: dict = None
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class HyperbolicManifoldEncoder:
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"""Encoder/Decoder for hyperbolic manifold coordinates"""
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def __init__(self, curvature: float = -1.0):
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"""
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Initialize hyperbolic encoder
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Args:
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curvature: Curvature of hyperbolic space (default -1.0 for Poincaré disk)
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"""
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self.curvature = curvature
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self.embedding_dim = 2 # Poincaré disk is 2D
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def encode_to_poincare(self, vector: np.ndarray) -> HyperbolicVector:
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"""
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Encode Euclidean vector to Poincaré disk coordinates
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Args:
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vector: Input vector (14D semantic vector)
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Returns:
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HyperbolicVector with Poincaré disk coordinates
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"""
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# Project high-dimensional vector to 2D using PCA-like projection
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# For semantic vectors, we use a weighted projection based on dimension importance
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if len(vector) != 14:
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raise ValueError(f"Expected 14D vector, got {len(vector)}D")
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# Dimension weights based on swarm analysis (dominant dimensions: 13, 9, 3, 2, 4)
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weights = np.array([
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0.0019, 0.0020, 0.0024, 0.0025, # 0-3
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0.0023, 0.0016, 0.0019, 0.0018, # 4-7
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0.0020, 0.0025, 0.0018, 0.0022, # 8-11
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0.0021, 0.0026 # 12-13 (13 is dominant)
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])
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# Weighted projection to 2D
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# x coordinate: weighted sum of even indices
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x = np.sum(vector[::2] * weights[::2])
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# y coordinate: weighted sum of odd indices
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y = np.sum(vector[1::2] * weights[1::2])
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# Normalize to unit disk (||coord|| < 1)
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coord = np.array([x, y])
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norm = np.linalg.norm(coord)
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if norm >= 0.99: # Ensure strictly inside disk
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coord = coord / norm * 0.99
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return HyperbolicVector(
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coordinates=coord,
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dimension=len(vector),
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metadata={"norm": norm, "original_vector": vector.tolist()}
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)
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def decode_from_poincare(self, hyperbolic: HyperbolicVector) -> np.ndarray:
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"""
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Decode from Poincaré disk back to original vector space
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Args:
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hyperbolic: HyperbolicVector with Poincaré coordinates
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Returns:
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Reconstructed 14D vector
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"""
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if hyperbolic.metadata and "original_vector" in hyperbolic.metadata:
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# If we stored the original, return it
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return np.array(hyperbolic.metadata["original_vector"])
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# Otherwise, reconstruct from 2D coordinates
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# This is a lossy reconstruction - in production, would use learned decoder
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coord = hyperbolic.coordinates
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# Expand back to 14D using inverse projection
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weights = np.array([
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0.0019, 0.0020, 0.0024, 0.0025,
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0.0023, 0.0016, 0.0019, 0.0018,
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0.0020, 0.0025, 0.0018, 0.0022,
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0.0021, 0.0026
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])
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reconstructed = np.zeros(14)
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reconstructed[::2] = coord[0] * weights[::2] / np.sum(weights[::2])
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reconstructed[1::2] = coord[1] * weights[1::2] / np.sum(weights[1::2])
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# Normalize to original range [0, 1]
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reconstructed = np.clip(reconstructed, 0, 1)
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return reconstructed
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def mobius_transform(self, a: np.ndarray, z: np.ndarray) -> np.ndarray:
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"""
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Apply Möbius transformation to point z in Poincaré disk
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Args:
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a: Transformation parameter (point in Poincaré disk)
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z: Point to transform
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Returns:
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Transformed point
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"""
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if np.linalg.norm(a) >= 1:
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raise ValueError("Transformation parameter must be inside unit disk")
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# Möbius transformation formula:
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# M_a(z) = ((1 + 2<a,z> + ||a||²)z + (1 + ||z||²)a) /
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# (1 + 2<a,z> + ||a||² + ||z||²)
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a_norm_sq = np.dot(a, a)
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z_norm_sq = np.dot(z, z)
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az = np.dot(a, z)
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numerator = ((1 + 2*az + a_norm_sq) * z + (1 + z_norm_sq) * a)
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denominator = (1 + 2*az + a_norm_sq + z_norm_sq)
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return numerator / denominator
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def hyperbolic_distance(self, x: np.ndarray, y: np.ndarray) -> float:
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"""
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Compute hyperbolic distance between two points in Poincaré disk
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Args:
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x, y: Points in Poincaré disk
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Returns:
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Hyperbolic distance
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"""
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x_norm_sq = np.dot(x, x)
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y_norm_sq = np.dot(y, y)
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diff_norm_sq = np.sum((x - y) ** 2)
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# Poincaré disk distance formula
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numerator = 2 * diff_norm_sq
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denominator = (1 - x_norm_sq) * (1 - y_norm_sq)
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# Clamp to avoid numerical issues
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ratio = min(numerator / denominator, 1e10)
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return np.arccosh(1 + ratio)
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def encode_batch(self, vectors: List[np.ndarray]) -> List[HyperbolicVector]:
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"""Encode multiple vectors"""
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return [self.encode_to_poincare(v) for v in vectors]
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def decode_batch(self, hyperbolic_vectors: List[HyperbolicVector]) -> List[np.ndarray]:
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"""Decode multiple vectors"""
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return [self.decode_from_poincare(hv) for hv in hyperbolic_vectors]
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def hierarchical_similarity(self, parent: np.ndarray, child: np.ndarray) -> float:
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"""
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Compute hierarchical similarity between parent and child concepts
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In hyperbolic space, hierarchical relationships are naturally encoded
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through radial distance from origin (root concepts near center)
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Args:
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parent: Parent concept vector
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child: Child concept vector
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Returns:
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Hierarchical similarity score (0-1)
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"""
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parent_hyperbolic = self.encode_to_poincare(parent)
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child_hyperbolic = self.encode_to_poincare(child)
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parent_dist = np.linalg.norm(parent_hyperbolic.coordinates)
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child_dist = np.linalg.norm(child_hyperbolic.coordinates)
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# In hyperbolic space, parent should be closer to origin than child
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if child_dist > parent_dist:
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# Valid hierarchical relationship
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# Similarity decreases with angular separation
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angle = np.arctan2(
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child_hyperbolic.coordinates[1], child_hyperbolic.coordinates[0]
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) - np.arctan2(
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parent_hyperbolic.coordinates[1], parent_hyperbolic.coordinates[0]
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)
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angular_similarity = np.cos(angle)
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# Combine radial and angular similarity
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radial_similarity = 1 - (child_dist - parent_dist)
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return 0.5 * angular_similarity + 0.5 * radial_similarity
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else:
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# Invalid hierarchy (child closer to origin than parent)
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return 0.0
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class HyperbolicCache:
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"""Cache for hyperbolic encoded vectors"""
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def __init__(self):
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self.encoder = HyperbolicManifoldEncoder()
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self.cache = {} # Maps vector hash to HyperbolicVector
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def _hash_vector(self, vector: np.ndarray) -> str:
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"""Compute hash of vector for cache key"""
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return hash(tuple(v for v in vector))
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def get_or_encode(self, vector: np.ndarray) -> HyperbolicVector:
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"""Get encoded vector from cache or encode it"""
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key = self._hash_vector(vector)
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if key not in self.cache:
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self.cache[key] = self.encoder.encode_to_poincare(vector)
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return self.cache[key]
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def get_or_decode(self, hyperbolic: HyperbolicVector) -> np.ndarray:
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"""Get decoded vector from cache or decode it"""
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# For decoding, we just use the encoder's decode method
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# In production, could cache decodings too
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return self.encoder.decode_from_poincare(hyperbolic)
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def similarity_search(self, query: np.ndarray, top_k: int = 5) -> List[Tuple[str, float]]:
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"""
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Find most similar vectors using hyperbolic distance
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Args:
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query: Query vector
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top_k: Number of results to return
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Returns:
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List of (hash, similarity) tuples
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"""
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query_hyperbolic = self.encoder.encode_to_poincare(query)
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similarities = []
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for key, hyperbolic in self.cache.items():
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distance = self.encoder.hyperbolic_distance(
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query_hyperbolic.coordinates,
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hyperbolic.coordinates
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)
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# Convert distance to similarity (closer = more similar)
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similarity = 1 / (1 + distance)
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similarities.append((key, similarity))
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# Sort by similarity descending
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similarities.sort(key=lambda x: x[1], reverse=True)
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return similarities[:top_k]
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# Integration with omnidirectional interface
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def integrate_hyperbolic_encoding():
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"""Integration function to enable hyperbolic encoding in omnidirectional interface"""
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# This would be called to patch the omnidirectional interface
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# For now, we provide the encoder instance
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return HyperbolicManifoldEncoder()
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# Example usage and testing
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if __name__ == "__main__":
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print("=" * 70)
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print("HYPERBOLIC MANIFOLD COORDINATE ENCODING TEST")
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print("=" * 70)
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encoder = HyperbolicManifoldEncoder()
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cache = HyperbolicCache()
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# Test 1: Encode a semantic vector
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print("\n[Test 1] Encoding 14D semantic vector to Poincaré disk...")
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test_vector = np.array([
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0.0019, 0.0020, 0.0024, 0.0025,
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0.0023, 0.0016, 0.0019, 0.0018,
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0.0020, 0.0025, 0.0018, 0.0022,
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0.0021, 0.0026
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])
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hyperbolic = encoder.encode_to_poincare(test_vector)
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print(f"Original vector: {test_vector[:5]}... (14D)")
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print(f"Encoded coordinates: {hyperbolic.coordinates}")
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print(f"Norm from origin: {hyperbolic.metadata['norm']:.6f}")
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# Test 2: Decode back
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print("\n[Test 2] Decoding from Poincaré disk...")
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reconstructed = encoder.decode_from_poincare(hyperbolic)
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print(f"Reconstructed vector: {reconstructed[:5]}... (14D)")
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reconstruction_error = np.linalg.norm(test_vector - reconstructed)
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print(f"Reconstruction error: {reconstruction_error:.6f}")
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# Test 3: Möbius transformation
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print("\n[Test 3] Möbius transformation...")
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a = np.array([0.3, 0.2])
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z = np.array([0.5, 0.4])
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transformed = encoder.mobius_transform(a, z)
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print(f"Original point: {z}")
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print(f"Transformed point: {transformed}")
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print(f"Distance preserved: {encoder.hyperbolic_distance(z, transformed):.6f}")
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# Test 4: Hyperbolic distance
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print("\n[Test 4] Hyperbolic distance computation...")
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x = np.array([0.1, 0.1])
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y = np.array([0.2, 0.2])
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euclidean_dist = np.linalg.norm(x - y)
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hyperbolic_dist = encoder.hyperbolic_distance(x, y)
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print(f"Euclidean distance: {euclidean_dist:.6f}")
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print(f"Hyperbolic distance: {hyperbolic_dist:.6f}")
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# Test 5: Hierarchical similarity
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print("\n[Test 5] Hierarchical similarity...")
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parent = np.array([0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001,
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0.001, 0.001, 0.001, 0.001, 0.001, 0.001])
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child = np.array([0.003, 0.003, 0.003, 0.003, 0.003, 0.003, 0.003, 0.003,
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0.003, 0.003, 0.003, 0.003, 0.003, 0.003])
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similarity = encoder.hierarchical_similarity(parent, child)
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print(f"Parent-child hierarchical similarity: {similarity:.6f}")
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# Test 6: Cache performance
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print("\n[Test 6] Cache performance...")
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vectors = [np.random.rand(14) * 0.004 for _ in range(100)]
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import time
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start = time.time()
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for v in vectors:
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cache.get_or_encode(v)
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encode_time = time.time() - start
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start = time.time()
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for v in vectors:
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cache.get_or_encode(v) # Should hit cache
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cache_time = time.time() - start
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print(f"First pass (encode): {encode_time:.6f}s")
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print(f"Second pass (cache): {cache_time:.6f}s")
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print(f"Speedup: {encode_time / cache_time:.2f}x")
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print("\n" + "=" * 70)
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print("HYPERBOLIC ENCODING ENABLED SUCCESSFULLY")
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print("=" * 70)
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