File size: 16,269 Bytes
dbb04e4 c3a3710 dbb04e4 c3a3710 dbb04e4 c3a3710 dbb04e4 c3a3710 dbb04e4 c3a3710 dbb04e4 7c8b011 dbb04e4 c3a3710 dbb04e4 c3a3710 dbb04e4 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 | """
Binary Hyperdimensional Vector (Binary HDV) Core
=================================================
Phase 3.0 implementation of binary VSA operations.
Based on Kanerva's Hyperdimensional Computing theory (2009).
Uses standard mathematical operations (XOR, Hamming distance, majority bundling)
that are fundamental VSA primitives — not derived from any proprietary implementation.
Key design choices:
- D = 16,384 bits (2^14) — configurable via config.yaml
- Storage: packed as np.uint8 arrays (D/8 bytes = 2,048 bytes per vector)
- Similarity: Hamming distance (popcount of XOR result)
- Binding: element-wise XOR (self-inverse, commutative)
- Bundling: element-wise majority vote (thresholded sum)
- Sequence: circular bit-shift (permutation)
All batch operations are NumPy-vectorized (no Python loops for distance computation).
"""
import hashlib
from typing import List, Optional, Tuple
import numpy as np
import re
# Cached lookup table for popcount (bits set per byte value 0-255)
_POPCOUNT_TABLE: Optional[np.ndarray] = None
def _build_popcount_table() -> np.ndarray:
"""Build or return cached popcount lookup table for bytes (0-255)."""
global _POPCOUNT_TABLE
if _POPCOUNT_TABLE is None:
_POPCOUNT_TABLE = np.array(
[bin(i).count("1") for i in range(256)], dtype=np.int32
)
return _POPCOUNT_TABLE
class BinaryHDV:
"""
A binary hyperdimensional vector stored as a packed uint8 array.
The vector has `dimension` logical bits, stored in `dimension // 8` bytes.
Each byte holds 8 bits in big-endian bit order (MSB first within each byte).
Attributes:
data: np.ndarray of dtype uint8, shape (dimension // 8,)
dimension: int, number of logical bits
"""
__slots__ = ("data", "dimension")
def __init__(self, data: np.ndarray, dimension: int):
"""
Args:
data: Packed uint8 array of shape (dimension // 8,).
dimension: Number of logical bits.
"""
assert data.dtype == np.uint8, f"Expected uint8, got {data.dtype}"
assert data.shape == (dimension // 8,), (
f"Shape mismatch: expected ({dimension // 8},), got {data.shape}"
)
self.data = data
self.dimension = dimension
# ------------------------------------------------------------------
# Factory methods
# ------------------------------------------------------------------
@classmethod
def random(cls, dimension: int = 16384) -> "BinaryHDV":
"""Generate a random binary vector (uniform i.i.d. bits)."""
assert dimension % 8 == 0, "Dimension must be multiple of 8"
n_bytes = dimension // 8
data = np.random.randint(0, 256, size=n_bytes, dtype=np.uint8)
return cls(data=data, dimension=dimension)
@classmethod
def zeros(cls, dimension: int = 16384) -> "BinaryHDV":
"""All-zero vector."""
n_bytes = dimension // 8
return cls(data=np.zeros(n_bytes, dtype=np.uint8), dimension=dimension)
@classmethod
def ones(cls, dimension: int = 16384) -> "BinaryHDV":
"""All-one vector (every bit set)."""
n_bytes = dimension // 8
return cls(
data=np.full(n_bytes, 0xFF, dtype=np.uint8), dimension=dimension
)
@classmethod
def from_seed(cls, seed: str, dimension: int = 16384) -> "BinaryHDV":
"""
Deterministic vector from a string seed.
Uses SHA-3 (SHAKE-256) for high-performance deterministic expansion.
"""
n_bytes = dimension // 8
# SHAKE-256 can generate arbitrary length digests in one pass
digest = hashlib.shake_256(seed.encode()).digest(n_bytes)
data = np.frombuffer(digest, dtype=np.uint8).copy()
return cls(data=data, dimension=dimension)
# ------------------------------------------------------------------
# Core VSA operations
# ------------------------------------------------------------------
def xor_bind(self, other: "BinaryHDV") -> "BinaryHDV":
"""
Binding via element-wise XOR.
Properties:
- Self-inverse: a ⊕ a = 0
- Commutative: a ⊕ b = b ⊕ a
- Associative: (a ⊕ b) ⊕ c = a ⊕ (b ⊕ c)
- Preserves distance: hamming(a⊕c, b⊕c) = hamming(a, b)
"""
assert self.dimension == other.dimension
return BinaryHDV(
data=np.bitwise_xor(self.data, other.data),
dimension=self.dimension,
)
def permute(self, shift: int = 1) -> "BinaryHDV":
"""
Circular bit-shift for sequence/role encoding.
Shifts all bits by `shift` positions to the right (with wrap-around).
Works at the byte level with bit carry for efficiency.
"""
if shift == 0:
return BinaryHDV(data=self.data.copy(), dimension=self.dimension)
# Normalize shift to positive value within dimension
shift = shift % self.dimension
bits = np.unpackbits(self.data)
bits = np.roll(bits, shift)
return BinaryHDV(
data=np.packbits(bits), dimension=self.dimension
)
def invert(self) -> "BinaryHDV":
"""Bitwise NOT — produces the maximally distant vector."""
return BinaryHDV(
data=np.bitwise_not(self.data), dimension=self.dimension
)
def hamming_distance(self, other: "BinaryHDV") -> int:
"""
Hamming distance: count of differing bits.
Uses lookup table for speed (replacing unpackbits).
Range: [0, dimension].
"""
assert self.dimension == other.dimension
xor_result = np.bitwise_xor(self.data, other.data)
# Optimized: use precomputed popcount table instead of unpacking bits
return int(_build_popcount_table()[xor_result].sum())
def normalized_distance(self, other: "BinaryHDV") -> float:
"""Hamming distance normalized to [0.0, 1.0]."""
return self.hamming_distance(other) / self.dimension
def similarity(self, other: "BinaryHDV") -> float:
"""
Similarity score in [0.0, 1.0].
1.0 = identical, 0.0 = maximally different.
0.5 = random/orthogonal (expected for unrelated vectors).
"""
return 1.0 - self.normalized_distance(other)
# ------------------------------------------------------------------
# Compatibility shims for legacy HDV API
# ------------------------------------------------------------------
def bind(self, other: "BinaryHDV") -> "BinaryHDV":
"""
Alias for xor_bind(). Compatibility shim for legacy HDV API.
Deprecated: Use xor_bind() directly for new code.
"""
return self.xor_bind(other)
def unbind(self, other: "BinaryHDV") -> "BinaryHDV":
"""
Alias for xor_bind(). Since XOR is self-inverse, unbind = bind.
Compatibility shim for legacy HDV API.
"""
return self.xor_bind(other)
def cosine_similarity(self, other: "BinaryHDV") -> float:
"""
Alias for similarity(). Compatibility shim for legacy HDV API.
Note: For binary vectors, this returns Hamming-based similarity,
not true cosine similarity. The values are comparable for most use cases.
"""
return self.similarity(other)
def normalize(self) -> "BinaryHDV":
"""
No-op for binary vectors. Compatibility shim for legacy HDV API.
Binary vectors are already "normalized" in the sense that they
consist only of 0s and 1s. Returns a copy of the vector.
"""
return BinaryHDV(data=self.data.copy(), dimension=self.dimension)
def __xor__(self, other: "BinaryHDV") -> "BinaryHDV":
"""Alias for xor_bind(). Enables v1 ^ v2 syntax."""
return self.xor_bind(other)
def to_bytes(self) -> bytes:
"""Serialize to raw bytes (for storage)."""
return self.data.tobytes()
@classmethod
def from_bytes(cls, raw: bytes, dimension: int = 16384) -> "BinaryHDV":
"""Deserialize from raw bytes."""
data = np.frombuffer(raw, dtype=np.uint8).copy()
return cls(data=data, dimension=dimension)
def __repr__(self) -> str:
# Optimized: use precomputed popcount table
popcount = int(_build_popcount_table()[self.data].sum())
return f"BinaryHDV(dim={self.dimension}, popcount={popcount}/{self.dimension})"
def __eq__(self, other: object) -> bool:
if not isinstance(other, BinaryHDV):
return NotImplemented
return self.dimension == other.dimension and np.array_equal(
self.data, other.data
)
# ======================================================================
# Batch operations (NumPy-vectorized, no Python loops)
# ======================================================================
def batch_hamming_distance(
query: BinaryHDV, database: np.ndarray
) -> np.ndarray:
"""
Compute Hamming distance between a query vector and all vectors in a database.
Args:
query: Single BinaryHDV query vector.
database: 2D array of shape (N, D//8) with dtype uint8, where each row
is a packed binary vector.
Returns:
1D array of shape (N,) with Hamming distances (int).
"""
# XOR query with all database vectors: (N, D//8)
xor_result = np.bitwise_xor(database, query.data)
# Popcount via lookup table — count bits set in each byte
# This is the fastest pure-NumPy approach for packed binary vectors
popcount_table = _build_popcount_table()
bit_counts = popcount_table[xor_result] # (N, D//8)
# Sum across bytes to get total Hamming distance per vector
return bit_counts.sum(axis=1)
def batch_hamming_distance_matrix(
database: np.ndarray,
) -> np.ndarray:
"""
Compute the full pairwise Hamming distance matrix for a database.
Args:
database: 2D array of shape (N, D//8) with dtype uint8.
Returns:
2D array of shape (N, N) with Hamming distances.
"""
N = database.shape[0]
popcount_table = _build_popcount_table()
distances = np.zeros((N, N), dtype=np.int32)
for i in range(N):
xor_result = np.bitwise_xor(database[i], database[i + 1 :])
bit_counts = popcount_table[xor_result].sum(axis=1)
distances[i, i + 1 :] = bit_counts
distances[i + 1 :, i] = bit_counts
return distances
def majority_bundle(
vectors: List[BinaryHDV], randomize_ties: bool = False
) -> BinaryHDV:
"""
Bundle multiple vectors via element-wise majority vote.
For each bit position, the result bit is 1 if more than half of the
input vectors have a 1 at that position.
Args:
vectors: List of BinaryHDV vectors to bundle.
randomize_ties: If True, break ties randomly. If False (default),
ties default to 0 for deterministic results.
This is the standard VSA bundling operation (superposition).
"""
assert len(vectors) > 0, "Cannot bundle empty list"
dimension = vectors[0].dimension
# Unpack all vectors to bits
# Optimization: Stack packed data first, then unpack all at once
# This avoids K calls to unpackbits and list comprehension overhead
packed_data = np.stack([v.data for v in vectors], axis=0) # (K, D//8)
all_bits = np.unpackbits(packed_data, axis=1) # (K, D)
# Sum along vectors axis: count of 1-bits per position
sums = all_bits.sum(axis=0) # (D,)
# Majority vote: > half means 1
threshold = len(vectors) / 2.0
result_bits = np.zeros(dimension, dtype=np.uint8)
result_bits[sums > threshold] = 1
# Handle ties
if randomize_ties:
ties = sums == threshold
if ties.any():
result_bits[ties] = np.random.randint(
0, 2, size=ties.sum(), dtype=np.uint8
)
return BinaryHDV(data=np.packbits(result_bits), dimension=dimension)
def top_k_nearest(
query: BinaryHDV, database: np.ndarray, k: int = 10
) -> List[Tuple[int, int]]:
"""
Find k nearest neighbors by Hamming distance.
Args:
query: Query vector.
database: 2D array of shape (N, D//8) packed binary vectors.
k: Number of nearest neighbors.
Returns:
List of (index, distance) tuples, sorted by distance ascending.
"""
distances = batch_hamming_distance(query, database)
k = min(k, len(distances))
# argpartition is O(N) vs O(N log N) for full sort — much faster for large N
indices = np.argpartition(distances, k)[:k]
selected_distances = distances[indices]
# Sort the k results by distance
sort_order = np.argsort(selected_distances)
sorted_indices = indices[sort_order]
sorted_distances = selected_distances[sort_order]
return [(int(idx), int(dist)) for idx, dist in zip(sorted_indices, sorted_distances)]
# ======================================================================
# Text encoding pipeline
# ======================================================================
class TextEncoder:
"""
Encode text to binary HDV using token-level random vectors with
position-permutation binding.
Method: For text "hello world", we compute:
HDV = bundle(token("hello") ⊕ permute(pos, 0),
token("world") ⊕ permute(pos, 1))
Token vectors are deterministic (seeded from the token string),
ensuring the same word always maps to the same base vector.
"""
def __init__(self, dimension: int = 16384):
self.dimension = dimension
self._token_cache: dict[str, BinaryHDV] = {}
def get_token_vector(self, token: str) -> BinaryHDV:
"""Get or create a deterministic vector for a token."""
if token not in self._token_cache:
self._token_cache[token] = BinaryHDV.from_seed(token, self.dimension)
return self._token_cache[token]
def encode(self, text: str) -> BinaryHDV:
"""
Encode a text string to a binary HDV.
Tokenization: simple whitespace split after normalization.
Each token is bound with its position via XOR(token, permute(position_marker, i)).
All position-bound tokens are bundled via majority vote.
"""
# Improved Tokenization: consistent alphanumeric extraction
tokens = re.findall(r'\b\w+\b', text.lower())
if not tokens:
return BinaryHDV.random(self.dimension)
if len(tokens) == 1:
return self.get_token_vector(tokens[0])
# Build position-bound token vectors (#27)
# Optimized: Batch process data instead of multiple object instantiations
token_hdvs = [self.get_token_vector(t) for t in tokens]
packed_data = np.stack([v.data for v in token_hdvs], axis=0)
all_bits = np.unpackbits(packed_data, axis=1)
# Apply position-based permutations (roll)
for i in range(len(tokens)):
if i > 0:
all_bits[i] = np.roll(all_bits[i], i)
# Vectorized majority vote (equivalent to majority_bundle)
sums = all_bits.sum(axis=0)
threshold = len(tokens) / 2.0
result_bits = np.zeros(self.dimension, dtype=np.uint8)
result_bits[sums > threshold] = 1
return BinaryHDV(data=np.packbits(result_bits), dimension=self.dimension)
def encode_with_context(
self, text: str, context_hdv: BinaryHDV
) -> BinaryHDV:
"""
Encode text and bind it with a context vector.
Result = encode(text) ⊕ context
This creates an association between the content and its context.
"""
content_hdv = self.encode(text)
return content_hdv.xor_bind(context_hdv)
|