This guide provides comprehensive strategies for optimizing Vector Symbolic Architecture (VSA) performance. We cover dimension selection, operation optimization, memory management, and hardware acceleration techniques.
| Operation | Time Complexity | Space Complexity | Bottleneck |
|---|---|---|---|
| Encoding | O(1) | O(d) | Memory allocation |
| Binding | O(d) to O(d log d) | O(d) | Element-wise ops / FFT |
| Bundling | O(nd) | O(d) | Memory bandwidth |
| Similarity | O(d) | O(1) | Cache efficiency |
| Cleanup | O(Md) | O(Md) | Memory access patterns |
Where:
- d = dimension
- n = number of items to bundle
- M = number of stored items
- Dimension Size: Affects all operations linearly
- Vector Type: Determines operation cost
- Binding Method: Varies from O(d) to O(d log d)
- Memory Layout: Impact on cache efficiency
- Parallelization: Potential for speedup
def calculate_optimal_dimension(num_items, error_rate=0.01):
"""Calculate dimension for desired capacity and error rate."""
# For bundling capacity
bundle_dim = int((num_items / error_rate) ** 2)
# For binding pairs
binding_dim = int(num_items * np.log(1/error_rate) * 100)
# Choose larger for safety
return max(bundle_dim, binding_dim, 1000)| Use Case | Items | Recommended Dimension |
|---|---|---|
| Small demos | < 10 | 1,000 (default) |
| Medium applications | 10-100 | 5,000 - 10,000 |
| Large systems | 100-1000 | 10,000 - 50,000 |
| Research/production | 1000+ | 50,000 - 100,000 |
class AdaptiveVSA:
def __init__(self, initial_dim=1000):
self.dimension = initial_dim
self.vsa = create_vsa(VSAConfig(dimension=initial_dim))
self.stored_items = 0
def check_capacity(self):
"""Increase dimension if approaching capacity."""
capacity = np.sqrt(self.dimension)
if self.stored_items > 0.7 * capacity:
self.increase_dimension()
def increase_dimension(self):
"""Double dimension and migrate vectors."""
new_dim = self.dimension * 2
# Pad existing vectors with zeros
# Or regenerate with new dimension| Vector Type | Memory/Element | Binding Speed | Best For |
|---|---|---|---|
| Binary | 1 bit | Fastest (XOR) | Hardware, memory-limited |
| Bipolar | 8 bits | Fast (multiply) | General purpose |
| Ternary | 2-8 bits | Fast (sparse) | Large-scale, sparse data |
| Complex | 128 bits | Slow (complex ops) | Frequency domain |
| Integer | 8-16 bits | Moderate | Special algorithms |
# Use bit-packed arrays for memory efficiency
import numpy as np
class PackedBinaryVector:
def __init__(self, dimension):
self.dimension = dimension
self.data = np.packbits(np.random.randint(0, 2, dimension))
def unpack(self):
return np.unpackbits(self.data)[:self.dimension]# Store only non-zero elements
class SparseTernaryVector:
def __init__(self, dimension, sparsity=0.1):
self.dimension = dimension
nnz = int(dimension * sparsity)
self.indices = np.random.choice(dimension, nnz, replace=False)
self.values = np.random.choice([-1, 1], nnz)
def to_dense(self):
dense = np.zeros(self.dimension, dtype=np.int8)
dense[self.indices] = self.values
return dense# Vectorized XOR for binary arrays
def fast_xor_binding(x, y):
"""Optimized XOR using NumPy."""
return np.bitwise_xor(x, y)
# For packed bits
def packed_xor_binding(x_packed, y_packed):
"""XOR on packed binary data."""
return np.bitwise_xor(x_packed, y_packed)# Use BLAS for large vectors
def fast_multiplication_binding(x, y):
"""Optimized multiplication."""
return np.multiply(x, y, dtype=np.int8) # Minimize precision
# SIMD-friendly version
def simd_multiplication(x, y):
"""Ensure alignment for SIMD."""
x_aligned = np.ascontiguousarray(x)
y_aligned = np.ascontiguousarray(y)
return np.multiply(x_aligned, y_aligned)# Cache FFT plans
from scipy import fft
class CachedConvolution:
def __init__(self, dimension):
self.dimension = dimension
self.fft_plan = fft.next_fast_len(dimension)
def convolve(self, x, y):
"""Convolution with cached FFT plan."""
x_fft = fft.fft(x, n=self.fft_plan)
y_fft = fft.fft(y, n=self.fft_plan)
return fft.ifft(x_fft * y_fft)[:self.dimension].realdef fast_bundle(vectors, weights=None):
"""Optimized bundling using matrix operations."""
if weights is None:
# Use matrix sum
matrix = np.vstack(vectors)
summed = np.sum(matrix, axis=0)
else:
# Weighted sum
matrix = np.vstack(vectors)
weights = np.array(weights).reshape(-1, 1)
summed = np.sum(matrix * weights, axis=0)
# Threshold for bipolar
return np.sign(summed)class IncrementalBundle:
"""Maintain running sum for efficiency."""
def __init__(self, dimension):
self.sum = np.zeros(dimension)
self.count = 0
def add(self, vector):
"""Add vector to bundle."""
self.sum += vector
self.count += 1
def get_bundle(self):
"""Get current bundle."""
return np.sign(self.sum)def batch_similarity(query, database):
"""Compute similarity to many vectors at once."""
# Normalize if needed
query_norm = query / np.linalg.norm(query)
# Matrix multiplication for dot products
similarities = np.dot(database, query_norm)
return similarities
# GPU acceleration with CuPy (if available)
try:
import cupy as cp
def gpu_batch_similarity(query, database):
"""GPU-accelerated similarity."""
query_gpu = cp.asarray(query)
database_gpu = cp.asarray(database)
similarities = cp.dot(database_gpu, query_gpu)
return cp.asnumpy(similarities)
except ImportError:
gpu_batch_similarity = batch_similarity# Column-major for better cache locality in some operations
vectors_fortran = np.asfortranarray(vectors)
# Ensure contiguous memory
vectors_c = np.ascontiguousarray(vectors)
# Memory-mapped arrays for large datasets
vectors_mmap = np.memmap('vectors.dat', dtype='float32',
mode='r', shape=(num_vectors, dimension))class VectorPool:
"""Reuse vector memory to reduce allocation overhead."""
def __init__(self, dimension, pool_size=100):
self.dimension = dimension
self.pool = [np.zeros(dimension) for _ in range(pool_size)]
self.available = list(range(pool_size))
self.in_use = set()
def get_vector(self):
"""Get a vector from pool."""
if self.available:
idx = self.available.pop()
self.in_use.add(idx)
return self.pool[idx]
else:
# Allocate new if pool exhausted
return np.zeros(self.dimension)
def return_vector(self, vector):
"""Return vector to pool."""
# Find index and return to available
# Clear vector data for reuse
vector.fill(0)class EfficientCleanupMemory:
"""Memory-efficient cleanup implementation."""
def __init__(self, dimension, max_items=10000):
self.dimension = dimension
self.max_items = max_items
# Use memory-mapped file for large storage
self.vectors = np.memmap(
'cleanup_memory.dat',
dtype='float32',
mode='w+',
shape=(max_items, dimension)
)
self.labels = []
self.count = 0
# Precompute normalized vectors for faster similarity
self.normalized = True
def add(self, vector, label):
"""Add normalized vector."""
if self.count >= self.max_items:
raise MemoryError("Cleanup memory full")
# Normalize and store
norm = np.linalg.norm(vector)
self.vectors[self.count] = vector / norm
self.labels.append(label)
self.count += 1
def find_nearest(self, query, k=1):
"""Efficient nearest neighbor search."""
# Normalize query
query_norm = query / np.linalg.norm(query)
# Batch similarity computation
similarities = np.dot(self.vectors[:self.count], query_norm)
# Get top-k
top_k_indices = np.argpartition(similarities, -k)[-k:]
top_k_indices = top_k_indices[np.argsort(similarities[top_k_indices])[::-1]]
return [(self.labels[i], similarities[i]) for i in top_k_indices]from concurrent.futures import ThreadPoolExecutor
import numpy as np
def parallel_binding(vectors_a, vectors_b, binding_fn, num_threads=4):
"""Parallel binding of vector pairs."""
n = len(vectors_a)
results = [None] * n
def bind_chunk(start, end):
for i in range(start, end):
results[i] = binding_fn(vectors_a[i], vectors_b[i])
chunk_size = n // num_threads
with ThreadPoolExecutor(max_workers=num_threads) as executor:
futures = []
for i in range(num_threads):
start = i * chunk_size
end = n if i == num_threads - 1 else (i + 1) * chunk_size
futures.append(executor.submit(bind_chunk, start, end))
# Wait for completion
for future in futures:
future.result()
return results# Vectorize custom operations
@np.vectorize
def custom_binding(x, y):
"""Custom element-wise operation."""
return (x * y + x + y) % 3
# Better: use NumPy's built-in vectorization
def vectorized_binding(X, Y):
"""Fully vectorized operation."""
return (X * Y + X + Y) % 3# Optional GPU support
try:
import cupy as cp
class GPUAcceleratedVSA:
def __init__(self, dimension):
self.dimension = dimension
self.use_gpu = True
def bind(self, x, y):
"""GPU-accelerated binding."""
x_gpu = cp.asarray(x)
y_gpu = cp.asarray(y)
result_gpu = x_gpu * y_gpu
return cp.asnumpy(result_gpu)
def bundle(self, vectors):
"""GPU-accelerated bundling."""
matrix_gpu = cp.asarray(vectors)
sum_gpu = cp.sum(matrix_gpu, axis=0)
result_gpu = cp.sign(sum_gpu)
return cp.asnumpy(result_gpu)
except ImportError:
print("CuPy not available, using CPU only")from functools import lru_cache
import hashlib
class CachedVSA(VSA):
def __init__(self, config):
super().__init__(config)
self._cache_size = 10000
@lru_cache(maxsize=10000)
def encode_cached(self, item):
"""Cache frequently encoded items."""
return self.encode(item)
def bind_cached(self, x_key, y_key):
"""Cache binding results."""
cache_key = f"{x_key}_{y_key}"
if cache_key not in self._bind_cache:
x = self.encode_cached(x_key)
y = self.encode_cached(y_key)
self._bind_cache[cache_key] = self.bind(x, y)
return self._bind_cache[cache_key]class PrecomputedVSA:
def __init__(self, dimension, vocabulary):
self.dimension = dimension
self.vsa = create_vsa(VSAConfig(dimension=dimension))
# Precompute all vocabulary vectors
self.vectors = {
item: self.vsa.encode(item)
for item in vocabulary
}
# Precompute common bindings
self.common_bindings = {}
for role in ['subject', 'verb', 'object']:
for item in vocabulary:
key = f"{role}_{item}"
role_vec = self.vectors[role]
item_vec = self.vectors[item]
self.common_bindings[key] = self.vsa.bind(role_vec, item_vec)import time
import cProfile
import pstats
def profile_vsa_operations(vsa, num_operations=1000):
"""Profile VSA operations."""
profiler = cProfile.Profile()
profiler.enable()
# Encoding
for i in range(num_operations):
_ = vsa.encode(f"item_{i}")
# Binding
vectors = [vsa.encode(f"vec_{i}") for i in range(100)]
for i in range(num_operations):
_ = vsa.bind(vectors[i % 100], vectors[(i + 1) % 100])
# Bundling
for i in range(num_operations // 10):
_ = vsa.bundle(vectors[:10])
profiler.disable()
# Print stats
stats = pstats.Stats(profiler)
stats.sort_stats('cumulative')
stats.print_stats(10)def benchmark_vsa_architectures():
"""Compare different VSA configurations."""
dimensions = [1000, 5000, 10000, 50000]
architectures = ['bsc', 'map', 'fhrr', 'sparse']
results = {}
for dim in dimensions:
for arch in architectures:
vsa = create_architecture(arch, dimension=dim)
# Time encoding
start = time.perf_counter()
for i in range(1000):
_ = vsa.encode(f"item_{i}")
encode_time = time.perf_counter() - start
# Time binding
vecs = [vsa.encode(f"v_{i}") for i in range(100)]
start = time.perf_counter()
for i in range(1000):
_ = vsa.bind(vecs[i % 100], vecs[(i + 1) % 100])
bind_time = time.perf_counter() - start
results[f"{arch}_{dim}"] = {
'encode': encode_time,
'bind': bind_time
}
return results- Choose appropriate dimension based on capacity needs
- Use batch operations when possible
- Preallocate memory for known sizes
- Cache frequently used vectors
- Profile before optimizing
- Use sparse representations when applicable
- Leverage NumPy's vectorization
- Don't use larger dimensions than necessary
- Don't create vectors in loops - batch instead
- Don't ignore memory layout - use contiguous arrays
- Don't neglect cleanup memory size
- Don't optimize prematurely - profile first
- Dimension appropriate for capacity?
- Vector type matches use case?
- Binding operation optimal for data?
- Batch operations used?
- Memory layout optimized?
- Caching implemented?
- Parallelization considered?
- Profiling completed?
# Use MKL-accelerated NumPy
import numpy as np
np.show_config() # Check for MKL
# Enable AVX instructions
import os
os.environ['MKL_ENABLE_INSTRUCTIONS'] = 'AVX2'# Use NEON optimizations
# Ensure NumPy compiled with NEON support# NVIDIA GPUs - use CuPy
# AMD GPUs - use ROCm
# Intel GPUs - use oneAPIVSA performance optimization involves:
- Algorithmic choices (dimension, vector type, binding)
- Implementation efficiency (vectorization, caching)
- Hardware utilization (parallelization, GPU)
- Memory management (layout, pooling)
Always profile first, optimize based on measurements, and consider the trade-offs between performance and code complexity.