Using binary embeddings, such as vectors where components are reduced to 0/1 bits or learned binary codes, drastically reduces storage by representing each dimension as a single bit instead of a multi-byte floating-point value. For example, a 128-dimensional vector stored as 32-bit floats requires 512 bytes (128 × 4 bytes), while a binary version uses 128 bits (16 bytes), cutting storage by 32×. This compact representation also allows efficient packing—e.g., storing 8 binary values in a single byte—further optimizing memory use. This is critical for large-scale systems like recommendation engines or image retrieval, where storing billions of high-dimensional vectors would otherwise be impractical.
Search algorithms optimized for binary vectors rely on fast bitwise operations. The Hamming distance, which counts mismatched bits using XOR and bit population count (popcount), is central to these methods. Locality-Sensitive Hashing (LSH) for binary codes hashes vectors into buckets where similar items collide, enabling approximate nearest-neighbor searches. Multi-index hashing splits binary codes into substrings, creating inverted indices for each block to accelerate candidate filtering. For exact searches, algorithms precompute lookup tables for partial Hamming distances or use SIMD instructions to parallelize bitwise operations. Libraries like FAISS implement these techniques with structures such as IndexBinaryFlat (brute-force Hamming search) and IndexBinaryIVF (inverted file indexing with clustering).
Practically, binary embeddings trade some precision for efficiency, making them ideal for latency-sensitive applications. For instance, image retrieval systems like Facebook’s FAIR use binary codes to search billions of images in milliseconds. Similarly, voice assistants employ binary hashing for fast voiceprint matching. While binary representations may not capture nuances as well as floating-point embeddings, their storage and computational advantages—combined with algorithms like LSH and multi-index hashing—make them indispensable for real-world systems prioritizing speed and scalability.