How does using a binary embedding (e.g., sign of components only, or learned binary codes) drastically cut down storage, and what kind of search algorithms support such binary vectors?

Binary embeddings drastically reduce storage by representing each vector component as a single bit (0 or 1) or a binary value (-1 or 1 via the sign function) instead of a full-precision floating-point number. For example, a 128-dimensional vector stored as 32-bit floats requires 512 bytes, but its binary equivalent uses just 16 bytes (128 bits). Even if stored as bytes for practical alignment (1 byte per bit), it would still occupy only 128 bytes—far smaller than the float version. This compression is critical for large-scale systems, such as recommendation engines or image retrieval, where storing billions of high-dimensional vectors becomes feasible. For instance, a database of 1 billion binary vectors at 128 dimensions would need ~16 GB of storage, whereas the same data in float32 would require ~512 GB, making binary embeddings 32x more efficient in raw bit terms.

Search algorithms for binary vectors rely heavily on Hamming distance (the count of differing bits) and bitwise operations optimized for speed. Calculating Hamming distance involves XOR-ing two binary vectors and counting the set bits, a process accelerated by hardware instructions like POPCNT (population count) on modern CPUs. For approximate nearest neighbor search, methods like Locality-Sensitive Hashing (LSH) are adapted to binary codes. For example, LSH might use random hyperplanes to hash similar vectors into the same buckets, allowing sublinear-time lookups. Libraries like FAISS support binary embeddings with techniques such as Binary IVFADC, which clusters vectors and uses asymmetric distance computations. Multi-index hashing splits binary codes into segments, enabling fast lookups by comparing partial hashes. These methods avoid the computational cost of floating-point arithmetic, making searches orders of magnitude faster.

Practical applications include image retrieval (e.g., mapping CNN features to binary codes) or text search (hashing word embeddings). Libraries like FAISS or Annoy provide built-in support for binary vectors, enabling efficient in-memory searches even for massive datasets. Learned binary codes, such as those from Deep Hashing models, further improve accuracy by training neural networks to produce semantically meaningful binary representations. For example, a model might optimize embeddings so that similar images have minimal Hamming distance. While binary embeddings sacrifice some precision, their storage and speed benefits make them indispensable for real-time systems where scalability and latency are critical. Developers can implement these using off-the-shelf tools, balancing trade-offs between accuracy and efficiency based on their use case.