Vector Database

The vector database will utilize Hierarchical Navigable Small Worlds (HNSW) for vector searching, as implemented in Qdrant. HNSW is chosen for its scalability and ability to provide fast searches at scale, which is essential for handling large datasets generated by LLMs.

Why HNSW is Feasible Under FHE:

HNSW is particularly suited for use with Fully Homomorphic Encryption (FHE) because of its efficient search algorithms and the ability to handle high-dimensional data. The key reasons for selecting HNSW are:

• Efficiency: HNSW offers logarithmic search complexity, which significantly reduces the time required for querying large datasets. This efficiency is crucial when dealing with the additional computational overhead of FHE.

• Scalability: HNSW can handle millions of vectors, making it suitable for large-scale applications such as LLM training and inference on encrypted data.

• Incremental Construction: HNSW allows for incremental construction of the graph, meaning new vectors can be added without the need to rebuild the entire structure. This flexibility is beneficial for continuously updating datasets.

• Adaptability to Encrypted Data: HNSW's search process involves distance calculations and neighbor traversals, which can be efficiently mapped to homomorphic operations on encrypted data.