IVF

Vector databases (such as ChromaDB, Milvus, and Pinecone) use indexing algorithms such as HNSW and IVF to achieve millisecond-level retrieval among millions or even hundreds of millions of vectors.

向量数据库的核心操作是近似最近邻搜索（ANN），通过HNSW、IVF等索引算法将相似度计算加速到毫秒级响应

The vector database index algorithms HNSW (graph structure) and IVF (clustering structure) present different engineering trade-offs between retrieval speed and recall rate

Vector databases excel at semantic fuzzy matching, but cannot natively express directed, transitive, and constrained structural relationships such as 'A depends on B', 'C covers D', or 'this rule cannot be overridden'.

Approximate nearest neighbor search (ANN) reduces retrieval complexity from O(N) for exact nearest neighbor to approximately O(log N) at the cost of a small amount of recall, making millisecond-level retrieval possible under registries of tens of thousands of entries.

Vector index structures (such as HNSW graphs or IVF inverted lists) may add an additional 30%–50% or even more space overhead.

HNSW achieves efficient retrieval through a multi-layer graph structure, using the ef parameter to control the size of the candidate queue during search; IVF first clusters the vectors and then searches within some of the clusters, using the nprobe parameter to determine the number of clusters to probe.

Approximate nearest neighbor (ANN) index structures (such as HNSW and IVF) need to be rebuilt or tuned after the data distribution changes, otherwise recall will decline.

HNSW的hnsw_ef参数在查询阶段生效，值越大召回率越高但单次查询延迟也越高

The cost of HNSW compared to IVF-type algorithms is higher memory usage during index construction and longer index build times.

Commonly used distance metrics for vector retrieval include cosine similarity and dot product; practical systems typically employ approximate nearest neighbor (ANN) index structures such as HNSW or IVF to trade a small amount of precision for speed.

The core principle of vector search is to convert text into high-dimensional numerical vectors via an embedding model, and then use approximate nearest neighbor algorithms (such as HNSW or IVF) to find the closest candidates.

The success rate of assisted reproductive technology is approximately one-third to one-half, and even lower for those over 40.

In the more than forty years since IVF was invented, at least approximately 10 million babies have been born through it.

Israel's national health insurance provides unlimited IVF subsidies for each woman until she has given birth to two children.

Nordic countries such as Denmark and Sweden include several IVF cycles within their public healthcare coverage.

The basic process of in vitro fertilization (IVF) includes hormonal stimulation of the ovaries for superovulation, retrieval of oocytes, fertilization with sperm outside the body to form embryos, and then transfer back into the uterus.

In the United States, the cost of a complete IVF cycle typically ranges from $12,000 to $15,000, and the total cost can exceed $20,000 after adding PGT and cryopreservation.

Using inner product indexing on normalized vectors can often reuse efficient approximate index structures such as HNSW and IVF, without needing to build a separate index for cosine similarity.

Mainstream ANN index structures include HNSW, IVF, and ScaNN proposed by Google, with different index structures presenting different trade-offs among recall rate, query latency, and memory usage.