Information Retrieval · Cluster
Vector Search
Embeddings and approximate nearest neighbors.
- 01 Cosine Similarity and the Geometry of Normalized Embedding Vectors What the cosine score actually measures, why length normalization turns it into a plain dot product, and when that normalization destroys information the model encoded.
- 02 Distance Concentration and Why Tree Indexes Collapse in High Dimensions Why bounding-box and ball-tree pruning stops helping as dimensionality grows, what the concentration effect does to nearest-neighbor contrast, and which index families survive it.
- 03 Random Hyperplane LSH and the Arithmetic of Banding How one random plane per bit turns cosine similarity into collision probability, and how band and row counts convert that probability into a practical recall curve with a sharp threshold.
- 04 Coarse Quantization with Inverted Files and the nprobe Setting How an inverted-file index reduces a full scan to a few cluster scans, what the centroid training step optimizes, and why the nprobe parameter buys recall at a nearly linear price in work.
- 05 Product Quantization and the Asymmetric Distance Computation How splitting a vector into subspaces and coding each against a small codebook replaces a distance computation with table lookups, and where the reconstruction error shows up in the ranking.
- 06 HNSW Layer Assignment and the Greedy Descent How a hierarchical proximity graph assigns levels by an exponential draw, why the top layers act as a coarse skip list, and what ef actually bounds during the search.
- 07 Metadata Filtering Inside a Vector Index and the Selectivity Collapse Why post-filtering silently returns fewer results than requested, how pre-filtering degrades graph traversal, and what the filter selectivity threshold does to each index family.
- 08 Disk-Resident Graph Indexes and the Memory Bandwidth Wall What changes when the vector index no longer fits in RAM: page-oriented adjacency storage, the cost of a random read per hop, and why compression and caching decide throughput.
- 09 Over-Fetch and Exact Reranking in Two-Stage Vector Retrieval Why an approximate candidate list must be wider than the final result set, how to size the over-fetch from the approximation error, and where the rerank stage changes the answer.
- 10 Tombstones, Merges, and the Cost of Keeping a Vector Index Current Why deleting from a proximity graph is harder than inserting, how segment-and-merge maintenance bounds the damage, and when a rebuild is cheaper than incremental repair.