# Vector Indexes and Approximate Search — Retrieval-Augmented Generation (RAG)

Source: https://www.geekswithgeeks.com/en/rag/v-index

> Understand why large collections use approximate nearest-neighbour indexes.

## Exact search does not scale

Comparing the query with every vector (**brute force**) is exact but slow for millions of vectors. **Approximate nearest neighbour (ANN)** indexes such as **HNSW** (a layered graph), **IVF** (clusters) and quantised variants find near-best matches much faster, trading a little **recall** for speed and memory. For a few thousand chunks, brute force is fine and simplest. Larger systems use a vector database or a search engine with vector support (for example pgvector, Elasticsearch/OpenSearch, Qdrant, Milvus, Pinecone, FAISS). Tune the recall-versus-latency settings against your own evaluation set.

## Size and cost arithmetic, run

I ran this plain-Python (standard library only) example. One million 768-dimension float32 vectors take about 3.07 GB; 100 brute-force queries need 76.8 billion multiplications; 8-bit quantisation cuts the vector storage to a quarter.

```python
import math

# brute-force nearest neighbour cost: queries * documents * dimensions multiplications
docs, dim, queries = 1_000_000, 768, 100
ops = docs * dim * queries
print("multiplications per 100 queries:", f"{ops:,}")
print("float32 index size (GB):", round(docs * dim * 4 / 1e9, 2))
print("with 8-bit quantisation (GB):", round(docs * dim * 1 / 1e9, 2))

```

Output:

```
multiplications per 100 queries: 76,800,000,000
float32 index size (GB): 3.07
with 8-bit quantisation (GB): 0.77
```

## Brute force is fine for small sets

Below roughly 100,000 vectors a plain exact search is often fast enough and removes ANN tuning entirely.

**Quiz:** What do ANN indexes trade for speed?

- [ ] All accuracy
- [x] A little recall (they may miss a true nearest neighbour)
- [ ] The ability to store metadata
- [ ] The language support

*Answer:* A little recall (they may miss a true nearest neighbour). Approximate means results are almost, not always exactly, the true top matches.