Recall composes multiplicatively

NumericalBeginner⏱ 15 minRAGrecallpipelineceilingsystem design

Theory: Vector Search — Exact and Approximate Nearest Neighbours →

Problem

A RAG pipeline has chunking recall $0.95$ , ANN index recall $0.90$ , top- $k$ truncation recall $0.95$ , and a reranker with recall $0.98$ within the candidate set.

Compute the end-to-end recall.
Compute the effect of improving the reranker to $1.0$ .
Compute the effect of improving the index to $0.98$ .
State the design principle.

Compute the requested quantities and say what they mean. A number without an interpretation is not an answer.

Solution

Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.

Related problems

All problems

Problem	Field	Type	Difficulty	Time
End-to-end recall arithmetic for a RAG system	RAG	Numerical	Beginner	15 min
Product quantisation budget arithmetic	RAG	Numerical	Beginner	30 min
The random-hyperplane collision probability	RAG	Proof	Intermediate	30 min
Implement SimHash LSH and measure recall run	RAG	Coding	Advanced	3 hours
Why space-partitioning trees fail in high dimension	RAG	Proof	Advanced	30 min