Core Retrieval Algorithms

Retrieval is how systems find relevant information before generation. It turns a user query into a ranked list of candidate documents. This chapter starts from zero and builds toward the concrete job skill: Implement toy BM25 scoring, dense cosine similarity, and reciprocal rank fusion for a small document set. ^[1][2][3]

Step map

Start here

Start with similarity. If two vectors point in similar directions, cosine similarity is high. If a document shares rare query terms, lexical retrieval scores it high. Production RAG often combines both.

Read this chapter once for the idea, then run the demo and change one value. For Core Retrieval Algorithms, progress means you can name the input, explain the operation, and say what result would prove the idea worked.

By the end, you should be able to explain Core Retrieval Algorithms with a worked example, not a library name. Keep one runnable file and one short note with the result you expected before you ran it.

Why this chapter matters

Core Retrieval Algorithms matters because later LLM work assumes this habit already exists. You will use it when you inspect data, debug model behavior, compare evaluations, or explain why a result should be trusted.

The job skill here is: Implement toy BM25 scoring, dense cosine similarity, and reciprocal rank fusion for a small document set. Treat the snippet as lab equipment: run it, change one input, and write down what changed before you move on.

Beginner mental model

Imagine a query and three short documents. Before using a vector database, calculate one similarity score yourself so the ranking is not a black box.

A useful beginner checklist for Core Retrieval Algorithms:

1. What object enters the system?
2. What transformation happens to it?
3. What evidence says the result is correct?

Keep the answer concrete. If you can't point to the value, shape, row, metric, or test that proves the point, the Core Retrieval Algorithms concept is still fuzzy.

Vocabulary in plain English

• BM25: lexical ranking method that rewards matching rare terms while controlling document length.
• cosine similarity: angle-based similarity between vectors.
• MIPS: maximum inner product search, used when dot product is the score.
• HNSW: graph-based approximate nearest-neighbor index.
• IVF: index that partitions vectors into coarse groups before search.
• product quantization: compression method for large vector collections.
• RRF: rank fusion rule that combines multiple ranked lists.

Use these definitions while reading the demo. Each term should map to a variable, an assertion, or a decision you could explain in review.

Build it

Start with the smallest version that can run from a terminal. The goal for this Core Retrieval Algorithms demo is visibility: one file, one output, and no hidden notebook state.

python
1import math
2
3def cosine(a, b):
4    dot = sum(x * y for x, y in zip(a, b))
5    na = math.sqrt(sum(x * x for x in a))
6    nb = math.sqrt(sum(y * y for y in b))
7    return dot / (na * nb)
8
9print(cosine([1, 0, 1], [0.5, 0.5, 1]))

Read the code in this order:

• dot measures how much two vectors point together.
• na and nb measure vector lengths.
• dot / (na * nb) normalizes by length so scale doesn't dominate.
• A real retriever repeats this score across many documents, then sorts by score.

After it runs, make three small edits. Add a normal-case test, add an edge-case test, then log the intermediate value a beginner would most likely misunderstand. That turns Core Retrieval Algorithms from a reading exercise into an engineering exercise.

For Core Retrieval Algorithms, a strong submission includes a runnable command, one test file, and notes for any assumptions. If data, randomness, training, or evaluation appears, save the split rule, seed, config, and metric definition.

Beginner failure case

A beginner may trust top-1 retrieval without checking whether relevant documents are missing from the candidate set.

For Core Retrieval Algorithms, make the failure visible before adding the fix. Write the symptom in plain English, then add the smallest guard that would catch it next time.

Good guards for Core Retrieval Algorithms are concrete: assertions, fixture rows, duplicate checks, seed control, metric intervals, or release checks. Pick the guard that makes the hidden assumption executable.

Practice ladder

1. Run the snippet exactly as written and save the output.
2. Change one input value and predict the output before running it again.
3. Add one assertion that would catch a beginner mistake.
4. Add three document vectors, rank them by cosine similarity, then test what happens when one vector has a much larger norm.
5. Write a two-line README: one command to run the demo, one command to run the test.

Keep this ladder small. Core Retrieval Algorithms should feel runnable before it feels impressive. The capstones later reuse the same habit at product scale.

Production check

Track recall@k, MRR, nDCG, latency, memory, index freshness, and per-query failure examples.

A production check for Core Retrieval Algorithms is proof another engineer can trust the result. At foundation level that means a reproducible command and tests. At capstone level it also means a design note, eval evidence, cost or latency notes, and rollback criteria.

Before moving on, answer four Core Retrieval Algorithms questions: What input does this accept? What output or metric proves it worked? What failure would fool you? What test catches that failure?

What to ship

Ship a small Core Retrieval Algorithms folder with code, tests, and notes. Make it boring to run: install dependencies, run tests, run the demo. That boring path is what makes the artifact useful in a portfolio.

Core Retrieval Algorithms feeds later LLM engineering work directly. Retrieval, fine-tuning, agents, evals, and serving all depend on small foundations like this being clear before systems get large.