Interactive explanations of how search behaves: scoring, metrics, phenomena, and even interpretability. Inspired by Distill and Complexity Explorables, which were always special for me.
Start with word rarity, build a score, combine rankers, evaluate the list, then discover the candidate ceiling.
idf and Zipf's law → BM25 → Rank fusion → Evaluation measures → Retrieve, then rerank
Choose a geometry, add eligibility constraints, search it approximately, inspect hubs, then keep token-level matches.
Similarity metrics → Filtered vector search → Approximate nearest neighbours → Hubness → Late interaction
Move from an explicit scoring rule to behavioural tests, soft counts, causal interventions and their costs.
BM25 → Behavioural tests → Soft term matching → Activation patching → Model editing
Understand the scoring limit, change the readout, intervene on a feature, then question its uniqueness.
Single-vector limits → Sparse readouts → Feature steering → Feature stability
Combine evidence, keep the needed candidates, then make room for distinct aspects.
The mechanisms every search stack is built from: the formula, a collection you can read, and the score worked out when you click.
BM25
Two constants nobody ever feels decide what BM25 thinks a document is about.
Robertson & Zaragoza, The Probabilistic Relevance Framework (2009)
idf and Zipf's law
Why a word's weight comes from how rare it is, and why that weight can go negative.
Spärck Jones, A Statistical Interpretation of Term Specificity (1972)
Similarity metrics
Same points, three metrics, three different nearest neighbours.
Steck, Ekanadham & Kallus, Is Cosine-Similarity Really About Similarity? (WWW 2024)
Rank fusion
Reciprocal rank fusion throws away the scores. That is its robustness and its blind spot.
Cormack, Clarke & Buettcher, Reciprocal Rank Fusion (SIGIR 2009)
Approximate nearest neighbours
Every approximate index is a bet about where you can afford to be wrong. Draw the trade-off yourself.
Malkov & Yashunin, Efficient and robust ANN search using HNSW (2016)
Evaluation measures
Drag one document and watch five evaluation measures disagree about whether you improved anything.
Järvelin & Kekäläinen, Cumulated gain-based evaluation of IR techniques (TOIS 2002)
Retrieve, then rerank
A perfect reranker still has to work with the documents it receives.
Filtered vector search
Nearest overall and nearest among eligible documents are different questions.
Result diversity
A useful list needs more than individually relevant documents.
Carbonell & Goldstein, The Use of MMR, Diversity-Based Reranking (SIGIR 1998)
Late interaction
Move one token and watch pooling and token-wise matching disagree.
Results from the literature, made draggable.
Hubness
Why a few documents in your vector database are everyone's nearest neighbour.
Radovanović, Nanopoulos & Ivanović, Hubs in Space (JMLR 2010)
Single-vector limits
Some patterns of relevance no single vector per document can express, however good the model.
Weller, Boratko, Naim & Lee, On the Theoretical Limitations of Embedding-Based Retrieval (2025)
Each page isolates one idea from the interpretability and retrieval essay on authored data, with the published results it rests on quoted and linked; none runs a model or reproduces a paper.
Activation patching
An active component is not necessarily a component that changes the answer.
Behavioural tests
Agreement on a few behaviours does not identify an algorithm.
Soft term matching
What changes when a match can be a synonym, or the wrong sense of a word?
Sparse readouts
Keep the vectors fixed. Change what you do with them.
Feature steering
A feature label is a hypothesis about what your edit will do.
Model editing
Suppress one signal and inspect both the success and the collateral failure.
Feature stability
Different dictionaries can reconstruct the same point.