Retrievability¶
A document-centric information-retrieval measure of how broadly and prominently a fixed system exposes an information object across a declared population of queries.
Core Idea¶
Retrievability is a document-centric property induced by an information-retrieval system: it measures how many, or how much probability mass of, a declared population of queries expose a particular information object at ranks a user is willing to inspect. Azzopardi and Vinay introduced it to evaluate the access that a retrieval system affords to individual documents and to the collection as a whole, complementing the usual query-centric measures of relevance effectiveness.
For a document \(d\), query set \(Q\), query weight \(o_q\), rank \(k_{dq}\) of \(d\) for query \(q\), rank cutoff \(c\), and a rank utility function \(f\), the general score is.
Scope of Application¶
The home scope is evaluation and auditing of ranked information-retrieval systems. It applies to web and enterprise search, digital libraries, web archives, legal and patent retrieval, news archives, scholarly search, and integrated search over publications, datasets, or other record types. The unit need not be a conventional text page, but it must be an object that a stable retrieval pipeline ranks for queries.
The construct is especially useful when relevance judgments are scarce or the question is collection exposure rather than average topical effectiveness.
Clarity¶
A complete retrievability result answers: retrievability of which object version, in which collection and index, under which query distribution, retrieval model, weights, rank utility, and cutoff? These are not optional reproducibility details. They define the property.
The cleanest diagnostic contrasts two axes:
- Fix a query \(q\) and compare documents: this is a ranked result and may support query-centric effectiveness evaluation.
- Fix a document \(d\) and aggregate over queries: this is document retrievability.
Manages Complexity¶
A collection with \(N\) documents and \(M\) queries produces up to \(N\times M\) ranks. Retrievability compresses each document's column of ranks into one score, and then compresses the \(N\) scores into a distribution that can be compared across systems. This makes otherwise invisible exposure structure tractable: inaccessible tails, overexposed domains, document-length effects, source bias, temporal-version bias, and parameter sensitivity.
Abstract Reasoning¶
The formula licenses precise counterfactuals. Holding the evaluation frame fixed, lowering an object's ranks increases its retrievability under a top-heavy utility. Increasing \(c\) weakly increases every binary score, but may change relative order and the apparent inequality of the collection. Upweighting frequent queries makes the score closer to expected exposure for observed users; equal weighting instead asks about breadth across the chosen query vocabulary.
Knowledge Transfer¶
The structure transfers within information access without metaphor. A web page, patent, archived page version, dataset record, and scholarly article each becomes the node; candidate queries become sources; the retrieval model supplies the friction field; rank supplies access cost; \(c\) supplies the tolerance horizon; and \(r(d)\) measures the weighted query catchment. This mapping is why the specific live parent Access Catchment is more accurate than a generic “measurement” parent.
Relationships to Other Abstractions¶
Current abstraction Retrievability Domain-specific
Parents (1) — more general patterns this builds on
-
Retrievability is a kind of Access Catchment Prime
Retrievability strictly instantiates prime:access_catchment.
Hierarchy path (1) — routes to 1 parentless root
- Retrievability → Access Catchment → Threshold
Neighborhood in Abstraction Space¶
Retrievability sits in a sparse region of the domain-specific corpus (84th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (1565 abstractions)
Nearest neighbors
- Extended Boolean model — 0.82
- Postings List — 0.81
- Retrieval-augmented generation — 0.80
- Inverted index — 0.80
- Relevance (information retrieval) — 0.80
Computed from structural-signature embeddings · 2026-09-08