Information Diversity Score (IDS) Overview

Updated 6 July 2026

Information Diversity Score (IDS) is a versatile metric that quantifies heterogeneity in information systems based on structural, not just cardinal, characteristics.
It is applied in multilingual NLP to assess linguistic coverage, in forecasting to gauge information overlap, and in digital libraries to measure metadata evenness.
By leveraging domain-specific primitives, IDS provides interpretable diagnostics and prescriptive insights for improving diversity representations.

Searching arXiv for the listed IDS-related papers and closely related work to ground the article in current research. I’m checking arXiv for the specific IDS papers and neighboring literature. Information Diversity Score (IDS) is not a single universally standardized quantity across arXiv literature. The term has been used for several distinct constructs that share a common objective—quantifying heterogeneity, coverage, or non-overlap in an information-bearing system—but differ substantially in ontology, mathematical form, and application domain. In multilingual natural language processing, IDS denotes a reference-based measure of structural linguistic coverage for multilingual data sets, defined from a min–max Jaccard comparison between a target set and a linguistically motivated reference sample (Samardzic et al., 2024). In probability aggregation, IDS denotes the complement of information overlap among forecasters in a Gaussian partial-information model, with direct implications for optimal extremization of pooled forecasts (Satopää et al., 2014). In digital libraries, IDS denotes a normalized diversity measure derived from Shannon-based Hill numbers and richness, used to characterize lexical, author, subject, or metadata diversity (Carrasco et al., 2023). Related but not identical uses include an ontology-based conceptual diversity score for text (Phd et al., 2023) and the Information-Vendi score, which measures prompt-induced diversity in conditional generative models through kernel-based mutual information (Jalali et al., 2024). Across these settings, the unifying idea is that diversity is treated as informational structure rather than as a simple count of items.

1. Terminological scope and domain-specific senses

The expression “Information Diversity Score” appears in multiple, largely independent research traditions. In multilingual NLP, the score was introduced as a transparent method for comparing the linguistic diversity of multilingual data sets against a reference sample, motivated by the observation that language counts and language-family counts do not capture structural properties of languages (Samardzic et al., 2024). In this usage, IDS is intended to diagnose omissions in typological coverage, including the under-representation of structurally extreme language types such as polysynthetic languages.

In forecast aggregation, the term arises in a probabilistic model where multiple experts observe partially overlapping information sets. There, IDS is defined from the degree of overlap among those sets and quantifies cognitive or informational heterogeneity across forecasters (Satopää et al., 2014). This version is not a dataset-diversity metric; it is a latent overlap parameter with operational consequences for aggregation.

In digital-library research, IDS refers to a normalized diversity quantity built from Shannon diversity and richness, intended to measure how evenly categories such as token types, authors, subject headings, or RDF classes are represented (Carrasco et al., 2023). This use is close to classical ecological diversity indices, but adapted to information objects and metadata.

A further related use appears in semantic text analysis, where IDS is defined as the Shannon entropy of an ontology-expanded concept distribution derived from WordNet hyponymy (Phd et al., 2023). In prompt-conditioned generative modeling, the “Information-Vendi” score measures the mutual-information-like component of diversity attributable to prompts rather than to internal model stochasticity (Jalali et al., 2024). Although not the same object, it belongs to the same broader family of information-theoretic diversity measures.

This multiplicity of definitions implies that IDS is best treated as a polysemous technical label rather than a single metric. The precise meaning depends on the object whose diversity is being assessed: languages, expert information sets, metadata categories, conceptual ontologies, or prompt-conditioned outputs.

2. IDS in multilingual NLP data sets

In multilingual NLP, IDS is a reference-based measure of how well a multilingual data set $D$ covers the space of linguistic diversity represented by a selected reference sample $\mathcal{R}$ (Samardzic et al., 2024). The goal is to move beyond raw language counts and instead quantify structural breadth. The motivating claim is that a data set with many languages can still be typologically narrow if those languages occupy similar regions of linguistic space, whereas a smaller set spanning distinct structural types may be more diverse.

Languages are represented as feature sets assembled from two complementary sources. The first source comprises expert typological features from URIEL/lang2vec, chiefly drawn from WALS. Each language is encoded by 103 binary syntactic features and 26 morphosyntactic features recast as numerical or binary values. Missing values are imputed via nearest-neighbour in typological space. The second source is text-based: mean word length (MWL) in Unicode NFC “user-perceived characters,” used as an automatically extractable proxy that correlates highly with an independent WALS-based morphological complexity score, with reported Spearman $\rho = 0.69$ (Samardzic et al., 2024). The paper notes that MWL captures the broad isolating $\Leftrightarrow$ polysynthetic continuum with only 500–2 000 tokens per language.

Given feature–value count vectors $F(D)$ and $F(\mathcal{R})$ , the method computes a min–max Jaccard similarity. If $a_j$ and $b_j$ denote the number of languages in $D$ and $\mathcal{R}$ , respectively, that realize feature-value $\mathcal{R}$ 0, the similarity is

$\mathcal{R}$ 1

Because the target and reference may differ in size, the smaller sample is scaled by

$\mathcal{R}$ 2

The Information Diversity Score is then defined as

$\mathcal{R}$ 3

Low IDS indicates that the target approximates the reference distribution well; high IDS indicates substantial omissions or over-selection of feature values (Samardzic et al., 2024).

A central property of this formulation is interpretability. Because the score is computed from feature-value histograms, one can inspect exactly which linguistic types are missing. The paper emphasizes that per-feature inspection can reveal under-represented MWL bins or missing word-order patterns, and suggests that diversity can be improved by removing surplus languages from over-represented bins and adding languages from under-populated bins. If MWL $\mathcal{R}$ 4 is absent, the recommended remedy is to seek additional polysynthetic or synthetic languages (Samardzic et al., 2024).

3. Empirical behavior in multilingual benchmark analysis

The multilingual-NLP IDS was applied to several widely used multilingual resources, including UD, Bible100, mBERT, XTREME, XGLUE, XNLI, XCOPA, TyDiQA, and XQuAD (Samardzic et al., 2024). The reported case-study summaries separate syntactic diversity from text-based morphological diversity, producing distinct Jaccard similarities and corresponding IDS values.

Data set	$\mathcal{R}$ 5 / IDS $\mathcal{R}$ 6	$\mathcal{R}$ 7 / IDS $\mathcal{R}$ 8
Universal Dependencies (UD)	0.736 / 0.264	0.650 / 0.350
Bible100	0.811 / 0.189	0.534 / 0.466
mBERT	0.710 / 0.290	0.603 / 0.397
XTREME	0.775 / 0.225	0.457 / 0.543

By syntactic IDS, the ranking reported is Bible100 $\mathcal{R}$ 9 XTREME $\rho = 0.69$ 0 UD $\rho = 0.69$ 1 mBERT, where lower is better. By morphological IDS, the ranking is UD $\rho = 0.69$ 2 mBERT $\rho = 0.69$ 3 Bible100 $\rho = 0.69$ 4 XTREME (Samardzic et al., 2024). These results show that performance depends on which aspect of linguistic structure is measured.

The paper explicitly states that adding more languages or more language families does not guarantee structural diversity. mBERT, despite containing 97 languages, does not necessarily dominate on IDS. The MWL-based analysis further indicates that morphologically rich and polysynthetic languages remain almost entirely missing from popular benchmarks, and the abstract states that “(poly)synthetic languages are missing in almost all of them” (Samardzic et al., 2024). This suggests that benchmark construction practices can systematically neglect precisely those structural extremes that are likely to stress-test multilingual models.

The practical workflow for computing IDS on a new multilingual data set is procedural and explicit: select a maximally diverse reference such as the WALS 100-language sample plus TeDDi text data; retrieve URIEL/lang2vec features for each language; compute MWL and bin it; form combined feature-value count vectors; scale the smaller vector; compute the min–max Jaccard similarity; and finally report $\rho = 0.69$ 5 (Samardzic et al., 2024). In this formulation, IDS is both diagnostic and prescriptive, because the mismatch with the reference directly identifies what kinds of languages should be added.

4. IDS as information non-overlap in probability forecasting

In the forecasting literature, IDS is defined in a very different way. Under the Gaussian partial-information model, each forecaster $\rho = 0.69$ 6 observes a Gaussian sum $\rho = 0.69$ 7 over a measurable subset $\rho = 0.69$ 8, where $\rho = 0.69$ 9 is the information amount and $\Leftrightarrow$ 0 is the pairwise overlap (Satopää et al., 2014). These quantities determine the covariance structure of the latent true signal and the forecasters’ observed signals.

In the compound-symmetric special case, all forecasters use the same amount of information, $\Leftrightarrow$ 1, and all pairs share the same overlap fraction, $\Leftrightarrow$ 2. The Information Diversity Score is then defined as

$\Leftrightarrow$ 3

In the more general unequal- $\Leftrightarrow$ 4 case, the paper summarizes an average normalized overlap

$\Leftrightarrow$ 5

so that IDS lies in $\Leftrightarrow$ 6, with $\Leftrightarrow$ 7 if all information sets coincide and $\Leftrightarrow$ 8 if they are mutually disjoint (Satopää et al., 2014).

This IDS is operational because it governs the appropriate degree of extremization when aggregating probability forecasts. In the symmetric model, the revealed aggregator in probit space is

$\Leftrightarrow$ 9

with extremization factor

$F(D)$ 0

As IDS approaches 0, $F(D)$ 1, so no extremization is required. As IDS approaches 1, $F(D)$ 2, corresponding to much stronger movement toward an extreme pooled probability (Satopää et al., 2014). In this setting, IDS interpolates between simple averaging and vote-like pooling.

Estimation proceeds by transforming observed forecasts $F(D)$ 3 into probit scores $F(D)$ 4. The model provides closed forms for $F(D)$ 5 and $F(D)$ 6, enabling either method-of-moments estimation in the symmetric case or likelihood-based estimation of the covariance matrix subject to coherence constraints such as $F(D)$ 7 and $F(D)$ 8 (Satopää et al., 2014). Thus IDS here is a latent structural parameter of information overlap rather than a diversity statistic on observed categorical frequencies.

5. IDS in digital libraries and metadata analysis

In digital-library research, IDS is rooted in classical diversity indices from ecology and information theory. A chosen feature space—such as vocabulary, authors, subject headings, RDF classes, or RDF properties—is partitioned into $F(D)$ 9 categories, with counts $F(\mathcal{R})$ 0, total sample size $F(\mathcal{R})$ 1, and relative abundances $F(\mathcal{R})$ 2 (Carrasco et al., 2023). Shannon entropy, Simpson concentration, Hill numbers, richness, and evenness are then computed in the standard way.

The specific “Information Diversity Score” described for metadata coverage is the diversity–richness ratio

$F(\mathcal{R})$ 3

where $F(\mathcal{R})$ 4 is the Shannon diversity and $F(\mathcal{R})$ 5 is richness (Carrasco et al., 2023). Because $F(\mathcal{R})$ 6, this IDS lies in $F(\mathcal{R})$ 7 and behaves as a normalized evenness indicator: low values indicate concentration in a small subset of categories despite large richness, whereas high values indicate broader and more even usage of the available category inventory.

For lexical diversity, the paper additionally describes an extrapolated asymptotic diversity based on a three-parameter saturating model,

$F(\mathcal{R})$ 8

where $F(\mathcal{R})$ 9 is the asymptotic diversity and $a_j$ 0 control the shape (Carrasco et al., 2023). Fitting this model to observed $a_j$ 1 yields a sample-size-robust lexical diversity estimate. This is described as an “extrapolated IDS” in the guide.

Several empirical illustrations are reported. For author diversity in MARC catalogs at 2020, approximate values are LoC: richness $a_j$ 2, Shannon diversity $a_j$ 3, IDS $a_j$ 4; UGent: $a_j$ 5, $a_j$ 6, $a_j$ 7; and BVC: $a_j$ 8, $a_j$ 9, $b_j$ 0 (Carrasco et al., 2023). For linked open data, distinct class-IDS and property-IDS values reveal different schema-adoption strategies. The paper also reports that the extrapolated- $b_j$ 1 lexical IDS is nearly uncorrelated with sample size, with Pearson $b_j$ 2 across 400 Lope de Vega works (Carrasco et al., 2023). In this tradition, IDS is explicitly meant to support fair comparisons across collections, periods, or repositories by separating variability from sheer abundance.

Two additional arXiv uses are closely related to the IDS label, though they are not direct equivalents of the multilingual or forecasting definitions.

In ontology-based semantic analysis, Dönmez and Haklıdır define IDS—also called the Conceptual Diversity Score—as the Shannon entropy of a concept distribution obtained by expanding literal noun mentions through WordNet hyponymy (Phd et al., 2023). If a text invokes concepts $b_j$ 3 with expanded frequencies $b_j$ 4, then

$b_j$ 5

The score ranges from $b_j$ 6 to $b_j$ 7, where $b_j$ 8 is the size of the WordNet concept inventory. The examples given are deliberately contrastive: “He discovered an unknown entity.” yields $b_j$ 9, while “The endoplasmic reticulum forms a series of flattened sacs within the cytoplasm of eukaryotic cells.” yields $D$ 0 (Phd et al., 2023). This formulation treats conceptual generality as high diversity because a general term inherits a wide ontology subtree.

In prompt-conditioned generative modeling, the Information-Vendi score is defined as

$D$ 1

where $D$ 2 is a kernel-based mutual-information term in a decomposition of matrix-based Rényi entropy: $D$ 3 Here $D$ 4 corresponds to Conditional-Vendi and measures model-induced internal diversity, while $D$ 5 measures prompt-induced diversity, that is, the statistical dependence of outputs on prompts (Jalali et al., 2024). The paper emphasizes that unconditional diversity metrics cannot distinguish prompt variety from model variety, and shows empirically that the two decomposed scores track different phenomena across text-to-image, text-to-video, and image-captioning systems.

These related uses reinforce a broader pattern: “information diversity” is often formalized through entropy or overlap, but what counts as an information-bearing unit differs sharply—ontology concepts, kernelized samples, or structural features of languages. This suggests that IDS is best understood as a family resemblance term for diversity measures grounded in information structure.

7. Interpretation, comparison, and recurring methodological themes

Across domains, IDS-like quantities share three recurring methodological commitments. First, they reject naive cardinality as a sufficient measure of diversity. Multilingual NLP rejects language counts alone (Samardzic et al., 2024); digital-library IDS rejects richness alone (Carrasco et al., 2023); forecasting IDS rejects the idea that disagreement is merely noise rather than a function of informational heterogeneity (Satopää et al., 2014).

Second, they are designed to be interpretable in terms of structural primitives. In multilingual NLP, the primitives are typological and text-derived feature values, enabling diagnosis of missing language types (Samardzic et al., 2024). In forecasting, the primitives are information amounts and overlaps, yielding an explicit extremization factor (Satopää et al., 2014). In digital libraries, the primitives are category abundances, so IDS can be read as normalized evenness (Carrasco et al., 2023). In conceptual diversity, the primitives are ontology nodes and inherited counts (Phd et al., 2023). In Information-Vendi, the primitives are kernel eigenvalues and prompt-conditioned decompositions of entropy (Jalali et al., 2024).

Third, these measures are typically bounded and comparative. Multilingual IDS lies in $D$ 6, with lower values indicating closer match to a reference (Samardzic et al., 2024). Forecasting IDS lies in $D$ 7, with higher values indicating greater non-overlap of information (Satopää et al., 2014). Digital-library IDS also lies in $D$ 8, with higher values indicating more even category use (Carrasco et al., 2023). Conceptual IDS is bounded by $D$ 9 (Phd et al., 2023). The directional interpretation is therefore domain-dependent and must not be transferred across formulations.

A common misconception is to assume that all IDS values are directly comparable because they share a name. They are not. The multilingual score is a distance from a reference distribution; the forecasting score is a complement of overlap; the digital-library score is a normalized Shannon diversity; the conceptual score is an ontology-expanded entropy; and the Information-Vendi score is an exponentiated mutual-information term. Another misconception is that diversity necessarily increases with the number of observed units. The multilingual case explicitly shows that more languages do not guarantee better structural coverage (Samardzic et al., 2024), and the digital-library formulation was introduced precisely because abundance is not equivalent to diversity (Carrasco et al., 2023).

Taken together, the IDS literature demonstrates that diversity assessment becomes technically meaningful when the underlying structure of the domain is made explicit. The substantive question is never only “how many items are present,” but rather “how are informational distinctions distributed, overlapped, or omitted.”