Since question says "how many", and model is theoretical, report the exact calculation. - Dyverse

Understanding the Context

Understanding “Theoretical Models” in Information Retrieval
A theoretical model in IR refers to a formalized framework or mathematical structure that models the process of retrieving relevant information from a collection without implementation constraints. These models define key assumptions about data (e.g., documents, queries), interactions (e.g., scoring mechanisms), and objectives (e.g., relevance).

Instead of counting physical implementations, we count conceptually distinct, well-defined theoretical frameworks that underpin IR theory.

Key Insights

Key Dimensions Defining Theoretical Models
To isolate theoretical models rigorously, we categorize IR theory across three dimensions:

1. Model Type (e.g., probabilistic, vector space, language models)
   
2. Scalability Dimension (single-document vs. large-scale information spaces)
   
3. Graph/theory Basis (logical formalisms, game theory, dynamical systems)

Step-by-Step Theoretical Calculation

We define a theoretical model as an intermediary or foundational framework, independent of practical implementations, incorporating at least one formal mathematical structure addressing core IR assumptions.

We analyze canonical IR theory from foundational papers and modern literature, identifying non-overlapping, primary models.

Final Thoughts

1. Probabilistic Retrieval Models

Rooted in classical IR theory, probabilistic models define relevance as conditional probability.

• Binary Independence Model (BIM) — single fundamental model assuming independence between terms.
  
• Bayesian Retrieval Model — extends BIM with full probabilistic calibration.
  
• Relevance Feedback (Smith’s Model) — iterative probability adjustment via user feedback.
  
• Normalized Ligma (NLigma) — modern probabilistic extension incorporating uncertainty distributions.
  
• Log-Linear Models — parametric families modeling項-query interactions via log-linear functions.

Count: 5 distinct theoretical variants.

2. Vector Space and Geometric Models

These models embed documents and queries in high-dimensional spaces for similarity computation.

• Vector Space Model (VSM) — classical linear algebra formulation.
  
• Latent Semantic Space Models (e.g., LSI, LSA) — dimensionality reduction over term-document matrices.
  
• Hypergeometric Optimal Model — probabilistic-to-geometric hybrid for graded relevance.
  
• Geometrical Graph Models — network-based retrieval using semantic graphs and shortest paths.
  
• Divergence-Based Models (e.g., Jensen-Shannon on Manifolds) — information geometry approaches.

Count: 5 theoretical geometric/hybrid models.