Entity-Level Knowledgeability Scores

• Entity-level knowledgeability scores are quantitative metrics that assess an entity’s grasp of specific topics by aggregating learning signals, text mentions, and behavioral data.
• They are computed through methods such as topic modeling, distributed representations, graph neural networks, and probabilistic approaches to yield interpretable, context-sensitive measures.
• These scores support practical applications including personalized learning, expert recommendation, and factual evaluation of language models while addressing calibration and scalability challenges.

Entity-level knowledgeability scores are quantitative metrics designed to assess the degree to which an individual, entity, or system possesses and retains knowledge about specific topics or knowledge points. These scores are foundational for personalized learning, expert identification, knowledge base completion, and the factual reliability evaluation of LLMs. Across applications, entity-level knowledgeability scoring frameworks typically aim to transform granular observed signals (learning activities, text mentions, behavioral data, or model predictions) into interpretable, context-sensitive measures of knowledge possession at the entity granularity. Methodologies range from aggregating topic modeling output in human knowledge tracking, to distributed representations in NLP, to graph-based and probabilistic modeling in LLM analysis.

1. Fundamental Methodologies for Quantifying Knowledgeability

The core methodological approach to computing entity-level knowledgeability scores combines (i) representation or extraction of relevant knowledge signals, (ii) aggregation or pooling over modalities and contexts, and (iii) normalization and decay modeling.

A prototypical example is the knowledge model for evaluating human knowledge workers (Liu, 2016), which records every learning event (reading, studying, or reviewing textual content) and converts the content into text via OCR, speech, or digital extraction. Topic models such as Latent Dirichlet Allocation (LDA) are then used to infer the share of each knowledge point in every session:

$$\varphi_{ij} = \frac{\pi_j \cdot p(t_i | \theta_j)}{\sum_{j=1}^k \sum_{i=1}^m (\pi_j \cdot p(t_i | \theta_j))}$$

where %%%%1%%%% is the weight for topic $j$, $p(t_i|\theta_j)$ is the probability of term $t_i$ under topic $j$, and only the $m$ highest-probability terms per topic contribute. For each knowledge point $k_i$, the cumulative familiarity is then:

$F_{k_i}(t) = \sum_{j=1}^{n} d_j \xi_{ij} b_j$

with $d_j$ the session duration, $\xi_{ij}$ the topic model-derived share, and $b_j$ a memory retention factor governed by Ebbinghaus' forgetting curve.

Beyond human tracking, LLM and KB-oriented frameworks adapt these principles via distributed representations of entities (Clark et al., 2016), probabilistic metrics of answerability (Dong et al., 2023), or via tensor and matrix factorization to represent latent expertise or skill vectors (Huang et al., 2018, Kuang et al., 19 Aug 2025).

2. Distributed Representations and Entity-level Signal Aggregation

Entity-level knowledgeability must reflect richer information than local observations alone; it should synthesize evidence across mentions, relationships, and contexts.

In coreference and entity typing systems, distributed and pooled representations over mention clusters or type assignments are central (Clark et al., 2016, Yaghoobzadeh et al., 2017):

• Cluster-level encodings pool all mention-pair representations, using

$r_c(c_i, c_j)_k = \max\{R_m(c_i,c_j)_{k, :}\}$

and averaging to capture both maximal and typical evidence.

• Fine-grained entity typing models (e.g., FIGMENT) combine global embedding-based representations (entity-contextualized distributed vectors) with context-sensitive MLPs and multi-instance aggregation:

$S_{JM}(e, t) = S_{GM}(e, t) + S_{CM}(e, t)$

with $S_{GM}$ the global score (entity embedding + MLP), $S_{CM}$ the aggregated (often mean or max-pooled) context-level scores.

Multi-level entity representations—combining entity, word, and character features—further enable robustness for sparse data and rare entities (Yaghoobzadeh et al., 2017).

Mechanisms like attention-based aggregation, e.g., MIML-ATT (Yaghoobzadeh et al., 2017), help weight contexts by informativeness for each type or knowledge aspect.

3. Statistical, Graph-based, and Probabilistic Models

Recent advances extend entity-level knowledgeability scoring to large-scale models and systems by leveraging statistical, graph-based, and cognitive diagnosis principles.

Statistical Measures for LLM Evaluation

KaRR (Knowledge Assessment Risk Ratio) (Dong et al., 2023) statistically quantifies the reliability of factual generation for a given entity-relation-object tuple across prompt variations:

$$\text{KaRR}_r(s, r, o) = \frac{P(o|s, r)}{P(o|s)} \qquad \text{KaRR}_s(s, r, o) = \frac{P(o|s, r)}{P(o|r)}$$

The aggregated KaRR score is the geometric mean, reflecting both subject and relation conditioning. Large evaluation suites (nearly one million entities, 600 relations) enable robust estimation, and KaRR correlates with human expert judgment (Kendall's $\tau=0.43$).

Graph and Homophily-based Scoring

Graph-based frameworks map knowledge into an entity–relation graph, where entity-level scores are computed by:

$$\mathcal{K}(v_i) = \frac{1}{|T(v_i)|} \sum_{(s,d,r)\in T(v_i)} \mathcal{K}(s,d,r)$$

with $\mathcal{K}(s,d,r)$ a triplet-level indicator (e.g., True/False on knowledge check) (Sahu et al., 28 Sep 2025). Homophily is then operationalized as:

$$\mathcal{H}(v_i) = 1 - \frac{1}{|\mathcal{N}(v_i)|} \sum_{j\in \mathcal{N}(v_i)} |\mathcal{K}(v_i)-\mathcal{K}(v_j)|$$

Graph neural networks can propagate and predict knowledgeability scores, enabling active sampling for prioritizing knowledge injection and multi-hop retrieval.

Cognitive Skill-level Diagnosis

Skill-level cognitive diagnosis decomposes model outputs into fine-grained knowledge concept mastery. Given a Q-matrix $Q$, cognitive diagnosis factorizes a response matrix $X$:

$X \approx E U, \quad Q \approx E V$

with $E$ encoding the relationship between questions and latent skills, $U$ model skill profiles, and $V$ the mapping to explicitly annotated financial (or other domain) concepts. These enable interpretable, component-level knowledgeability scores for each entity/model (Kuang et al., 19 Aug 2025).

4. Applications and Empirical Findings

Entity-level knowledgeability scores have been utilized in:

• Knowledge worker assessment and personalized learning: tracking individual research concentrations, identifying knowledge gaps, and highlighting interdisciplinary overlap (Liu, 2016).
• Expert recommendation: using tensor factorization and hierarchical regularization to derive user–topic expertise maps in collaborative Q&A systems (Huang et al., 2018).
• Enterprise reputation/ranking: Bayesian models (beta distribution) take positive and negative feedback to produce entity-level credibility that adapts to dynamic contexts and collusion-resilient evidence streams (Mahmood et al., 2020).
• Automated factual evaluation: in summarization, metrics such as entity-level F1, precision-source, and recall-target quantify the factual knowledgeability and hallucination rate of text generated by neural models (Nan et al., 2021, Yeh et al., 17 Feb 2025).
• LLM knowledge auditing: KaRR and entity-level homophily provide rigorous, prompt- and context-agnostic measurement of model knowledge and guide efficient knowledge injection (Dong et al., 2023, Sahu et al., 28 Sep 2025).
• Fine-grained model diagnostics: Cognitive diagnosis models (FinCDM) reveal domain-specific knowledge and hidden gaps in LLMs (CPA-level finance, tax, regulatory compliance) that are not visible from standard aggregate accuracy (Kuang et al., 19 Aug 2025).

5. Normalization, Calibration, and Practical Implementation Challenges

Normalization for entity-level scoring is frequently necessary:

• Knowledge points may vary in complexity; scores must be normalized to avoid over- or under-valuing simple facts versus advanced topics (Liu, 2016).
• Temporal decay (Ebbinghaus' curve) accounts for retention loss between learning and assessment (Liu, 2016).
• For LLM and factual reliability, prompt selection and answer distribution artifacts must be controlled (e.g., by measuring KL divergence between prompt-only and actual answer distributions) (Cao et al., 2021).
• Aggregation of token-level or span-level uncertainty must be carefully mapped to entity-level confidence and adjusted for linguistic factors as evidenced by variable hallucination risks (Yeh et al., 17 Feb 2025).

Implementation in practice must also address:

• Scalability of probabilistic or neural computations for millions of entities or facts (Dong et al., 2023).
• Privacy concerns related to personal learning histories (Liu, 2016).
• Disentangling observable versus unobservable learning activities.
• Robustness to annotation quality, entity linking noise, and the dynamic updating of skill/concept mappings.

6. Limitations and Future Research Directions

Several open challenges persist:

• Moving beyond atomic fact evaluation to capture multi-hop, compositional, or relational knowledge remains underexplored (Dong et al., 2023, Sahu et al., 28 Sep 2025).
• The definition of "knowledgeability" must be carefully tailored to the application domain—the same score may signify memorization in one context and robust inferential ability in another.
• Open benchmarking datasets (e.g., HalluEntity (Yeh et al., 17 Feb 2025), CPA-KQA (Kuang et al., 19 Aug 2025)) and diagnostic frameworks are essential for community advances, but their design and coverage strongly influence diagnostic power and generalization.
• Adaptive, context-aware methods (attention, uncertainty propagation, cognitive modeling) show promise for improved granularity and interpretability, but require further investigation regarding calibration and domain transferability.

7. Summary Table of Methodological Paradigms

Approach	Key Metric/Score	Domain/Application
Topic Model Aggregation	Familiarity ($F_{ki}(t)$)	Human knowledge quantification
Distributed Representation	Pooled entity vector	NLP (typing, coreference)
Bayesian Probability	$E(v)=\frac{p+1}{p+n+2}$	Reputation, expert ranking
KaRR Statistical Ratio	KaRR($s, r, o$)	LLM knowledge assessment
Graph Aggregation & GNN	$\mathcal{K}(v_i)$	LLM knowledge homophily, QA
Cognitive Diagnosis (FinCDM)	Skill mastery matrix	Financial/multiskill model eval

These frameworks collectively define and operationalize entity-level knowledgeability scores, enabling quantitative, interpretable, and context-sensitive measurement of knowledge in individuals, automated systems, and LLMs.