# CHI: A Composite Hallucination Index Unifying Entity, Relation, and Quantity Dimensions for Summarization Evaluation

arXiv: https://arxiv.org/abs/2609.33343 · HTML: https://mlsanity.com/paper/2609.33343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
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- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [PEGASUS: Pre-training with Extracted Gap-sentences for Abstractive Summarization](https://mlsanity.com/paper/1912.08777/) (2019)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [SummEval: Re-evaluating Summarization Evaluation](https://mlsanity.com/paper/2007.12626/) (2020)
- [SummaC: Re-Visiting NLI-based Models for Inconsistency Detection in Summarization](https://mlsanity.com/paper/2111.09525/) (2021)
- [AlignScore: Evaluating Factual Consistency with a Unified Alignment Function](https://mlsanity.com/paper/2305.16739/) (2023)
- [MiniCheck: Efficient Fact-Checking of LLMs on Grounding Documents](https://mlsanity.com/paper/2404.10774/) (2024)
- [Long-form factuality in large language models](https://mlsanity.com/paper/2403.18802/) (2024)
- [Evaluating Factuality in Generation with Dependency-level Entailment](https://mlsanity.com/paper/2010.05478/) (2020)
- [LMUnit: Fine-grained Evaluation with Natural Language Unit Tests](https://mlsanity.com/paper/2412.13091/) (2024)
- [UniSumEval: Towards Unified, Fine-Grained, Multi-Dimensional Summarization Evaluation for LLMs](https://mlsanity.com/paper/2409.19898/) (2024)
- [AMRFact: Enhancing Summarization Factuality Evaluation with AMR-Driven Negative Samples Generation](https://mlsanity.com/paper/2311.09521/) (2023)
- [Evaluating Evaluation Metrics -- The Mirage of Hallucination Detection](https://mlsanity.com/paper/2504.18114/) (2025)
- [Evaluating Factual Consistency of Texts with Semantic Role Labeling](https://mlsanity.com/paper/2305.13309/) (2023)

## Abstract (arXiv)

Faithfulness evaluation of abstractive summaries remains an open challenge, with existing metrics addressing only isolated hallucination types: factual entity errors, relational inconsistencies, or numerical fabrications, without capturing their co-occurrence or interaction. We introduce CHI (Composite Hallucination Index), the first unified hallucination metric that decomposes faithfulness errors into three orthogonal dimensions: entity hallucination (EHI), relation hallucination (RHI*), and quantity hallucination (QHI). Each dimension employs a shared softmax-normalized architecture over Venn diagram-derived factors representing extractiveness, positive hallucination, over-focus, negative hallucination, and lost focus. The novel QHI component introduces tolerance-aware numerical matching with exact, epsilon, derived, and temporal comparison modes. We fuse the three dimensions via harmonic mean to produce a single composite score that penalizes weakness in any dimension. We validate CHI on 800 source articles spanning four domains (news, medical, legal, financial) with summaries from five generation systems. Empirical results demonstrate that: (i) the three dimensions are statistically orthogonal (mean rho = 0.148), confirming they capture distinct error types; (ii) CHI achieves the highest system-level correlation with human judgments (rho = 0.66, p = 0.006) on SummEval, outperforming ROUGE (rho = 0.53), EHI (rho = 0.58), and all individual components; and (iii) ablation studies confirm that all three dimensions contribute unique variance, with the full composite outperforming any individual component while providing decomposable error diagnostics unavailable from single-score baselines. CHI provides practitioners with a decomposable, interpretable, and efficient faithfulness metric suitable for both offline evaluation and online monitoring of summarization systems.