# An Information-Geometric Justification for Composite Coherence in Event-Based Narrative Extraction

arXiv: https://arxiv.org/abs/2606.29118 · HTML: https://mlsanity.com/paper/2606.29118/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 60 references that are in the map.
- First posted on arXiv 28 Jun 2026.

## Builds on (most cited first, 14 of 14)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [SPECTER: Document-level Representation Learning using Citation-informed Transformers](https://mlsanity.com/paper/2004.07180/) (2020)
- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [SciRepEval: A Multi-Format Benchmark for Scientific Document Representations](https://mlsanity.com/paper/2211.13308/) (2022)
- [An elementary introduction to information geometry](https://mlsanity.com/paper/1808.08271/) (2018)
- [InfoLM: A New Metric to Evaluate Summarization & Data2Text Generation](https://mlsanity.com/paper/2112.01589/) (2021)
- [A Survey on Event-based News Narrative Extraction](https://mlsanity.com/paper/2302.08351/) (2023)
- [Growing Story Forest Online from Massive Breaking News](https://mlsanity.com/paper/1803.00189/) (2018)
- [Design guidelines for narrative maps in sensemaking tasks](https://mlsanity.com/paper/2112.12205/) (2021)
- [Narrative Trails: A Method for Coherent Storyline Extraction via Maximum Capacity Path Optimization](https://mlsanity.com/paper/2503.15681/) (2025)
- [Semantic Interaction for Narrative Map Sensemaking: An Insight-based Evaluation](https://mlsanity.com/paper/2603.29651/) (2026)
- [Semi-Supervised Image-Based Narrative Extraction: A Case Study with Historical Photographic Records](https://mlsanity.com/paper/2501.09884/) (2025)

## Abstract (arXiv)

Graph-based narrative extraction relies on a coherence function to score transitions between events, but the coherence metrics in current use are defined operationally and lack an information-theoretic foundation. We study the composite metric C=√A· T, where A is the angular similarity of document embeddings and T=1-dJS is a topic proximity from the Jensen-Shannon distance of soft memberships, and give it an information-geometric reading together with an axiomatic characterization of the geometric-mean combinator. On the product manifold mathbbSd-1×DeltaK-1, the negative log-coherence decomposes additively into an angular and a topic cost. Because the Riemannian metric tensor induced by the Jensen-Shannon distance on the simplex is proportional to the Fisher information matrix, the topic component is locally consistent with the Fisher-Rao metric singled out by Chentsov's theorem. Within the compensability spectrum of combinators, the geometric mean is the unique one consistent with four natural axioms (a boundary/veto condition, symmetry, log-additivity, normalization), and the construction motivates a proper product metric d_×. Experiments on four corpora, three embedding families, and three topic models are consistent with the framework: the Fisher identity holds (R≥0.99), the geometric mean tracks d_× closely (ρ=0.999), and a downstream LLM-as-judge check finds it is not dominated by any alternative combinator or single-channel baseline. Sweeping the spectrum, the bottleneck-coherence gap between extracted and random storylines splits into a symmetric component, maximized at the geometric mean across five corpora, and a displacement term; a cross-modal image-narrative case study reproduces the effect. These results justify the composite coherence metric and articulate when the geometric mean is the natural choice.