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

• URL: http://arxiv.org/abs/2606.29118v1
• Date: Sun, 28 Jun 2026 00:05:15 GMT
• Title: An Information-Geometric Justification for Composite Coherence in Event-Based Narrative Extraction
• Abstract summary: We study the composite metric $C=sqrtAcdot T$, where $A$ is the angular similarity of document embeddings and $T=1-d_mathrmJS$.<n>Experiments on four corpora, three embedding families, and three topic models are consistent with the framework.
• Score: 0.27074235008521247
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $C=\sqrt{A\cdot T}$, where $A$ is the angular similarity of document embeddings and $T=1-d_{\mathrm{JS}}$ 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 $\mathbb{S}^{d-1}\timesΔ^{K-1}$, 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 $d_\times$. Experiments on four corpora, three embedding families, and three topic models are consistent with the framework: the Fisher identity holds ($R\ge0.99$), the geometric mean tracks $d_\times$ 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.

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