Report series: Ixnos Research Reports Report number: IRR-003 This paper proposes a geometric framework for reasoning about training data in generative AI systems. Rather than treating training corpora as static collections of documents, the framework models them as density fields over a semantic point cloud in embedding space, where each training fragment occupies a location and the global distribution of fragments defines the corpus geometry. The Semantic Void Hypothesis is introduced: hallucination risk for a query is hypothesised to increase with distance from populated regions of the training data geometry and decrease with local fragment density. A concrete operationalisation is provided specifying the embedding function, density estimator, and distance metric required to compute a corpus-coverage risk proxy. A preliminary synthetic validation experiment demonstrates feasibility of the scoring framework, showing strong separation between dense and void query regions using a small constructed corpus. The results establish conceptual plausibility and computational feasibility but do not constitute validation on production-scale corpora or real model outputs. The framework is proposed as a data-centric hypothesis linking training data geometry to model reliability.
Antalouzia Bianka Alexandra Elliott (Thu,) studied this question.