From Scalars to Tensors: Declared Losses Recover Epistemic Distinctions That Neutrosophic Scalars Cannot Express

Computer Science > Artificial Intelligence [Submitted on 10 Mar 2026] From Scalars to Tensors: Declared Losses Recover Epistemic Distinctions That Neutrosophic Scalars Cannot Express Tony Mason Leyva-Vázquez and Smarandache (2025) demonstrated that neutrosophic T/I/F evaluation, where Truth, Indeterminacy, and Falsity are independent dimensions not constrained to sum to 1.0, which reveals "hyper-truth"' (T+I+F > 1.0) in 35% of complex epistemic cases evaluated by LLMs. We extend their work in two directions. First, we replicate and extend their experiment across five model families from five vendors (Anthropic, Meta, DeepSeek, Alibaba, Mistral), finding hyper-truth in 84% of unconstrained evaluations, which confirms the phenomenon is cross-vendor under our prompt protocol. Second, and more significantly, we identify a limitation of scalar T/I/F that their framework cannot address: models adopting an `"Absorption" position (T=0, I=1, F=0) produce identical scalar outputs for fundamentally different epistemic situations (paradox, ignorance, contingency), collapsing the very distinctions neutrosophic logic was designed to preserve. We demonstrate that extending the evaluation to include declared losses (structured descriptions of what the model cannot evaluate and why) substantially recovers these distinctions. Models producing identical scalars for paradox and ignorance produce nearly disjoint loss vocabularies (Jaccard similarity < 0.10 on loss description keywords), with domain-specific, severity-rated loss declarations that differentiate the nature of their uncertainty. This suggests that scalar T/I/F is a necessary but insufficient representation of epistemic state, and that tensor-structured output (scalars + losses) provides a more faithful model of LLM epistemic capabilities. Subjects: Artificial Intelligence (cs.AI); Software Engineering (cs.SE) Cite as: arXiv:2604.09602 [cs.AI]   (or arXiv:2604.09602v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.09602 Focus to learn more Submission history From: Tony Mason [view email] [v1] Tue, 10 Mar 2026 01:02:26 UTC (412 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.SE References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)