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

TL;DR

This paper demonstrates that extending scalar evaluations with structured loss descriptions better captures the epistemic distinctions in LLMs, addressing limitations of neutrosophic scalar logic.

Contribution

It extends neutrosophic evaluation to include tensor-structured outputs with loss vocabularies, improving epistemic state representation in LLMs.

Findings

Hyper-truth phenomenon confirmed across multiple vendors.

Scalar T/I/F cannot distinguish certain epistemic states.

Loss vocabularies nearly disjoint for paradox and ignorance cases.

Abstract

Leyva-V\'azquez 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.