From Scalars to Tensors: Declared Losses Recover Epistemic Distinctions That Neutrosophic Scalars Cannot Express
Summary: arXiv:2604.09602v1 Announce Type: new
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, reveals “hyper-truth” (T+I+F > 1.0) in 35% of complex epistemic cases evaluated by LLMs. We extend their work in two directions.
Key Findings
- We replicate and extend their experiment across five model families from five vendors: Anthropic, Meta, DeepSeek, Alibaba, and Mistral.
- Our findings reveal hyper-truth in 84% of unconstrained evaluations, confirming that this phenomenon is cross-vendor under our prompt protocol.
Identifying Limitations
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, such as paradox, ignorance, and contingency. This collapse undermines the very distinctions that neutrosophic logic was designed to preserve.
Extending the Evaluation
Our research demonstrates that extending the evaluation to include declared losses—structured descriptions of what the model cannot evaluate and why—substantially recovers these distinctions. For instance, models that yield identical scalars for paradox and ignorance produce nearly disjoint loss vocabularies, with a Jaccard similarity of less than 0.10 on loss description keywords.
Domain-Specific Insights
Additionally, we observe that these models can provide domain-specific, severity-rated loss declarations. Such declarations significantly differentiate the nature of their uncertainties, suggesting that scalar T/I/F, while necessary, is an insufficient representation of the epistemic state.
The Case for Tensor-Structured Output
We conclude that tensor-structured output—which combines scalars and losses—provides a more faithful model of LLM epistemic capabilities. This approach not only addresses the limitations of the scalar framework but also enhances our understanding of how language models perceive and articulate uncertainty.
Future Directions
As AI systems continue to evolve, understanding the nuances of their epistemic evaluations will become increasingly crucial. Our findings pave the way for future research aimed at refining LLM evaluation frameworks, ensuring that the complexities of human-like reasoning are better represented and understood.
In summary, the integration of declared losses into the evaluation of LLMs not only enhances the fidelity of their epistemic representations but also opens up new avenues for research and application in artificial intelligence.