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Mathematical Framework for Characterizing Emotional Individuality in Large Language Models: Temperature Control, Fuzzy Entropy, and Persona-Based Diversity Analysis
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DOI：10.3390/math14071224.png)
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Abstract
En 中文
Evaluating emotional understanding in Large Language Models (LLMs) is challenging because assessments are subjective, ambiguous, multidimensional, and sensitive to controllable generation parameters. We developed a unified mathematical framework for characterizing LLM emotional individuality that integrates softmax sampling-temperature control (the decoding-time temperature parameter exposed by the API and typically used to modulate output randomness during token generation), fuzzy set theory with Shannon-type fuzzy entropy, and persona-based cognitive diversity analysis. We evaluated 36 API-accessible LLMs from seven major vendors on Japanese literary texts, using four personas each assigned a sampling temperature (T is an element of{0.1,0.4,0.7,0.9}), yielding 4227/4320 trial responses (97.8% coverage), of which 4067/4227 contained valid numeric emotion scores (96.2%). Temperature controllability varied approximately 25-fold (kappa M is an element of[0.039,0.982]) with both positive and negative temperature-variance relationships across models. Because each sampling temperature is deterministically assigned to a persona in our design, kappa M should be interpreted as an operational temperature-variance association across persona conditions rather than an isolated causal temperature effect. The model-level mean fuzzy entropy ranged from approximately 0.40 to 0.66, and the numerical stability consistency scores ranged from approximately 0.548 to 0.780. We also observed text-dependent structure, including genre-specific variation in the Interest-Sadness relationship. For practitioners, the framework is most directly useful as a benchmark-design and model-screening template for structured emotion-scoring tasks; its empirical conclusions remain limited to the present Japanese literary, text-only setting.
Keywords:
large language models
fuzzy entropy
softmax sampling temperature
emotional intelligence evaluation
mathematical modeling
persona-based assessment
cognitive diversity analysis
benchmarking
reproducibility
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