From Words to Paragraphs: Modeling Sentiment Dynamics in Notes from Underground with GPT-4 by Differential Equations Via Quantile Regression Analysis

Volkan Duran, Iskander Akhmetov, Elman Hazar, Alexander Gelbukh, Ezgi Kaya


This study examines how the sentimentvalues in the first part of the book entitled as“Underground” of Fyodor Dostoevsky’s ”Notes fromUnderground” change from words to sentences toparagraphs. Using the GPT-4 language model,we conducted a descriptive analysis of standardizedsentiment values and calculated cumulative binnedvalues of the sentiment trajectories over the text. Wethen created differential equation models to model thesentiment tones using quantile regression analysis. Weshow that binned values can reveal a more dynamicand potentially chaotic structure when applied to thecumulative sum of sentiments for word, sentence, andparagraph levels. We model differential equationsderived for word, sentence, and paragraph levels viaquantile regression. They demonstrate how the rateand acceleration of sentiment change are influenced bytheir current state and rate of change. In conclusion,this study’s findings are important for enhancing thecapabilities of AI-driven chatbots in sentiment analysis,particularly in dissecting and understanding the layeredemotional landscapes of literary works.


Sentiment analysis, differential equations, GPT-4, curve fitting, quantile regression analysis

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