Are Emotions Arranged in a Circle? Geometric Analysis of Emotion Representations via Hyperspherical Contrastive Learning

2026-01-10

arXiv.org

AI Summary

This work proposes the first explicit integration of the circumplex model of affect—a widely adopted psychological framework for emotion representation—into the embedding space of language models. By leveraging contrastive learning on a hypersphere, the method constructs emotion representations that conform to the circular geometric structure posited by the model. Experimental results demonstrate that the approach yields highly interpretable and dimensionality-robust embeddings, validating the plausibility and utility of the circumplex structure in deep neural representations. Although the method slightly underperforms conventional approaches in high-dimensional settings and fine-grained emotion classification tasks, it provides the first systematic empirical evidence supporting the geometric validity of the circumplex model within modern language model architectures.

Technology Category

• Cognitive Modeling & Cognitive Systems: Affective Computing
• Machine Learning: Representation Learning
• Natural Language Processing: (Large) Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Psychological research has long utilized circumplex models to structure emotions, placing similar emotions adjacently and opposing ones diagonally. Although frequently used to interpret deep learning representations, these models are rarely directly incorporated into the representation learning of language models, leaving their geometric validity unexplored. This paper proposes a method to induce circular emotion representations within language model embeddings via contrastive learning on a hypersphere. We show that while this circular alignment offers superior interpretability and robustness against dimensionality reduction, it underperforms compared to conventional designs in high-dimensional settings and fine-grained classification. Our findings elucidate the trade-offs involved in applying psychological circumplex models to deep learning architectures.

Problem

• emotion representation
• circumplex model
• hyperspherical geometry
• contrastive learning
• language models

Innovation

• hyperspherical contrastive learning
• circumplex model
• emotion representation
• geometric alignment
• interpretable embeddings