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

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 LLMs, leaving their geometric validity unexplored. This paper proposes a method to induce circular emotion representations within LLM 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.