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

arXiv: https://arxiv.org/abs/2601.06575 · HTML: https://mlsanity.com/paper/2601.06575/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 53 references that are in the map.
- First posted on arXiv 10 Jan 2026.

## Builds on (most cited first, 21 of 21)

- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
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- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [GoEmotions: A Dataset of Fine-Grained Emotions](https://mlsanity.com/paper/2005.00547/) (2020)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Towards Understanding Grokking: An Effective Theory of Representation Learning](https://mlsanity.com/paper/2205.10343/) (2022)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
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- [Llama-Embed-Nemotron-8B: A Universal Text Embedding Model for Multilingual and Cross-Lingual Tasks](https://mlsanity.com/paper/2511.07025/) (2025)
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- [Emotions Where Art Thou: Understanding and Characterizing the Emotional Latent Space of Large Language Models](https://mlsanity.com/paper/2510.22042/) (2025)
- [A Circular-Structured Representation for Visual Emotion Distribution Learning](https://mlsanity.com/paper/2106.12450/) (2021)
- [AMC-Loss: Angular Margin Contrastive Loss for Improved Explainability in Image Classification](https://mlsanity.com/paper/2004.09805/) (2020)
- [Interpretable Text Embeddings and Text Similarity Explanation: A Survey](https://mlsanity.com/paper/2502.14862/) (2025)
- [Persona-Based Synthetic Data Generation Using Multi-Stage Conditioning with Large Language Models for Emotion Recognition](https://mlsanity.com/paper/2507.13380/) (2025)
- [Enhancing Cognitive Models of Emotions with Representation Learning](https://mlsanity.com/paper/2104.10117/) (2021)
- [SINCERE: Supervised Information Noise-Contrastive Estimation REvisited](https://mlsanity.com/paper/2309.14277/) (2023)
- [Mapping Semantic & Syntactic Relationships with Geometric Rotation](https://mlsanity.com/paper/2510.09790/) (2025)

## Abstract (arXiv)

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.