# The Circumplex Degeneracy Behind the Rare-Class Limit in Affect Recognition

arXiv: https://arxiv.org/abs/2606.15763 · HTML: https://mlsanity.com/paper/2606.15763/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 45 references that are in the map.
- First posted on arXiv 14 Jun 2026.

## Builds on (most cited first, 30 of 35)

- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [AffectNet: A Database for Facial Expression, Valence, and Arousal Computing in the Wild](https://mlsanity.com/paper/1708.03985/) (2017)
- [Expression, Affect, Action Unit Recognition: Aff-Wild2, Multi-Task Learning and ArcFace](https://mlsanity.com/paper/1910.04855/) (2019)
- [Deep Affect Prediction in-the-wild: Aff-Wild Database and Challenge, Deep Architectures, and Beyond](https://mlsanity.com/paper/1804.10938/) (2018)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [General Facial Representation Learning in a Visual-Linguistic Manner](https://mlsanity.com/paper/2112.03109/) (2021)
- [Analysing Affective Behavior in the First ABAW 2020 Competition](https://mlsanity.com/paper/2001.11409/) (2020)
- [Affect Analysis in-the-wild: Valence-Arousal, Expressions, Action Units and a Unified Framework](https://mlsanity.com/paper/2103.15792/) (2021)
- [Analysing Affective Behavior in the second ABAW2 Competition](https://mlsanity.com/paper/2106.15318/) (2021)
- [ABAW: Valence-Arousal Estimation, Expression Recognition, Action Unit Detection & Multi-Task Learning Challenges](https://mlsanity.com/paper/2202.10659/) (2022)
- [Face Behavior a la carte: Expressions, Affect and Action Units in a Single Network](https://mlsanity.com/paper/1910.11111/) (2019)
- [ABAW: Learning from Synthetic Data & Multi-Task Learning Challenges](https://mlsanity.com/paper/2207.01138/) (2022)
- [ABAW: Valence-Arousal Estimation, Expression Recognition, Action Unit Detection & Emotional Reaction Intensity Estimation Challenges](https://mlsanity.com/paper/2303.01498/) (2023)
- [The 6th Affective Behavior Analysis in-the-wild (ABAW) Competition](https://mlsanity.com/paper/2402.19344/) (2024)
- [Distribution Matching for Multi-Task Learning of Classification Tasks: a Large-Scale Study on Faces & Beyond](https://mlsanity.com/paper/2401.01219/) (2024)
- [7th ABAW Competition: Multi-Task Learning and Compound Expression Recognition](https://mlsanity.com/paper/2407.03835/) (2024)
- [Cross-Domain Facial Expression Recognition: A Unified Evaluation Benchmark and Adversarial Graph Learning](https://mlsanity.com/paper/2008.00923/) (2020)
- [Squared Earth Mover's Distance-based Loss for Training Deep Neural Networks](https://mlsanity.com/paper/1611.05916/) (2016)
- [EmoCLIP: A Vision-Language Method for Zero-Shot Video Facial Expression Recognition](https://mlsanity.com/paper/2310.16640/) (2023)
- [Uncertainty-aware Label Distribution Learning for Facial Expression Recognition](https://mlsanity.com/paper/2209.10448/) (2022)
- [FSFM: A Generalizable Face Security Foundation Model via Self-Supervised Facial Representation Learning](https://mlsanity.com/paper/2412.12032/) (2024)
- [Enhancing Zero-Shot Facial Expression Recognition by LLM Knowledge Transfer](https://mlsanity.com/paper/2405.19100/) (2024)
- [Behaviour4All: in-the-wild Facial Behaviour Analysis Toolkit](https://mlsanity.com/paper/2409.17717/) (2024)
- [Distilling Privileged Multimodal Information for Expression Recognition using Optimal Transport](https://mlsanity.com/paper/2401.15489/) (2024)
- [Towards End-to-End Explainable Facial Action Unit Recognition via Vision-Language Joint Learning](https://mlsanity.com/paper/2408.00644/) (2024)
- [Affective Behavior Analysis using Action Unit Relation Graph and Multi-task Cross Attention](https://mlsanity.com/paper/2207.10293/) (2022)

## Built on by (most cited first, 1 of 1)

- [A Shared Latent for Partially-Labeled Multi-Task Facial Affect Recognition](https://mlsanity.com/paper/2607.16285/) (2026)

## Abstract (arXiv)

In-the-wild expression recognition persistently fails on a few rare emotions, and the standard explanation is class imbalance. Through a controlled multi-task study on two benchmarks, we show the failure is instead a property of affect geometry: the rare classes are degenerate on Russell's circumplex, and that degeneracy bounds what any loss or cost can achieve. Our instrument is a circumplex-cost optimal-transport term that prices expression confusions by their valence-arousal distance. The term improves the official score and expression macro-F1, but a control most studies omit shows the gain is not geometric: a uniform cost, equivalent to a generic confidence penalty, matches it on Aff-Wild2 (p=0.625) and significantly exceeds it on AffectNet (+0.057 over base, larger than the circumplex). What the geometry reshapes is the structure of the errors, making them affectively nearer the truth on Aff-Wild2 (p=0.031 against the uniform control), an effect that does not survive on AffectNet, where a visual confound at the far corner of the circumplex overwhelms it. The rare-class failure, by contrast, is stable across both datasets we examine: the degenerate pairs (anger-fear on Aff-Wild2, anger-contempt on AffectNet) resist frequency-based interventions, the transport term, and an action-unit-augmented cost built specifically to separate them. We conclude that progress on rare expressions requires representations that distinguish the classes, not supervision that reprices their confusions, and we provide the controls and metrics needed to tell the two apart.