# Towards Calibrated Hyper-Sphere Representation via Distribution Overlap Coefficient for Long-tailed Learning

arXiv: https://arxiv.org/abs/2208.10043 · HTML: https://mlsanity.com/paper/2208.10043/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 57 references that are in the map.
- First posted on arXiv 22 Aug 2022.

## Builds on (most cited first, 30 of 40)

- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [LVIS: A Dataset for Large Vocabulary Instance Segmentation](https://mlsanity.com/paper/1908.03195/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Cascade R-CNN: High Quality Object Detection and Instance Segmentation](https://mlsanity.com/paper/1906.09756/) (2019)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [BBN: Bilateral-Branch Network with Cumulative Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/1912.02413/) (2019)
- [Balanced Meta-Softmax for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2007.10740/) (2020)
- [Equalization Loss for Long-Tailed Object Recognition](https://mlsanity.com/paper/2003.05176/) (2020)
- [Long-tailed Recognition by Routing Diverse Distribution-Aware Experts](https://mlsanity.com/paper/2010.01809/) (2020)
- [Long-Tailed Classification by Keeping the Good and Removing the Bad Momentum Causal Effect](https://mlsanity.com/paper/2009.12991/) (2020)
- [Parametric Contrastive Learning](https://mlsanity.com/paper/2107.12028/) (2021)
- [Rethinking the Value of Labels for Improving Class-Imbalanced Learning](https://mlsanity.com/paper/2006.07529/) (2020)
- [Improving Calibration for Long-Tailed Recognition](https://mlsanity.com/paper/2104.00466/) (2021)
- [Distribution Alignment: A Unified Framework for Long-tail Visual Recognition](https://mlsanity.com/paper/2103.16370/) (2021)
- [Disentangling Label Distribution for Long-tailed Visual Recognition](https://mlsanity.com/paper/2012.00321/) (2020)
- [Overcoming Classifier Imbalance for Long-tail Object Detection with Balanced Group Softmax](https://mlsanity.com/paper/2006.10408/) (2020)
- [Seesaw Loss for Long-Tailed Instance Segmentation](https://mlsanity.com/paper/2008.10032/) (2020)
- [OCNet: Object Context Network for Scene Parsing](https://mlsanity.com/paper/1809.00916/) (2018)
- [Targeted Supervised Contrastive Learning for Long-Tailed Recognition](https://mlsanity.com/paper/2111.13998/) (2021)
- [Contrastive Learning based Hybrid Networks for Long-Tailed Image Classification](https://mlsanity.com/paper/2103.14267/) (2021)
- [Range Loss for Deep Face Recognition with Long-tail](https://mlsanity.com/paper/1611.08976/) (2016)
- [Equalization Loss v2: A New Gradient Balance Approach for Long-tailed Object Detection](https://mlsanity.com/paper/2012.08548/) (2020)
- [Distributional Robustness Loss for Long-tail Learning](https://mlsanity.com/paper/2104.03066/) (2021)

## Built on by (most cited first, 17 of 17)

- [Probabilistic Contrastive Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2403.06726/) (2024)
- [Learning Imbalanced Data with Vision Transformers](https://mlsanity.com/paper/2212.02015/) (2022)
- [A Systematic Review on Long-Tailed Learning](https://mlsanity.com/paper/2408.00483/) (2024)
- [On the Effectiveness of Out-of-Distribution Data in Self-Supervised Long-Tail Learning](https://mlsanity.com/paper/2306.04934/) (2023)
- [FreqDebias: Towards Generalizable Deepfake Detection via Consistency-Driven Frequency Debiasing](https://mlsanity.com/paper/2509.22412/) (2025)
- [Towards Distribution-Agnostic Generalized Category Discovery](https://mlsanity.com/paper/2310.01376/) (2023)
- [Seeing Unseen: Discover Novel Biomedical Concepts via Geometry-Constrained Probabilistic Modeling](https://mlsanity.com/paper/2403.01053/) (2024)
- [GeNIe: Generative Hard Negative Images Through Diffusion](https://mlsanity.com/paper/2312.02548/) (2023)
- [VLM-KD: Knowledge Distillation from VLM for Long-Tail Visual Recognition](https://mlsanity.com/paper/2408.16930/) (2024)
- [Adaptive Parametric Activation: Unifying and Generalising Activation Functions Across Tasks](https://mlsanity.com/paper/2407.08567/) (2024)
- [Uniformly Distributed Category Prototype-Guided Vision-Language Framework for Long-Tail Recognition](https://mlsanity.com/paper/2308.12522/) (2023)
- [Generative Data Mining with Longtail-Guided Diffusion](https://mlsanity.com/paper/2502.01980/) (2025)
- [Gradient-Aware Logit Adjustment Loss for Long-tailed Classifier](https://mlsanity.com/paper/2403.09036/) (2024)
- [IMWA: Iterative Model Weight Averaging Benefits Class-Imbalanced Learning Tasks](https://mlsanity.com/paper/2404.16331/) (2024)
- [Dynamic Feature Learning and Matching for Class-Incremental Learning](https://mlsanity.com/paper/2405.08533/) (2024)
- [BAPE: Learning an Explicit Bayes Classifier for Long-tailed Visual Recognition](https://mlsanity.com/paper/2506.23280/) (2025)
- [Class Instance Balanced Learning for Long-Tailed Classification](https://mlsanity.com/paper/2307.05322/) (2023)

## Abstract (arXiv)

Long-tailed learning aims to tackle the crucial challenge that head classes dominate the training procedure under severe class imbalance in real-world scenarios. However, little attention has been given to how to quantify the dominance severity of head classes in the representation space. Motivated by this, we generalize the cosine-based classifiers to a von Mises-Fisher (vMF) mixture model, denoted as vMF classifier, which enables to quantitatively measure representation quality upon the hyper-sphere space via calculating distribution overlap coefficient. To our knowledge, this is the first work to measure representation quality of classifiers and features from the perspective of distribution overlap coefficient. On top of it, we formulate the inter-class discrepancy and class-feature consistency loss terms to alleviate the interference among the classifier weights and align features with classifier weights. Furthermore, a novel post-training calibration algorithm is devised to zero-costly boost the performance via inter-class overlap coefficients. Our method outperforms previous work with a large margin and achieves state-of-the-art performance on long-tailed image classification, semantic segmentation, and instance segmentation tasks (e.g., we achieve 55.0% overall accuracy with ResNetXt-50 in ImageNet-LT). Our code is available at https://github.com/VipaiLab/vMFOP.