# ELM: Embedding and Logit Margins for Long-Tail Learning

arXiv: https://arxiv.org/abs/2204.13208 · HTML: https://mlsanity.com/paper/2204.13208/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 77 references that are in the map.
- First posted on arXiv 27 Apr 2022.

## Builds on (most cited first, 30 of 45)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (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)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [Exploring the Limits of Weakly Supervised Pretraining](https://mlsanity.com/paper/1805.00932/) (2018)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [Balanced Meta-Softmax for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2007.10740/) (2020)
- [Debiased Contrastive Learning](https://mlsanity.com/paper/2007.00224/) (2020)
- [Equalization Loss for Long-Tailed Object Recognition](https://mlsanity.com/paper/2003.05176/) (2020)
- [Long-Tailed Classification by Keeping the Good and Removing the Bad Momentum Causal Effect](https://mlsanity.com/paper/2009.12991/) (2020)
- [Rethinking the Value of Labels for Improving Class-Imbalanced Learning](https://mlsanity.com/paper/2006.07529/) (2020)
- [Distribution Alignment: A Unified Framework for Long-tail Visual Recognition](https://mlsanity.com/paper/2103.16370/) (2021)
- [Deep Learning Face Representation by Joint Identification-Verification](https://mlsanity.com/paper/1406.4773/) (2014)
- [Seesaw Loss for Long-Tailed Instance Segmentation](https://mlsanity.com/paper/2008.10032/) (2020)
- [Rethinking Class-Balanced Methods for Long-Tailed Visual Recognition from a Domain Adaptation Perspective](https://mlsanity.com/paper/2003.10780/) (2020)
- [Feature Space Augmentation for Long-Tailed Data](https://mlsanity.com/paper/2008.03673/) (2020)
- [Contrastive Learning based Hybrid Networks for Long-Tailed Image Classification](https://mlsanity.com/paper/2103.14267/) (2021)
- [Distribution-Balanced Loss for Multi-Label Classification in Long-Tailed Datasets](https://mlsanity.com/paper/2007.09654/) (2020)
- [Deep Representation Learning on Long-tailed Data: A Learnable Embedding Augmentation Perspective](https://mlsanity.com/paper/2002.10826/) (2020)

## Built on by (most cited first, 10 of 10)

- [Are All Losses Created Equal: A Neural Collapse Perspective](https://mlsanity.com/paper/2210.02192/) (2022)
- [Probabilistic Contrastive Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2403.06726/) (2024)
- [On the Implicit Geometry of Cross-Entropy Parameterizations for Label-Imbalanced Data](https://mlsanity.com/paper/2303.07608/) (2023)
- [Distributionally Robust Post-hoc Classifiers under Prior Shifts](https://mlsanity.com/paper/2309.08825/) (2023)
- [A Survey of Deep Long-Tail Classification Advancements](https://mlsanity.com/paper/2404.15593/) (2024)
- [Uncertainty-guided Boundary Learning for Imbalanced Social Event Detection](https://mlsanity.com/paper/2310.19247/) (2023)
- [Symmetric Neural-Collapse Representations with Supervised Contrastive Loss: The Impact of ReLU and Batching](https://mlsanity.com/paper/2306.07960/) (2023)
- [Supervised Contrastive Representation Learning: Landscape Analysis with Unconstrained Features](https://mlsanity.com/paper/2402.18884/) (2024)
- [Long-Tail Learning with Rebalanced Contrastive Loss](https://mlsanity.com/paper/2312.01753/) (2023)
- [Reducing Class-Wise Performance Disparity via Margin Regularization](https://mlsanity.com/paper/2602.00205/) (2026)

## Abstract (arXiv)

Long-tail learning is the problem of learning under skewed label distributions, which pose a challenge for standard learners. Several recent approaches for the problem have proposed enforcing a suitable margin in logit space. Such techniques are intuitive analogues of the guiding principle behind SVMs, and are equally applicable to linear models and neural models. However, when applied to neural models, such techniques do not explicitly control the geometry of the learned embeddings. This can be potentially sub-optimal, since embeddings for tail classes may be diffuse, resulting in poor generalization for these classes. We present Embedding and Logit Margins (ELM), a unified approach to enforce margins in logit space, and regularize the distribution of embeddings. This connects losses for long-tail learning to proposals in the literature on metric embedding, and contrastive learning. We theoretically show that minimising the proposed ELM objective helps reduce the generalisation gap. The ELM method is shown to perform well empirically, and results in tighter tail class embeddings.