# Balanced Meta-Softmax for Long-Tailed Visual Recognition

arXiv: https://arxiv.org/abs/2007.10740 · HTML: https://mlsanity.com/paper/2007.10740/

## Key facts

- Cited by 400 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2020.

## Built on by (most cited first, 30 of 400)

- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
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- [Balanced Contrastive Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2207.09052/) (2022)
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- [Parametric Classification for Generalized Category Discovery: A Baseline Study](https://mlsanity.com/paper/2211.11727/) (2022)
- [Long-Tailed Recognition via Weight Balancing](https://mlsanity.com/paper/2203.14197/) (2022)
- [The Majority Can Help The Minority: Context-rich Minority Oversampling for Long-tailed Classification](https://mlsanity.com/paper/2112.00412/) (2021)
- [Self-Supervised Aggregation of Diverse Experts for Test-Agnostic Long-Tailed Recognition](https://mlsanity.com/paper/2107.09249/) (2021)
- [Influence-Balanced Loss for Imbalanced Visual Classification](https://mlsanity.com/paper/2110.02444/) (2021)
- [Balanced MSE for Imbalanced Visual Regression](https://mlsanity.com/paper/2203.16427/) (2022)
- [FASA: Feature Augmentation and Sampling Adaptation for Long-Tailed Instance Segmentation](https://mlsanity.com/paper/2102.12867/) (2021)
- [A Survey on Long-Tailed Visual Recognition](https://mlsanity.com/paper/2205.13775/) (2022)
- [Distilling Virtual Examples for Long-tailed Recognition](https://mlsanity.com/paper/2103.15042/) (2021)
- [LPT: Long-tailed Prompt Tuning for Image Classification](https://mlsanity.com/paper/2210.01033/) (2022)
- [ABC: Auxiliary Balanced Classifier for Class-imbalanced Semi-supervised Learning](https://mlsanity.com/paper/2110.10368/) (2021)
- [Nested Collaborative Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2203.15359/) (2022)
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- [Expanding Small-Scale Datasets with Guided Imagination](https://mlsanity.com/paper/2211.13976/) (2022)
- [Long-Tail Learning with Foundation Model: Heavy Fine-Tuning Hurts](https://mlsanity.com/paper/2309.10019/) (2023)
- [Adaptive Class Suppression Loss for Long-Tail Object Detection](https://mlsanity.com/paper/2104.00885/) (2021)
- [No Fear of Classifier Biases: Neural Collapse Inspired Federated Learning with Synthetic and Fixed Classifier](https://mlsanity.com/paper/2303.10058/) (2023)
- [A Hard-to-Beat Baseline for Training-free CLIP-based Adaptation](https://mlsanity.com/paper/2402.04087/) (2024)
- [RankSim: Ranking Similarity Regularization for Deep Imbalanced Regression](https://mlsanity.com/paper/2205.15236/) (2022)
- [DASO: Distribution-Aware Semantics-Oriented Pseudo-label for Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2106.05682/) (2021)
- [Exploring Classification Equilibrium in Long-Tailed Object Detection](https://mlsanity.com/paper/2108.07507/) (2021)
- [Adversarial Robustness under Long-Tailed Distribution](https://mlsanity.com/paper/2104.02703/) (2021)
- [A Simple Long-Tailed Recognition Baseline via Vision-Language Model](https://mlsanity.com/paper/2111.14745/) (2021)
- [Equalized Focal Loss for Dense Long-Tailed Object Detection](https://mlsanity.com/paper/2201.02593/) (2022)

## Abstract (arXiv)

Deep classifiers have achieved great success in visual recognition. However, real-world data is long-tailed by nature, leading to the mismatch between training and testing distributions. In this paper, we show that the Softmax function, though used in most classification tasks, gives a biased gradient estimation under the long-tailed setup. This paper presents Balanced Softmax, an elegant unbiased extension of Softmax, to accommodate the label distribution shift between training and testing. Theoretically, we derive the generalization bound for multiclass Softmax regression and show our loss minimizes the bound. In addition, we introduce Balanced Meta-Softmax, applying a complementary Meta Sampler to estimate the optimal class sample rate and further improve long-tailed learning. In our experiments, we demonstrate that Balanced Meta-Softmax outperforms state-of-the-art long-tailed classification solutions on both visual recognition and instance segmentation tasks.