# Balanced Product of Calibrated Experts for Long-Tailed Recognition

arXiv: https://arxiv.org/abs/2206.05260 · HTML: https://mlsanity.com/paper/2206.05260/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 81 references that are in the map.
- First posted on arXiv 10 Jun 2022.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [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)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [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)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [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)
- [Model-Ensemble Trust-Region Policy Optimization](https://mlsanity.com/paper/1802.10592/) (2018)
- [Parametric Contrastive Learning](https://mlsanity.com/paper/2107.12028/) (2021)
- [Improving Calibration for Long-Tailed Recognition](https://mlsanity.com/paper/2104.00466/) (2021)

## Built on by (most cited first, 20 of 20)

- [LTGC: Long-tail Recognition via Leveraging LLMs-driven Generated Content](https://mlsanity.com/paper/2403.05854/) (2024)
- [A Systematic Review on Long-Tailed Learning](https://mlsanity.com/paper/2408.00483/) (2024)
- [A Unified Perspective for Loss-Oriented Imbalanced Learning via Localization](https://mlsanity.com/paper/2310.04752/) (2023)
- [Focal-SAM: Focal Sharpness-Aware Minimization for Long-Tailed Classification](https://mlsanity.com/paper/2505.01660/) (2025)
- [On the Role of Long-tail Knowledge in Retrieval Augmented Large Language Models](https://mlsanity.com/paper/2406.16367/) (2024)
- [Long-tailed Recognition with Model Rebalancing](https://mlsanity.com/paper/2510.08177/) (2025)
- [Flexible Distribution Alignment: Towards Long-tailed Semi-supervised Learning with Proper Calibration](https://mlsanity.com/paper/2306.04621/) (2023)
- [A Square Peg in a Square Hole: Meta-Expert for Long-Tailed Semi-Supervised Learning](https://mlsanity.com/paper/2505.16341/) (2025)
- [LTRL: Boosting Long-tail Recognition via Reflective Learning](https://mlsanity.com/paper/2407.12568/) (2024)
- [Fractal Calibration for long-tailed object detection](https://mlsanity.com/paper/2410.11774/) (2024)
- [MoENAS: Mixture-of-Expert based Neural Architecture Search for jointly Accurate, Fair, and Robust Edge Deep Neural Networks](https://mlsanity.com/paper/2502.07422/) (2025)
- [High-fidelity Pseudo-labels for Boosting Weakly-Supervised Segmentation](https://mlsanity.com/paper/2304.02621/) (2023)
- [Keep It on a Leash: Controllable Pseudo-label Generation Towards Realistic Long-Tailed Semi-Supervised Learning](https://mlsanity.com/paper/2510.03993/) (2025)
- [Clean Label Disentangling for Medical Image Segmentation with Noisy Labels](https://mlsanity.com/paper/2311.16580/) (2023)
- [Training Over a Distribution of Hyperparameters for Enhanced Performance and Adaptability on Imbalanced Classification](https://mlsanity.com/paper/2410.03588/) (2024)
- [PI-H2T: Enhancing Long-Tailed Visual Recognition with Permutation-Invariant and Head-to-Tail Feature Fusion](https://mlsanity.com/paper/2506.00625/) (2025)
- [Exploring "Many in Few" and "Few in Many" Properties in Long-Tailed, Highly-Imbalanced IC Defect Classification](https://mlsanity.com/paper/2510.19463/) (2025)
- [Compensating Visual Insufficiency with Stratified Language Guidance for Long-Tail Class Incremental Learning](https://mlsanity.com/paper/2603.21708/) (2026)
- [HMR-Net: Hierarchical Modular Routing for Cross-Domain Object Detection in Aerial Images](https://mlsanity.com/paper/2604.18866/) (2026)
- [VICAL: Vicinal Consistency Alignment for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2609.04948/) (2026)

## Abstract (arXiv)

Many real-world recognition problems are characterized by long-tailed label distributions. These distributions make representation learning highly challenging due to limited generalization over the tail classes. If the test distribution differs from the training distribution, e.g. uniform versus long-tailed, the problem of the distribution shift needs to be addressed. A recent line of work proposes learning multiple diverse experts to tackle this issue. Ensemble diversity is encouraged by various techniques, e.g. by specializing different experts in the head and the tail classes. In this work, we take an analytical approach and extend the notion of logit adjustment to ensembles to form a Balanced Product of Experts (BalPoE). BalPoE combines a family of experts with different test-time target distributions, generalizing several previous approaches. We show how to properly define these distributions and combine the experts in order to achieve unbiased predictions, by proving that the ensemble is Fisher-consistent for minimizing the balanced error. Our theoretical analysis shows that our balanced ensemble requires calibrated experts, which we achieve in practice using mixup. We conduct extensive experiments and our method obtains new state-of-the-art results on three long-tailed datasets: CIFAR-100-LT, ImageNet-LT, and iNaturalist-2018. Our code is available at https://github.com/emasa/BalPoE-CalibratedLT.