# Generalised Balanced Softmax: A Finite-Data Perspective on Logit Adjustment for Long-Tailed Recognition

arXiv: https://arxiv.org/abs/2607.22258 · HTML: https://mlsanity.com/paper/2607.22258/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 24 Jul 2026.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [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)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (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)
- [YOLOv7: Trainable bag-of-freebies sets new state-of-the-art for real-time object detectors](https://mlsanity.com/paper/2207.02696/) (2022)
- [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)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Balanced Meta-Softmax for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2007.10740/) (2020)
- [Long-tailed Recognition by Routing Diverse Distribution-Aware Experts](https://mlsanity.com/paper/2010.01809/) (2020)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [Balanced Contrastive Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2207.09052/) (2022)
- [Inducing Neural Collapse in Imbalanced Learning: Do We Really Need a Learnable Classifier at the End of Deep Neural Network?](https://mlsanity.com/paper/2203.09081/) (2022)
- [ResLT: Residual Learning for Long-tailed Recognition](https://mlsanity.com/paper/2101.10633/) (2021)
- [A Survey on Long-Tailed Visual Recognition](https://mlsanity.com/paper/2205.13775/) (2022)
- [Generalized Parametric Contrastive Learning](https://mlsanity.com/paper/2209.12400/) (2022)
- [Probabilistic Contrastive Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2403.06726/) (2024)
- [On Model Calibration for Long-Tailed Object Detection and Instance Segmentation](https://mlsanity.com/paper/2107.02170/) (2021)
- [A Systematic Review on Long-Tailed Learning](https://mlsanity.com/paper/2408.00483/) (2024)
- [NCL++: Nested Collaborative Learning for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2306.16709/) (2023)
- [LCReg: Long-Tailed Image Classification with Latent Categories based Recognition](https://mlsanity.com/paper/2309.07186/) (2023)
- [Difficulty-aware Balancing Margin Loss for Long-tailed Recognition](https://mlsanity.com/paper/2412.15477/) (2024)
- [Improved Balanced Classification with Theoretically Grounded Loss Functions](https://mlsanity.com/paper/2512.23947/) (2025)
- [DBN-Mix: Training Dual Branch Network Using Bilateral Mixup Augmentation for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2207.02173/) (2022)
- [Fractal Calibration for long-tailed object detection](https://mlsanity.com/paper/2410.11774/) (2024)

## Abstract (arXiv)

Models trained on long-tailed data using standard softmax tend to exhibit higher training error and a larger generalisation gap for classes with fewer training samples. We characterise this class-wise disparity as the preference issue and quantify it using a new metric, the model imbalance level I. To understand this issue, we analyse how imbalanced training data adversely affects class-wise gradients under standard softmax training. This paper then develops a finite-data Generalised Balanced Softmax (GBS) framework for analysing and mitigating the preference issue. The framework uses the training-time logit adjustment znc+βlog|Nc|, which is algebraically identical to the training-time logit-adjusted loss of Menon et al. (2021) when τ=β. The case β=1 also coincides with Balanced Softmax and with the unit adjustment supported by the Fisher-consistency argument under the true data distribution, corresponding to an idealised infinite-data setting. Building on this existing loss family, this paper uses a heuristic power-law assumption to motivate the adjustable coefficient and studies how β affects trained models. Across the evaluated long-tailed benchmarks, β=1 does not attain the highest average testing recall on most datasets, showing that a different coefficient can be preferable when training on finite data. The selected values of β reduce I and improve average testing recall relative to the β=1 reference, while retaining negligible computational overhead and compatibility with existing representation-learning frameworks.