# Online Continual Learning via Logit Adjusted Softmax

arXiv: https://arxiv.org/abs/2311.06460 · HTML: https://mlsanity.com/paper/2311.06460/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 75 references that are in the map.
- First posted on arXiv 11 Nov 2023.

## Builds on (most cited first, 30 of 44)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [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)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [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)
- [End-to-End Incremental Learning](https://mlsanity.com/paper/1807.09536/) (2018)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [On Tiny Episodic Memories in Continual Learning](https://mlsanity.com/paper/1902.10486/) (2019)
- [CORe50: a New Dataset and Benchmark for Continuous Object Recognition](https://mlsanity.com/paper/1705.03550/) (2017)
- [Equalization Loss for Long-Tailed Object Recognition](https://mlsanity.com/paper/2003.05176/) (2020)
- [Co2L: Contrastive Continual Learning](https://mlsanity.com/paper/2106.14413/) (2021)
- [New Insights on Reducing Abrupt Representation Change in Online Continual Learning](https://mlsanity.com/paper/2104.05025/) (2021)
- [Supervised Contrastive Replay: Revisiting the Nearest Class Mean Classifier in Online Class-Incremental Continual Learning](https://mlsanity.com/paper/2103.13885/) (2021)
- [SS-IL: Separated Softmax for Incremental Learning](https://mlsanity.com/paper/2003.13947/) (2020)
- [Online Coreset Selection for Rehearsal-based Continual Learning](https://mlsanity.com/paper/2106.01085/) (2021)
- [Class-Incremental Learning by Knowledge Distillation with Adaptive Feature Consolidation](https://mlsanity.com/paper/2204.00895/) (2022)
- [Continual Learning in Low-rank Orthogonal Subspaces](https://mlsanity.com/paper/2010.11635/) (2020)
- [On Learning the Geodesic Path for Incremental Learning](https://mlsanity.com/paper/2104.08572/) (2021)
- [Identifying and Compensating for Feature Deviation in Imbalanced Deep Learning](https://mlsanity.com/paper/2001.01385/) (2020)
- [Online Continual Learning on Class Incremental Blurry Task Configuration with Anytime Inference](https://mlsanity.com/paper/2110.10031/) (2021)
- [Task Agnostic Continual Learning Using Online Variational Bayes](https://mlsanity.com/paper/1803.10123/) (2018)
- [On the Stability-Plasticity Dilemma of Class-Incremental Learning](https://mlsanity.com/paper/2304.01663/) (2023)

## Built on by (most cited first, 5 of 5)

- [Theoretical Insights into Overparameterized Models in Multi-Task and Replay-Based Continual Learning](https://mlsanity.com/paper/2408.16939/) (2024)
- [DELTA: Decoupling Long-Tailed Online Continual Learning](https://mlsanity.com/paper/2404.04476/) (2024)
- [Online Analytic Exemplar-Free Continual Learning with Large Models for Imbalanced Autonomous Driving Task](https://mlsanity.com/paper/2405.17779/) (2024)
- [Unlearning-based sliding window for continual learning under concept drift](https://mlsanity.com/paper/2603.14484/) (2026)
- [HyCal: A Training-Free Prototype Calibration Method for Cross-Discipline Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2604.15678/) (2026)

## Abstract (arXiv)

Online continual learning is a challenging problem where models must learn from a non-stationary data stream while avoiding catastrophic forgetting. Inter-class imbalance during training has been identified as a major cause of forgetting, leading to model prediction bias towards recently learned classes. In this paper, we theoretically analyze that inter-class imbalance is entirely attributed to imbalanced class-priors, and the function learned from intra-class intrinsic distributions is the Bayes-optimal classifier. To that end, we present that a simple adjustment of model logits during training can effectively resist prior class bias and pursue the corresponding Bayes-optimum. Our proposed method, Logit Adjusted Softmax, can mitigate the impact of inter-class imbalance not only in class-incremental but also in realistic general setups, with little additional computational cost. We evaluate our approach on various benchmarks and demonstrate significant performance improvements compared to prior arts. For example, our approach improves the best baseline by 4.6% on CIFAR10.