# A Theoretical Study on Solving Continual Learning

arXiv: https://arxiv.org/abs/2211.02633 · HTML: https://mlsanity.com/paper/2211.02633/

## Key facts

- Cited by 80 papers in the map (data through 14 Oct 2026).
- Builds on 68 of its 86 references that are in the map.
- First posted on arXiv 4 Nov 2022.

## Builds on (most cited first, 30 of 68)

- [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)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [End-to-End Incremental Learning](https://mlsanity.com/paper/1807.09536/) (2018)
- [Large Batch Training of Convolutional Networks](https://mlsanity.com/paper/1708.03888/) (2017)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [Expert Gate: Lifelong Learning with a Network of Experts](https://mlsanity.com/paper/1611.06194/) (2016)

## Built on by (most cited first, 30 of 80)

- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Continual Learning of Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2404.16789/) (2024)
- [Class-Incremental Learning: A Survey](https://mlsanity.com/paper/2302.03648/) (2023)
- [Continual Pre-training of Language Models](https://mlsanity.com/paper/2302.03241/) (2023)
- [Hierarchical Decomposition of Prompt-Based Continual Learning: Rethinking Obscured Sub-optimality](https://mlsanity.com/paper/2310.07234/) (2023)
- [Continual Learning of Natural Language Processing Tasks: A Survey](https://mlsanity.com/paper/2211.12701/) (2022)
- [Continual Learning and Catastrophic Forgetting](https://mlsanity.com/paper/2403.05175/) (2024)
- [A Comprehensive Survey of Forgetting in Deep Learning Beyond Continual Learning](https://mlsanity.com/paper/2307.09218/) (2023)
- [Continual Learning: Applications and the Road Forward](https://mlsanity.com/paper/2311.11908/) (2023)
- [Federated Continual Learning via Knowledge Fusion: A Survey](https://mlsanity.com/paper/2312.16475/) (2023)
- [Mixture of Experts Meets Prompt-Based Continual Learning](https://mlsanity.com/paper/2405.14124/) (2024)
- [A Unified Approach to Domain Incremental Learning with Memory: Theory and Algorithm](https://mlsanity.com/paper/2310.12244/) (2023)
- [Learnability and Algorithm for Continual Learning](https://mlsanity.com/paper/2306.12646/) (2023)
- [The Joint Effect of Task Similarity and Overparameterization on Catastrophic Forgetting -- An Analytical Model](https://mlsanity.com/paper/2401.12617/) (2024)
- [Dealing with Cross-Task Class Discrimination in Online Continual Learning](https://mlsanity.com/paper/2305.14657/) (2023)
- [ImageNet-OOD: Deciphering Modern Out-of-Distribution Detection Algorithms](https://mlsanity.com/paper/2310.01755/) (2023)
- [OVOR: OnePrompt with Virtual Outlier Regularization for Rehearsal-Free Class-Incremental Learning](https://mlsanity.com/paper/2402.04129/) (2024)
- [HiDe-PET: Continual Learning via Hierarchical Decomposition of Parameter-Efficient Tuning](https://mlsanity.com/paper/2407.05229/) (2024)
- [Class Incremental Learning via Likelihood Ratio Based Task Prediction](https://mlsanity.com/paper/2309.15048/) (2023)
- [Class Incremental Learning with Self-Supervised Pre-Training and Prototype Learning](https://mlsanity.com/paper/2308.02346/) (2023)
- [Two Complementary Perspectives to Continual Learning: Ask Not Only What to Optimize, But Also How](https://mlsanity.com/paper/2311.04898/) (2023)
- [Prediction Error-based Classification for Class-Incremental Learning](https://mlsanity.com/paper/2305.18806/) (2023)
- [Continual Learning Using a Kernel-Based Method Over Foundation Models](https://mlsanity.com/paper/2412.15571/) (2024)
- [Refined Coreset Selection: Towards Minimal Coreset Size under Model Performance Constraints](https://mlsanity.com/paper/2311.08675/) (2023)
- [On the Diminishing Returns of Width for Continual Learning](https://mlsanity.com/paper/2403.06398/) (2024)
- [Replay-and-Forget-Free Graph Class-Incremental Learning: A Task Profiling and Prompting Approach](https://mlsanity.com/paper/2410.10341/) (2024)
- [Class-Incremental Learning based on Label Generation](https://mlsanity.com/paper/2306.12619/) (2023)
- [Continual Evidential Deep Learning for Out-of-Distribution Detection](https://mlsanity.com/paper/2309.02995/) (2023)
- [Integrating Present and Past in Unsupervised Continual Learning](https://mlsanity.com/paper/2404.19132/) (2024)
- [PASS++: A Dual Bias Reduction Framework for Non-Exemplar Class-Incremental Learning](https://mlsanity.com/paper/2407.14029/) (2024)

## Abstract (arXiv)

Continual learning (CL) learns a sequence of tasks incrementally. There are two popular CL settings, class incremental learning (CIL) and task incremental learning (TIL). A major challenge of CL is catastrophic forgetting (CF). While a number of techniques are already available to effectively overcome CF for TIL, CIL remains to be highly challenging. So far, little theoretical study has been done to provide a principled guidance on how to solve the CIL problem. This paper performs such a study. It first shows that probabilistically, the CIL problem can be decomposed into two sub-problems: Within-task Prediction (WP) and Task-id Prediction (TP). It further proves that TP is correlated with out-of-distribution (OOD) detection, which connects CIL and OOD detection. The key conclusion of this study is that regardless of whether WP and TP or OOD detection are defined explicitly or implicitly by a CIL algorithm, good WP and good TP or OOD detection are necessary and sufficient for good CIL performances. Additionally, TIL is simply WP. Based on the theoretical result, new CIL methods are also designed, which outperform strong baselines in both CIL and TIL settings by a large margin.