# Generalisation Guarantees for Continual Learning with Orthogonal Gradient Descent

arXiv: https://arxiv.org/abs/2006.11942 · HTML: https://mlsanity.com/paper/2006.11942/

## Key facts

- Cited by 68 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2020.

## Built on by (most cited first, 30 of 68)

- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Continual Learning in the Teacher-Student Setup: Impact of Task Similarity](https://mlsanity.com/paper/2107.04384/) (2021)
- [How catastrophic can catastrophic forgetting be in linear regression?](https://mlsanity.com/paper/2205.09588/) (2022)
- [A Theoretical Study on Solving Continual Learning](https://mlsanity.com/paper/2211.02633/) (2022)
- [Theory on Forgetting and Generalization of Continual Learning](https://mlsanity.com/paper/2302.05836/) (2023)
- [Theory on Mixture-of-Experts in Continual Learning](https://mlsanity.com/paper/2406.16437/) (2024)
- [The Ideal Continual Learner: An Agent That Never Forgets](https://mlsanity.com/paper/2305.00316/) (2023)
- [Continual Learning in Linear Classification on Separable Data](https://mlsanity.com/paper/2306.03534/) (2023)
- [A Statistical Theory of Regularization-Based Continual Learning](https://mlsanity.com/paper/2406.06213/) (2024)
- [Understanding Forgetting in Continual Learning with Linear Regression](https://mlsanity.com/paper/2405.17583/) (2024)
- [Analysis of Catastrophic Forgetting for Random Orthogonal Transformation Tasks in the Overparameterized Regime](https://mlsanity.com/paper/2207.06475/) (2022)
- [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)
- [Formalizing the Generalization-Forgetting Trade-off in Continual Learning](https://mlsanity.com/paper/2109.14035/) (2021)
- [Fixed Design Analysis of Regularization-Based Continual Learning](https://mlsanity.com/paper/2303.10263/) (2023)
- [How do Quadratic Regularizers Prevent Catastrophic Forgetting: The Role of Interpolation](https://mlsanity.com/paper/2102.02805/) (2021)
- [Disentangling and Mitigating the Impact of Task Similarity for Continual Learning](https://mlsanity.com/paper/2405.20236/) (2024)
- [Continual Learning Beyond a Single Model](https://mlsanity.com/paper/2202.09826/) (2022)
- [Provable Lifelong Learning of Representations](https://mlsanity.com/paper/2110.14098/) (2021)
- [Provable Continual Learning via Sketched Jacobian Approximations](https://mlsanity.com/paper/2112.05095/) (2021)
- [Learning Curves for Continual Learning in Neural Networks: Self-Knowledge Transfer and Forgetting](https://mlsanity.com/paper/2112.01653/) (2021)
- [Provable and Efficient Continual Representation Learning](https://mlsanity.com/paper/2203.02026/) (2022)
- [Order parameters and phase transitions of continual learning in deep neural networks](https://mlsanity.com/paper/2407.10315/) (2024)
- [On the Diminishing Returns of Width for Continual Learning](https://mlsanity.com/paper/2403.06398/) (2024)
- [Selective Amnesia: On Efficient, High-Fidelity and Blind Suppression of Backdoor Effects in Trojaned Machine Learning Models](https://mlsanity.com/paper/2212.04687/) (2022)
- [Last Iterate Convergence of Incremental Methods and Applications in Continual Learning](https://mlsanity.com/paper/2403.06873/) (2024)
- [Continual Memorization of Factoids in Language Models](https://mlsanity.com/paper/2411.07175/) (2024)
- [NTK-Guided Few-Shot Class Incremental Learning](https://mlsanity.com/paper/2403.12486/) (2024)
- [Restricted Orthogonal Gradient Projection for Continual Learning](https://mlsanity.com/paper/2301.12131/) (2023)

## Abstract (arXiv)

In Continual Learning settings, deep neural networks are prone to Catastrophic Forgetting. Orthogonal Gradient Descent was proposed to tackle the challenge. However, no theoretical guarantees have been proven yet. We present a theoretical framework to study Continual Learning algorithms in the Neural Tangent Kernel regime. This framework comprises closed form expression of the model through tasks and proxies for Transfer Learning, generalisation and tasks similarity. In this framework, we prove that OGD is robust to Catastrophic Forgetting then derive the first generalisation bound for SGD and OGD for Continual Learning. Finally, we study the limits of this framework in practice for OGD and highlight the importance of the Neural Tangent Kernel variation for Continual Learning with OGD.