# SketchOGD: Memory-Efficient Continual Learning

arXiv: https://arxiv.org/abs/2305.16424 · HTML: https://mlsanity.com/paper/2305.16424/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 52 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 26 of 26)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [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)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data](https://mlsanity.com/paper/1808.01204/) (2018)
- [Interactive Supercomputing on 40,000 Cores for Machine Learning and Data Analysis](https://mlsanity.com/paper/1807.07814/) (2018)
- [A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix](https://mlsanity.com/paper/2010.04003/) (2020)
- [Latent Replay for Real-Time Continual Learning](https://mlsanity.com/paper/1912.01100/) (2019)
- [R-GAP: Recursive Gradient Attack on Privacy](https://mlsanity.com/paper/2010.07733/) (2020)
- [Efficient Continual Learning with Modular Networks and Task-Driven Priors](https://mlsanity.com/paper/2012.12631/) (2020)
- [Generalisation Guarantees for Continual Learning with Orthogonal Gradient Descent](https://mlsanity.com/paper/2006.11942/) (2020)
- [Continual Learning via Local Module Composition](https://mlsanity.com/paper/2111.07736/) (2021)
- [Stochastic Mirror Descent on Overparameterized Nonlinear Models: Convergence, Implicit Regularization, and Generalization](https://mlsanity.com/paper/1906.03830/) (2019)
- [Practical sketching algorithms for low-rank matrix approximation](https://mlsanity.com/paper/1609.00048/) (2016)
- [HOUDINI: Lifelong Learning as Program Synthesis](https://mlsanity.com/paper/1804.00218/) (2018)
- [Sketching Curvature for Efficient Out-of-Distribution Detection for Deep Neural Networks](https://mlsanity.com/paper/2102.12567/) (2021)
- [Stochastic Gradient/Mirror Descent: Minimax Optimality and Implicit Regularization](https://mlsanity.com/paper/1806.00952/) (2018)
- [The Fast Convergence of Incremental PCA](https://mlsanity.com/paper/1501.03796/) (2015)
- [ORFit: One-Pass Learning via Bridging Orthogonal Gradient Descent and Recursive Least-Squares](https://mlsanity.com/paper/2207.13853/) (2022)

## Built on by (most cited first, 1 of 1)

- [SLE-FNO: Single-Layer Extensions for Task-Agnostic Continual Learning in Fourier Neural Operators](https://mlsanity.com/paper/2603.20410/) (2026)

## Abstract (arXiv)

When machine learning models are trained continually on a sequence of tasks, they are often liable to forget what they learned on previous tasks--a phenomenon known as catastrophic forgetting. Proposed solutions to catastrophic forgetting tend to involve storing information about past tasks, meaning that memory usage is a chief consideration in determining their practicality. This paper develops a memory-efficient solution to catastrophic forgetting using the idea of matrix sketching, in the context of a simple continual learning algorithm known as orthogonal gradient descent (OGD). OGD finds weight updates that aim to preserve performance on prior datapoints, using gradients of the model on those datapoints. However, since the memory cost of storing prior model gradients grows with the runtime of the algorithm, OGD is ill-suited to continual learning over long time horizons. To address this problem, we propose SketchOGD. SketchOGD employs an online sketching algorithm to compress model gradients as they are encountered into a matrix of a fixed, user-determined size. In contrast to existing memory-efficient variants of OGD, SketchOGD runs online without the need for advance knowledge of the total number of tasks, is simple to implement, and is more amenable to analysis. We provide theoretical guarantees on the approximation error of the relevant sketches under a novel metric suited to the downstream task of OGD. Experimentally, we find that SketchOGD tends to outperform current state-of-the-art variants of OGD given a fixed memory budget.