# Online Curvature-Aware Replay: Leveraging mathbf2nd Order Information for Online Continual Learning

arXiv: https://arxiv.org/abs/2502.01866 · HTML: https://mlsanity.com/paper/2502.01866/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 53 references that are in the map.
- First posted on arXiv 3 Feb 2025.

## Builds on (most cited first, 30 of 36)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [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)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [Class-incremental learning: survey and performance evaluation on image classification](https://mlsanity.com/paper/2010.15277/) (2020)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (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)
- [Online Continual Learning in Image Classification: An Empirical Survey](https://mlsanity.com/paper/2101.10423/) (2021)
- [Task-Free Continual Learning](https://mlsanity.com/paper/1812.03596/) (2018)
- [New Insights on Reducing Abrupt Representation Change in Online Continual Learning](https://mlsanity.com/paper/2104.05025/) (2021)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Understanding the Role of Training Regimes in Continual Learning](https://mlsanity.com/paper/2006.06958/) (2020)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [Linear Mode Connectivity in Multitask and Continual Learning](https://mlsanity.com/paper/2010.04495/) (2020)
- [Supervised Contrastive Replay: Revisiting the Nearest Class Mean Classifier in Online Class-Incremental Continual Learning](https://mlsanity.com/paper/2103.13885/) (2021)
- [Rotate your Networks: Better Weight Consolidation and Less Catastrophic Forgetting](https://mlsanity.com/paper/1802.02950/) (2018)
- [Continual Deep Learning by Functional Regularisation of Memorable Past](https://mlsanity.com/paper/2004.14070/) (2020)
- [The CLEAR Benchmark: Continual LEArning on Real-World Imagery](https://mlsanity.com/paper/2201.06289/) (2022)
- [Probing Representation Forgetting in Supervised and Unsupervised Continual Learning](https://mlsanity.com/paper/2203.13381/) (2022)
- [Continual evaluation for lifelong learning: Identifying the stability gap](https://mlsanity.com/paper/2205.13452/) (2022)
- [Online Prototype Learning for Online Continual Learning](https://mlsanity.com/paper/2308.00301/) (2023)
- [Natural continual learning: success is a journey, not (just) a destination](https://mlsanity.com/paper/2106.08085/) (2021)
- [Elastic Feature Consolidation for Cold Start Exemplar-Free Incremental Learning](https://mlsanity.com/paper/2402.03917/) (2024)

## Built on by (most cited first, 8 of 8)

- [Harness Continual Learning: Continual Adaptation Beyond Model Parameters](https://mlsanity.com/paper/2608.19013/) (2026)
- [InTAct: Interval-based Task Activation Consolidation for Continual Learning](https://mlsanity.com/paper/2511.17439/) (2025)
- [C-Flat++: Towards a More Efficient and Powerful Framework for Continual Learning](https://mlsanity.com/paper/2508.18860/) (2025)
- [Theoretical Foundations of Continual Learning via Drift-Plus-Penalty](https://mlsanity.com/paper/2606.08452/) (2026)
- [Online Continual Learning for Time Series: a Natural Score-driven Approach](https://mlsanity.com/paper/2601.12931/) (2026)
- [Memory-efficient Continual Learning with Prototypical Exemplar Condensation](https://mlsanity.com/paper/2603.13804/) (2026)
- [Preventing Latent Rehearsal Decay in Online Continual SSL with SOLAR](https://mlsanity.com/paper/2604.10586/) (2026)
- [Normative Loss Landscape Navigation: A Trajectory-Based Approach to Mitigating Forgetting in Incremental Learning](https://mlsanity.com/paper/2609.35926/) (2026)

## Abstract (arXiv)

Online Continual Learning (OCL) models continuously adapt to nonstationary data streams, usually without task information. These settings are complex and many traditional CL methods fail, while online methods (mainly replay-based) suffer from instabilities after the task shift. To address this issue, we formalize replay-based OCL as a second-order online joint optimization with explicit KL-divergence constraints on replay data. We propose Online Curvature-Aware Replay (OCAR) to solve the problem: a method that leverages second-order information of the loss using a K-FAC approximation of the Fisher Information Matrix (FIM) to precondition the gradient. The FIM acts as a stabilizer to prevent forgetting while also accelerating the optimization in non-interfering directions. We show how to adapt the estimation of the FIM to a continual setting stabilizing second-order optimization for non-iid data, uncovering the role of the Tikhonov regularization in the stability-plasticity tradeoff. Empirical results show that OCAR outperforms state-of-the-art methods in continual metrics achieving higher average accuracy throughout the training process in three different benchmarks.