# Unbiased Online Curvature Approximation for Regularized Graph Continual Learning

arXiv: https://arxiv.org/abs/2509.12727 · HTML: https://mlsanity.com/paper/2509.12727/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1805.07810/) (2018)
- [Rotate your Networks: Better Weight Consolidation and Less Catastrophic Forgetting](https://mlsanity.com/paper/1802.02950/) (2018)
- [Scalable and Order-robust Continual Learning with Additive Parameter Decomposition](https://mlsanity.com/paper/1902.09432/) (2019)
- [Optimal Continual Learning has Perfect Memory and is NP-hard](https://mlsanity.com/paper/2006.05188/) (2020)
- [CaT: Balanced Continual Graph Learning with Graph Condensation](https://mlsanity.com/paper/2309.09455/) (2023)
- [Natural continual learning: success is a journey, not (just) a destination](https://mlsanity.com/paper/2106.08085/) (2021)
- [Continual Learning on Dynamic Graphs via Parameter Isolation](https://mlsanity.com/paper/2305.13825/) (2023)
- [On the Computation of the Fisher Information in Continual Learning](https://mlsanity.com/paper/2502.11756/) (2025)
- [Replay-and-Forget-Free Graph Class-Incremental Learning: A Task Profiling and Prompting Approach](https://mlsanity.com/paper/2410.10341/) (2024)

## Abstract (arXiv)

Graph continual learning (GCL) aims to learn from a continuous sequence of graph-based tasks. Regularization methods are vital for preventing catastrophic forgetting in GCL, particularly in the challenging replay-free, class-incremental setting, where each task consists of a set of unique classes. In this work, we first establish a general regularization framework for GCL based on the curved parameter space induced by the Fisher information matrix (FIM). We show that the dominant Elastic Weight Consolidation (EWC) and its variants are a special case within this framework, using a diagonal approximation of the empirical FIM based on parameters from previous tasks. To overcome their limitations, we propose a new unbiased online curvature approximation of the full FIM based on the model's current learning state. Our method directly estimates the regularization term in an online manner without explicitly evaluating and storing the FIM itself. This enables the model to better capture the loss landscape during learning new tasks while retaining the knowledge learned from previous tasks. Extensive experiments on three graph datasets demonstrate that our method significantly outperforms existing regularization-based methods, achieving a superior trade-off between stability (retaining old knowledge) and plasticity (acquiring new knowledge).