# AL-GNN: Privacy-Preserving and Replay-Free Continual Graph Learning via Analytic Learning

arXiv: https://arxiv.org/abs/2512.18295 · HTML: https://mlsanity.com/paper/2512.18295/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 51 references that are in the map.
- First posted on arXiv 20 Dec 2025.

## Builds on (most cited first, 30 of 34)

- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [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)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [A Survey on Knowledge Graph-Based Recommender Systems](https://mlsanity.com/paper/2003.00911/) (2020)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [ROLAND: Graph Learning Framework for Dynamic Graphs](https://mlsanity.com/paper/2208.07239/) (2022)
- [Scalable and Order-robust Continual Learning with Additive Parameter Decomposition](https://mlsanity.com/paper/1902.09432/) (2019)
- [Less-forgetting Learning in Deep Neural Networks](https://mlsanity.com/paper/1607.00122/) (2016)
- [Overcoming Catastrophic Forgetting in Graph Neural Networks](https://mlsanity.com/paper/2012.06002/) (2020)
- [Dynamic Graph Convolutional Networks](https://mlsanity.com/paper/1704.06199/) (2017)
- [Graph Representation Learning: A Survey](https://mlsanity.com/paper/1909.00958/) (2019)
- [A Survey of Graph Neural Networks for Social Recommender Systems](https://mlsanity.com/paper/2212.04481/) (2022)
- [Streaming Graph Neural Networks via Continual Learning](https://mlsanity.com/paper/2009.10951/) (2020)
- [A Survey on Embedding Dynamic Graphs](https://mlsanity.com/paper/2101.01229/) (2021)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [CaT: Balanced Continual Graph Learning with Graph Condensation](https://mlsanity.com/paper/2309.09455/) (2023)
- [Continual Learning on Dynamic Graphs via Parameter Isolation](https://mlsanity.com/paper/2305.13825/) (2023)
- [DS-AL: A Dual-Stream Analytic Learning for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2403.17503/) (2024)

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

- [SLAM: Structured and Localized Analytic Manifold Adaptation for Forgetting-Immune and Domain-Robust Lifelong VPR](https://mlsanity.com/paper/2607.04764/) (2026)

## Abstract (arXiv)

Continual graph learning (CGL) aims to enable graph neural networks to incrementally learn from a stream of graph structured data without forgetting previously acquired knowledge. Existing methods particularly those based on experience replay typically store and revisit past graph data to mitigate catastrophic forgetting. However, these approaches pose significant limitations, including privacy concerns, inefficiency. In this work, we propose AL GNN, a novel framework for continual graph learning that eliminates the need for backpropagation and replay buffers. Instead, AL GNN leverages principles from analytic learning theory to formulate learning as a recursive least squares optimization process. It maintains and updates model knowledge analytically through closed form classifier updates and a regularized feature autocorrelation matrix. This design enables efficient one pass training for each task, and inherently preserves data privacy by avoiding historical sample storage. Extensive experiments on multiple dynamic graph classification benchmarks demonstrate that AL GNN achieves competitive or superior performance compared to existing methods. For instance, it improves average performance by 10% on CoraFull and reduces forgetting by over 30% on Reddit, while also reducing training time by nearly 50% due to its backpropagation free design.