# Learning Continually on a Sequence of Graphs -- The Dynamical System Way

arXiv: https://arxiv.org/abs/2305.12030 · HTML: https://mlsanity.com/paper/2305.12030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 19 May 2023.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Overcoming Catastrophic Forgetting in Graph Neural Networks](https://mlsanity.com/paper/2012.06002/) (2020)
- [Lifelong Graph Learning](https://mlsanity.com/paper/2009.00647/) (2020)
- [Graph Lifelong Learning: A Survey](https://mlsanity.com/paper/2202.10688/) (2022)
- [Hierarchical Prototype Networks for Continual Graph Representation Learning](https://mlsanity.com/paper/2111.15422/) (2021)
- [Graph-Based Continual Learning](https://mlsanity.com/paper/2007.04813/) (2020)
- [Formalizing the Generalization-Forgetting Trade-off in Continual Learning](https://mlsanity.com/paper/2109.14035/) (2021)
- [Lifelong Learning of Graph Neural Networks for Open-World Node Classification](https://mlsanity.com/paper/2006.14422/) (2020)
- [Continual Graph Learning: A Survey](https://mlsanity.com/paper/2301.12230/) (2023)
- [Representation Learning over Dynamic Graphs](https://mlsanity.com/paper/1803.04051/) (2018)
- [AgEBO-Tabular: Joint Neural Architecture and Hyperparameter Search with Autotuned Data-Parallel Training for Tabular Data](https://mlsanity.com/paper/2010.16358/) (2020)
- [The convergence of the Stochastic Gradient Descent (SGD) : a self-contained proof](https://mlsanity.com/paper/2103.14350/) (2021)
- [Meta Continual Learning via Dynamic Programming](https://mlsanity.com/paper/2008.02219/) (2020)

## Abstract (arXiv)

Continual learning~(CL) is a field concerned with learning a series of inter-related task with the tasks typically defined in the sense of either regression or classification. In recent years, CL has been studied extensively when these tasks are defined using Euclidean data -- data, such as images, that can be described by a set of vectors in an n-dimensional real space. However, the literature is quite sparse, when the data corresponding to a CL task is nonEuclidean -- data , such as graphs, point clouds or manifold, where the notion of similarity in the sense of Euclidean metric does not hold. For instance, a graph is described by a tuple of vertices and edges and similarities between two graphs is not well defined through a Euclidean metric. Due to this fundamental nature of the data, developing CL for nonEuclidean data presents several theoretical and methodological challenges. In particular, CL for graphs requires explicit modelling of nonstationary behavior of vertices and edges and their effects on the learning problem. Therefore, in this work, we develop a adaptive dynamic programming viewpoint for CL with graphs. In this work, we formulate a two-player sequential game between the act of learning new tasks~(generalization) and remembering previously learned tasks~(forgetting). We prove mathematically the existence of a solution to the game and demonstrate convergence to the solution of the game. Finally, we demonstrate the efficacy of our method on a number of graph benchmarks with a comprehensive ablation study while establishing state-of-the-art performance.