# MAGIC: Topology-Aware Analytic Graph Few-Shot Class-Incremental Learning

arXiv: https://arxiv.org/abs/2610.04963 · HTML: https://mlsanity.com/paper/2610.04963/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 29 of 29)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2004.10956/) (2020)
- [Few-Shot Incremental Learning with Continually Evolved Classifiers](https://mlsanity.com/paper/2104.03047/) (2021)
- [Forward Compatible Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2203.06953/) (2022)
- [Overcoming Catastrophic Forgetting in Graph Neural Networks](https://mlsanity.com/paper/2012.06002/) (2020)
- [ACIL: Analytic Class-Incremental Learning with Absolute Memorization and Privacy Protection](https://mlsanity.com/paper/2205.14922/) (2022)
- [AnyGraph: Graph Foundation Model in the Wild](https://mlsanity.com/paper/2408.10700/) (2024)
- [CaT: Balanced Continual Graph Learning with Graph Condensation](https://mlsanity.com/paper/2309.09455/) (2023)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Graph Few-shot Class-incremental Learning](https://mlsanity.com/paper/2112.12819/) (2021)
- [Geometer: Graph Few-Shot Class-Incremental Learning via Prototype Representation](https://mlsanity.com/paper/2205.13954/) (2022)
- [An Efficient Memory Module for Graph Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2411.06659/) (2024)
- [PUMA: Efficient Continual Graph Learning for Node Classification with Graph Condensation](https://mlsanity.com/paper/2312.14439/) (2023)
- [Graph Continual Learning with Debiased Lossless Memory Replay](https://mlsanity.com/paper/2404.10984/) (2024)
- [Semi-Supervised Node Classification on Graphs: Markov Random Fields vs. Graph Neural Networks](https://mlsanity.com/paper/2012.13085/) (2020)
- [View Space: Learning Representation across Arbitrary Graphs](https://mlsanity.com/paper/2512.11561/) (2025)
- [GraphKeeper: Graph Domain-Incremental Learning via Knowledge Disentanglement and Preservation](https://mlsanity.com/paper/2511.00097/) (2025)
- [Inductive Graph Few-shot Class Incremental Learning](https://mlsanity.com/paper/2411.06634/) (2024)

## Abstract (arXiv)

Graph few-shot class-incremental learning (GFSCIL) requires a model to continually recognize emerging classes from only a few labeled nodes while preserving previously acquired knowledge. Beyond the catastrophic forgetting inherited from conventional graph continual learning, GFSCIL presents two distinctive challenges: extremely limited novel-class supervision causes severe overfitting, while cross-session edges---edges connecting newly arriving nodes with historical nodes---alter historical propagation neighborhoods and thereby induce representation drift. We propose MAGIC, a replay-free GFSCIL framework that combines a frozen graph representation backbone (e.g., an intrinsically parameter-free backbone such as SGC or a pretrained graph foundation model) with closed-form analytic continual learning. To alleviate novel-session overfitting, MAGIC learns a topological prior from the base graph that can characterize both homophilous and heterophilous relations, and injects this prior through Potts Markov random field inference to refine supervision for novel classes. To mitigate representation drift, MAGIC transfers previous predictions from the old representations of affected historical nodes to their updated representations through drift-aware analytic distillation. Experiments across five datasets and eight baselines demonstrate the effectiveness of MAGIC. Under the 5-shot setting, MAGIC improves Mean Accuracy and Final Accuracy by 5.48 percentage points and 9.33 percentage points on average, and reduces Performance Drop by 10.78 percentage points on average compared with the best baselines. MAGIC also shows clear advantages under the 1- and 3-shot settings, with larger gains as the number of supports increases. Moreover, MAGIC requires substantially less training time.