# Topology-Aware Active Learning on Graphs

arXiv: https://arxiv.org/abs/2510.25892 · HTML: https://mlsanity.com/paper/2510.25892/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 63 references that are in the map.
- First posted on arXiv 29 Oct 2025.

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

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Label Propagation for Deep Semi-supervised Learning](https://mlsanity.com/paper/1904.04717/) (2019)
- [Learning to Propagate Labels: Transductive Propagation Network for Few-shot Learning](https://mlsanity.com/paper/1805.10002/) (2018)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Coverage-centric Coreset Selection for High Pruning Rates](https://mlsanity.com/paper/2210.15809/) (2022)
- [FoSR: First-order spectral rewiring for addressing oversquashing in GNNs](https://mlsanity.com/paper/2210.11790/) (2022)
- [On the Trade-off between Over-smoothing and Over-squashing in Deep Graph Neural Networks](https://mlsanity.com/paper/2212.02374/) (2022)
- [Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates](https://mlsanity.com/paper/2006.11184/) (2020)
- [Analysis of p-Laplacian Regularization in Semi-Supervised Learning](https://mlsanity.com/paper/1707.06213/) (2017)
- [A variational approach to the consistency of spectral clustering](https://mlsanity.com/paper/1508.01928/) (2015)
- [Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms](https://mlsanity.com/paper/1805.09450/) (2018)
- [Properly-weighted graph Laplacian for semi-supervised learning](https://mlsanity.com/paper/1810.04351/) (2018)
- [Consistency of Lipschitz learning with infinite unlabeled data and finite labeled data](https://mlsanity.com/paper/1710.10364/) (2017)
- [Curvature-based Clustering on Graphs](https://mlsanity.com/paper/2307.10155/) (2023)
- [Spectral Analysis Of Weighted Laplacians Arising In Data Clustering](https://mlsanity.com/paper/1909.06389/) (2019)
- [Graph Pooling via Ricci Flow](https://mlsanity.com/paper/2407.04236/) (2024)
- [PTN: A Poisson Transfer Network for Semi-supervised Few-shot Learning](https://mlsanity.com/paper/2012.10844/) (2020)
- [Model-Change Active Learning in Graph-Based Semi-Supervised Learning](https://mlsanity.com/paper/2110.07739/) (2021)
- [Graph-based Active Learning for Semi-supervised Classification of SAR Data](https://mlsanity.com/paper/2204.00005/) (2022)
- [Heterophily-Aware Graph Attention Network](https://mlsanity.com/paper/2302.03228/) (2023)
- [Poisson Reweighted Laplacian Uncertainty Sampling for Graph-based Active Learning](https://mlsanity.com/paper/2210.15786/) (2022)
- [Cautious Active Clustering](https://mlsanity.com/paper/2008.01245/) (2020)
- [LaplaceNet: A Hybrid Graph-Energy Neural Network for Deep Semi-Supervised Classification](https://mlsanity.com/paper/2106.04527/) (2021)
- [Multiscale Laplacian Learning](https://mlsanity.com/paper/2109.03718/) (2021)
- [Novel Batch Active Learning Approach and Its Application to Synthetic Aperture Radar Datasets](https://mlsanity.com/paper/2307.10495/) (2023)
- [Graph Interpolating Activation Improves Both Natural and Robust Accuracies in Data-Efficient Deep Learning](https://mlsanity.com/paper/1907.06800/) (2019)

## Abstract (arXiv)

We propose a graph-topological approach to active learning that directly targets the core challenge of exploration versus exploitation under scarce label budgets. To guide exploration, we introduce a coreset construction algorithm based on Balanced Forman Curvature (BFC), which selects representative initial labels that reflect the graph's cluster structure. This method includes a data-driven stopping criterion that signals when the graph has been sufficiently explored. We further use BFC to dynamically trigger the shift from exploration to exploitation within active learning routines, replacing hand-tuned heuristics. To improve exploitation, we introduce a localized graph rewiring strategy that efficiently incorporates multiscale information around labeled nodes, enhancing label propagation while preserving sparsity. Experiments on benchmark classification tasks show that our methods consistently outperform existing graph-based semi-supervised baselines at low label rates.