# Nonparametric Teaching for Graph Property Learners

arXiv: https://arxiv.org/abs/2505.14170 · HTML: https://mlsanity.com/paper/2505.14170/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 81 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 30 of 58)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Data-Efficient Image Recognition with Contrastive Predictive Coding](https://mlsanity.com/paper/1905.09272/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [GraphNorm: A Principled Approach to Accelerating Graph Neural Network Training](https://mlsanity.com/paper/2009.03294/) (2020)
- [RelBench: A Benchmark for Deep Learning on Relational Databases](https://mlsanity.com/paper/2407.20060/) (2024)

## Built on by (most cited first, 5 of 5)

- [NTK-Guided Implicit Neural Teaching](https://mlsanity.com/paper/2511.15487/) (2025)
- [Nonparametric Teaching of Attention Learners](https://mlsanity.com/paper/2602.20461/) (2026)
- [Large-Scale Bayesian Tensor Reconstruction via Approximate Message Passing](https://mlsanity.com/paper/2505.16305/) (2025)
- [Fighter: Unveiling the Graph Convolutional Nature of Transformers in Time Series Modeling](https://mlsanity.com/paper/2510.17106/) (2025)
- [Model Evolution Under Zeroth-Order Optimization: A Neural Tangent Kernel Perspective](https://mlsanity.com/paper/2603.21169/) (2026)

## Abstract (arXiv)

Inferring properties of graph-structured data, e.g., the solubility of molecules, essentially involves learning the implicit mapping from graphs to their properties. This learning process is often costly for graph property learners like Graph Convolutional Networks (GCNs). To address this, we propose a paradigm called Graph Neural Teaching (GraNT) that reinterprets the learning process through a novel nonparametric teaching perspective. Specifically, the latter offers a theoretical framework for teaching implicitly defined (i.e., nonparametric) mappings via example selection. Such an implicit mapping is realized by a dense set of graph-property pairs, with the GraNT teacher selecting a subset of them to promote faster convergence in GCN training. By analytically examining the impact of graph structure on parameter-based gradient descent during training, and recasting the evolution of GCNs--shaped by parameter updates--through functional gradient descent in nonparametric teaching, we show for the first time that teaching graph property learners (i.e., GCNs) is consistent with teaching structure-aware nonparametric learners. These new findings readily commit GraNT to enhancing learning efficiency of the graph property learner, showing significant reductions in training time for graph-level regression (-36.62%), graph-level classification (-38.19%), node-level regression (-30.97%) and node-level classification (-47.30%), all while maintaining its generalization performance.