# Learning to Approximate Adaptive Kernel Convolution on Graphs

arXiv: https://arxiv.org/abs/2401.11840 · HTML: https://mlsanity.com/paper/2401.11840/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 41 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (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)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classification](https://mlsanity.com/paper/2306.08385/) (2023)
- [How to Find Your Friendly Neighborhood: Graph Attention Design with Self-Supervision](https://mlsanity.com/paper/2204.04879/) (2022)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Graph Convolutional Encoders for Syntax-aware Neural Machine Translation](https://mlsanity.com/paper/1704.04675/) (2017)
- [Structural Entropy Guided Graph Hierarchical Pooling](https://mlsanity.com/paper/2206.13510/) (2022)
- [Text Level Graph Neural Network for Text Classification](https://mlsanity.com/paper/1910.02356/) (2019)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Deep Iterative and Adaptive Learning for Graph Neural Networks](https://mlsanity.com/paper/1912.07832/) (2019)
- [Node-wise Diffusion for Scalable Graph Learning](https://mlsanity.com/paper/2305.14000/) (2023)
- [Time-aware Random Walk Diffusion to Improve Dynamic Graph Learning](https://mlsanity.com/paper/2211.01214/) (2022)
- [Fast Polynomial Approximation of Heat Kernel Convolution on Manifolds and Its Application to Brain Sulcal and Gyral Graph Pattern Analysis](https://mlsanity.com/paper/1911.02721/) (2019)

## Built on by (most cited first, 6 of 6)

- [OCL: Ordinal Contrastive Learning for Imputating Features with Progressive Labels](https://mlsanity.com/paper/2503.02899/) (2025)
- [Modality-Agnostic Style Transfer for Holistic Feature Imputation](https://mlsanity.com/paper/2503.02898/) (2025)
- [Machine Learning on Dynamic Functional Connectivity: Promise, Pitfalls, and Interpretations](https://mlsanity.com/paper/2409.11377/) (2024)
- [Learning Multi-Scale Hypergraph for High-Order Brain Connectivity Analysis](https://mlsanity.com/paper/2606.03310/) (2026)
- [Multi-Modal Graph Neural Network with Transformer-Guided Adaptive Diffusion for Preclinical Alzheimer Classification](https://mlsanity.com/paper/2606.03322/) (2026)
- [Spectral Graph Neural Networks with Hermite Polynomials: A Comprehensive Study](https://mlsanity.com/paper/2609.28979/) (2026)

## Abstract (arXiv)

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers increases. The issue stems from the intrinsic formulation of conventional graph convolution where the nodal features are aggregated from a direct neighborhood per layer across the entire nodes in the graph. As setting different number of hidden layers per node is infeasible, recent works leverage a diffusion kernel to redefine the graph structure and incorporate information from farther nodes. Unfortunately, such approaches suffer from heavy diagonalization of a graph Laplacian or learning a large transform matrix. In this regards, we propose a diffusion learning framework, where the range of feature aggregation is controlled by the scale of a diffusion kernel. For efficient computation, we derive closed-form derivatives of approximations of the graph convolution with respect to the scale, so that node-wise range can be adaptively learned. With a downstream classifier, the entire framework is made trainable in an end-to-end manner. Our model is tested on various standard datasets for node-wise classification for the state-of-the-art performance, and it is also validated on a real-world brain network data for graph classifications to demonstrate its practicality for Alzheimer classification.