# Layer-wise Adaptive Graph Convolution Networks Using Generalized Pagerank

arXiv: https://arxiv.org/abs/2108.10636 · HTML: https://mlsanity.com/paper/2108.10636/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 21 references that are in the map.
- First posted on arXiv 24 Aug 2021.

## Builds on (most cited first, 17 of 17)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks](https://mlsanity.com/paper/2012.07690/) (2020)
- [Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks](https://mlsanity.com/paper/2003.08414/) (2020)
- [Optimizing Generalized PageRank Methods for Seed-Expansion Community Detection](https://mlsanity.com/paper/1905.10881/) (2019)
- [Optimization and Generalization Analysis of Transduction through Gradient Boosting and Application to Multi-scale Graph Neural Networks](https://mlsanity.com/paper/2006.08550/) (2020)
- [Transductive Rademacher Complexity and its Applications](https://mlsanity.com/paper/1401.3441/) (2014)

## Built on by (most cited first, 2 of 2)

- [Graph in Graph Neural Network](https://mlsanity.com/paper/2407.00696/) (2024)
- [LGRPool: Hierarchical Graph Pooling Via Local-Global Regularisation](https://mlsanity.com/paper/2504.08530/) (2025)

## Abstract (arXiv)

We investigate adaptive layer-wise graph convolution in deep GCN models. We propose AdaGPR to learn generalized Pageranks at each layer of a GCNII network to induce adaptive convolution. We show that the generalization bound for AdaGPR is bounded by a polynomial of the eigenvalue spectrum of the normalized adjacency matrix in the order of the number of generalized Pagerank coefficients. By analysing the generalization bounds we show that oversmoothing depends on both the convolutions by the higher orders of the normalized adjacency matrix and the depth of the model. We performed evaluations on node-classification using benchmark real data and show that AdaGPR provides improved accuracies compared to existing graph convolution networks while demonstrating robustness against oversmoothing. Further, we demonstrate that analysis of coefficients of layer-wise generalized Pageranks allows us to qualitatively understand convolution at each layer enabling model interpretations.