# Beyond Graph Convolutional Network: An Interpretable Regularizer-centered Optimization Framework

arXiv: https://arxiv.org/abs/2301.04318 · HTML: https://mlsanity.com/paper/2301.04318/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 37 references that are in the map.
- First posted on arXiv 11 Jan 2023.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Multi-Label Image Recognition with Graph Convolutional Networks](https://mlsanity.com/paper/1904.03582/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [AM-GCN: Adaptive Multi-channel Graph Convolutional Networks](https://mlsanity.com/paper/2007.02265/) (2020)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [Multi-Range Attentive Bicomponent Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/1911.12093/) (2019)
- [Graph Neural Networks Inspired by Classical Iterative Algorithms](https://mlsanity.com/paper/2103.06064/) (2021)
- [AdaGCN: Adaboosting Graph Convolutional Networks into Deep Models](https://mlsanity.com/paper/1908.05081/) (2019)
- [Multi-level Graph Convolutional Networks for Cross-platform Anchor Link Prediction](https://mlsanity.com/paper/2006.01963/) (2020)
- [A New Perspective on the Effects of Spectrum in Graph Neural Networks](https://mlsanity.com/paper/2112.07160/) (2021)
- [Learnable Graph Convolutional Network and Feature Fusion for Multi-view Learning](https://mlsanity.com/paper/2211.09155/) (2022)
- [Connecting Graph Convolutional Networks and Graph-Regularized PCA](https://mlsanity.com/paper/2006.12294/) (2020)

## Built on by (most cited first, 3 of 3)

- [Bridging Trustworthiness and Open-World Learning: An Exploratory Neural Approach for Enhancing Interpretability, Generalization, and Robustness](https://mlsanity.com/paper/2308.03666/) (2023)
- [DGNN: Decoupled Graph Neural Networks with Structural Consistency between Attribute and Graph Embedding Representations](https://mlsanity.com/paper/2401.15584/) (2024)
- [BAED: a New Paradigm for Few-shot Graph Learning with Explanation in the Loop](https://mlsanity.com/paper/2603.01941/) (2026)

## Abstract (arXiv)

Graph convolutional networks (GCNs) have been attracting widespread attentions due to their encouraging performance and powerful generalizations. However, few work provide a general view to interpret various GCNs and guide GCNs' designs. In this paper, by revisiting the original GCN, we induce an interpretable regularizer-centerd optimization framework, in which by building appropriate regularizers we can interpret most GCNs, such as APPNP, JKNet, DAGNN, and GNN-LF/HF. Further, under the proposed framework, we devise a dual-regularizer graph convolutional network (dubbed tsGCN) to capture topological and semantic structures from graph data. Since the derived learning rule for tsGCN contains an inverse of a large matrix and thus is time-consuming, we leverage the Woodbury matrix identity and low-rank approximation tricks to successfully decrease the high computational complexity of computing infinite-order graph convolutions. Extensive experiments on eight public datasets demonstrate that tsGCN achieves superior performance against quite a few state-of-the-art competitors w.r.t. classification tasks.