# DFNets: Spectral CNNs for Graphs with Feedback-Looped Filters

arXiv: https://arxiv.org/abs/1910.10866 · HTML: https://mlsanity.com/paper/1910.10866/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2019.

## Built on by (most cited first, 10 of 10)

- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [Regular Splitting Graph Network for 3D Human Pose Estimation](https://mlsanity.com/paper/2305.05785/) (2023)
- [Motif Graph Neural Network](https://mlsanity.com/paper/2112.14900/) (2021)
- [Higher-Order Implicit Fairing Networks for 3D Human Pose Estimation](https://mlsanity.com/paper/2111.00950/) (2021)
- [Graph Neural Networks With Lifting-based Adaptive Graph Wavelets](https://mlsanity.com/paper/2108.01660/) (2021)
- [Node Copying: A Random Graph Model for Effective Graph Sampling](https://mlsanity.com/paper/2208.02435/) (2022)
- [Self-Supervised Graph Representation Learning via Topology Transformations](https://mlsanity.com/paper/2105.11689/) (2021)
- [BiGCN: A Bi-directional Low-Pass Filtering Graph Neural Network](https://mlsanity.com/paper/2101.05519/) (2021)
- [Addressing the Impact of Localized Training Data in Graph Neural Networks](https://mlsanity.com/paper/2307.12689/) (2023)
- [Graph Self-Supervised Learning with Learnable Structural and Positional Encodings](https://mlsanity.com/paper/2502.16233/) (2025)

## Abstract (arXiv)

We propose a novel spectral convolutional neural network (CNN) model on graph structured data, namely Distributed Feedback-Looped Networks (DFNets). This model is incorporated with a robust class of spectral graph filters, called feedback-looped filters, to provide better localization on vertices, while still attaining fast convergence and linear memory requirements. Theoretically, feedback-looped filters can guarantee convergence w.r.t. a specified error bound, and be applied universally to any graph without knowing its structure. Furthermore, the propagation rule of this model can diversify features from the preceding layers to produce strong gradient flows. We have evaluated our model using two benchmark tasks: semi-supervised document classification on citation networks and semi-supervised entity classification on a knowledge graph. The experimental results show that our model considerably outperforms the state-of-the-art methods in both benchmark tasks over all datasets.