# Spectral Networks and Locally Connected Networks on Graphs

arXiv: https://arxiv.org/abs/1312.6203 · HTML: https://mlsanity.com/paper/1312.6203/

## Key facts

- Cited by 1,102 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2013.

## Built on by (most cited first, 30 of 1102)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
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- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Vision GNN: An Image is Worth Graph of Nodes](https://mlsanity.com/paper/2206.00272/) (2022)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Sign and Basis Invariant Networks for Spectral Graph Representation Learning](https://mlsanity.com/paper/2202.13013/) (2022)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [Training Graph Neural Networks with 1000 Layers](https://mlsanity.com/paper/2106.07476/) (2021)
- [On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology](https://mlsanity.com/paper/2302.02941/) (2023)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
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- [Large-scale Multi-Modal Pre-trained Models: A Comprehensive Survey](https://mlsanity.com/paper/2302.10035/) (2023)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [GraphSMOTE: Imbalanced Node Classification on Graphs with Graph Neural Networks](https://mlsanity.com/paper/2103.08826/) (2021)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Nested Graph Neural Networks](https://mlsanity.com/paper/2110.13197/) (2021)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Decoupled Dynamic Spatial-Temporal Graph Neural Network for Traffic Forecasting](https://mlsanity.com/paper/2206.09112/) (2022)

## Abstract (arXiv)

Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures.