# Infinite-Horizon Graph Filters: Leveraging Power Series to Enhance Sparse Information Aggregation

arXiv: https://arxiv.org/abs/2401.09943 · HTML: https://mlsanity.com/paper/2401.09943/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 43 references that are in the map.
- First posted on arXiv 18 Jan 2024.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [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)
- [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)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Representing Long-Range Context for Graph Neural Networks with Global Attention](https://mlsanity.com/paper/2201.08821/) (2022)
- [Adaptive Graph Encoder for Attributed Graph Embedding](https://mlsanity.com/paper/2007.01594/) (2020)
- [Dissecting the Diffusion Process in Linear Graph Convolutional Networks](https://mlsanity.com/paper/2102.10739/) (2021)
- [GRAND+: Scalable Graph Random Neural Networks](https://mlsanity.com/paper/2203.06389/) (2022)
- [Learning Strong Graph Neural Networks with Weak Information](https://mlsanity.com/paper/2305.18457/) (2023)
- [Feature Overcorrelation in Deep Graph Neural Networks: A New Perspective](https://mlsanity.com/paper/2206.07743/) (2022)
- [Uncertainty Quantification via Spatial-Temporal Tweedie Model for Zero-inflated and Long-tail Travel Demand Prediction](https://mlsanity.com/paper/2306.09882/) (2023)
- [Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes](https://mlsanity.com/paper/2309.12971/) (2023)
- [A Generalized Neural Diffusion Framework on Graphs](https://mlsanity.com/paper/2312.08616/) (2023)
- [Rethinking Spectral Graph Neural Networks with Spatially Adaptive Filtering](https://mlsanity.com/paper/2401.09071/) (2024)
- [Why Rumors Spread Fast in Social Networks, and How to Stop It](https://mlsanity.com/paper/2305.08558/) (2023)

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

- [FaiMA: Feature-aware In-context Learning for Multi-domain Aspect-based Sentiment Analysis](https://mlsanity.com/paper/2403.01063/) (2024)
- [Rethinking Graph Domain Adaptation: A Spectral Contrastive Perspective](https://mlsanity.com/paper/2510.13254/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have shown considerable effectiveness in a variety of graph learning tasks, particularly those based on the message-passing approach in recent years. However, their performance is often constrained by a limited receptive field, a challenge that becomes more acute in the presence of sparse graphs. In light of the power series, which possesses infinite expansion capabilities, we propose a novel Graph Power Filter Neural Network (GPFN) that enhances node classification by employing a power series graph filter to augment the receptive field. Concretely, our GPFN designs a new way to build a graph filter with an infinite receptive field based on the convergence power series, which can be analyzed in the spectral and spatial domains. Besides, we theoretically prove that our GPFN is a general framework that can integrate any power series and capture long-range dependencies. Finally, experimental results on three datasets demonstrate the superiority of our GPFN over state-of-the-art baselines.