# AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filter

arXiv: https://arxiv.org/abs/2104.12840 · HTML: https://mlsanity.com/paper/2104.12840/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 60 references that are in the map.
- First posted on arXiv 26 Apr 2021.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [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)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Convolutional Neural Networks for Sentence Classification](https://mlsanity.com/paper/1408.5882/) (2014)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)

## Built on by (most cited first, 30 of 43)

- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [ARC: A Generalist Graph Anomaly Detector with In-Context Learning](https://mlsanity.com/paper/2405.16771/) (2024)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [Partitioning Message Passing for Graph Fraud Detection](https://mlsanity.com/paper/2412.00020/) (2024)
- [How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implications](https://mlsanity.com/paper/2106.07767/) (2021)
- [Homophily-oriented Heterogeneous Graph Rewiring](https://mlsanity.com/paper/2302.06299/) (2023)
- [Node-oriented Spectral Filtering for Graph Neural Networks](https://mlsanity.com/paper/2212.03654/) (2022)
- [On Manipulating Signals of User-Item Graph: A Jacobi Polynomial-based Graph Collaborative Filtering](https://mlsanity.com/paper/2306.03624/) (2023)
- [Graph Neural Networks with Diverse Spectral Filtering](https://mlsanity.com/paper/2312.09041/) (2023)
- [From Few-Shot to Zero-Shot: Towards Generalist Graph Anomaly Detection](https://mlsanity.com/paper/2602.18793/) (2026)
- [A Piece-wise Polynomial Filtering Approach for Graph Neural Networks](https://mlsanity.com/paper/2112.03499/) (2021)
- [Finding Heterophilic Neighbors via Confidence-based Subgraph Matching for Semi-supervised Node Classification](https://mlsanity.com/paper/2302.09755/) (2023)
- [Robust Graph Representation Learning for Local Corruption Recovery](https://mlsanity.com/paper/2202.04936/) (2022)
- [A Comprehensive Benchmark on Spectral GNNs: The Impact on Efficiency, Memory, and Effectiveness](https://mlsanity.com/paper/2406.09675/) (2024)
- [MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks](https://mlsanity.com/paper/2409.05100/) (2024)
- [Improving Your Graph Neural Networks: A High-Frequency Booster](https://mlsanity.com/paper/2210.08251/) (2022)
- [Rethinking Spectral Graph Neural Networks with Spatially Adaptive Filtering](https://mlsanity.com/paper/2401.09071/) (2024)
- [Cross-Space Adaptive Filter: Integrating Graph Topology and Node Attributes for Alleviating the Over-smoothing Problem](https://mlsanity.com/paper/2401.14876/) (2024)
- [Graph Neural Networks Are More Than Filters: Revisiting and Benchmarking from A Spectral Perspective](https://mlsanity.com/paper/2412.07188/) (2024)
- [Complementarity-Supervised Spectral-Band Routing for Multimodal Emotion Recognition](https://mlsanity.com/paper/2603.13340/) (2026)
- [Uplifting Message Passing Neural Network with Graph Original Information](https://mlsanity.com/paper/2210.05382/) (2022)
- [GANN: Graph Alignment Neural Network for Semi-Supervised Learning](https://mlsanity.com/paper/2303.07778/) (2023)
- [Muti-scale Graph Neural Network with Signed-attention for Social Bot Detection: A Frequency Perspective](https://mlsanity.com/paper/2307.01968/) (2023)
- [Differentiable Cluster Graph Neural Network](https://mlsanity.com/paper/2405.16185/) (2024)
- [Efficient Identity and Position Graph Embedding via Spectral-Based Random Feature Aggregation](https://mlsanity.com/paper/2505.20992/) (2025)
- [Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification](https://mlsanity.com/paper/2402.09600/) (2024)

## Abstract (arXiv)

Graph Neural Networks have recently become a prevailing paradigm for various high-impact graph analytical problems. Existing efforts can be mainly categorized as spectral-based and spatial-based methods. The major challenge for the former is to find an appropriate graph filter to distill discriminative information from input signals for learning. Recently, myriads of explorations are made to achieve better graph filters, e.g., Graph Convolutional Network (GCN), which leverages Chebyshev polynomial truncation to seek an approximation of graph filters and bridge these two families of methods. Nevertheless, it has been shown in recent studies that GCN and its variants are essentially employing fixed low-pass filters to perform information denoising. Thus their learning capability is rather limited and may over-smooth node representations at deeper layers. To tackle these problems, we develop a novel graph neural network framework AdaGNN with a well-designed adaptive frequency response filter. At its core, AdaGNN leverages a simple but elegant trainable filter that spans across multiple layers to capture the varying importance of different frequency components for node representation learning. The inherent differences among different feature channels are also well captured by the filter. As such, it empowers AdaGNN with stronger expressiveness and naturally alleviates the over-smoothing problem. We empirically validate the effectiveness of the proposed framework on various benchmark datasets. Theoretical analysis is also provided to show the superiority of the proposed AdaGNN. The open-source implementation of AdaGNN can be found here: https://github.com/yushundong/AdaGNN.