# HeroFilter: Adaptive Spectral Graph Filter for Varying Heterophilic Relations

arXiv: https://arxiv.org/abs/2510.10864 · HTML: https://mlsanity.com/paper/2510.10864/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 48 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Builds on (most cited first, 30 of 37)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [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)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [A Survey of Transformers](https://mlsanity.com/paper/2106.04554/) (2021)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Semantic Graph Convolutional Networks for 3D Human Pose Regression](https://mlsanity.com/paper/1904.03345/) (2019)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Exphormer: Sparse Transformers for Graphs](https://mlsanity.com/paper/2303.06147/) (2023)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillation](https://mlsanity.com/paper/2110.08727/) (2021)
- [PolyFormer: Referring Image Segmentation as Sequential Polygon Generation](https://mlsanity.com/paper/2302.07387/) (2023)
- [NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs](https://mlsanity.com/paper/2206.04910/) (2022)
- [A Survey of Visual Transformers](https://mlsanity.com/paper/2111.06091/) (2021)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [SNAP: A General Purpose Network Analysis and Graph Mining Library](https://mlsanity.com/paper/1606.07550/) (2016)
- [Gradient Gating for Deep Multi-Rate Learning on Graphs](https://mlsanity.com/paper/2210.00513/) (2022)
- [SkipGNN: Predicting Molecular Interactions with Skip-Graph Networks](https://mlsanity.com/paper/2004.14949/) (2020)
- [VCR-Graphormer: A Mini-batch Graph Transformer via Virtual Connections](https://mlsanity.com/paper/2403.16030/) (2024)
- [Block Modeling-Guided Graph Convolutional Neural Networks](https://mlsanity.com/paper/2112.13507/) (2021)
- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [Revisiting Graph-Based Fraud Detection in Sight of Heterophily and Spectrum](https://mlsanity.com/paper/2312.06441/) (2023)
- [Learning Graph Quantized Tokenizers](https://mlsanity.com/paper/2410.13798/) (2024)

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

- [GegenbauerNet: Finding the Optimal Compromise in the GNN Flexibility-Stability Trade-off](https://mlsanity.com/paper/2511.13730/) (2025)
- [L-JacobiNet and S-JacobiNet: An Analysis of Adaptive Generalization, Stabilization, and Spectral Domain Trade-offs in GNNs](https://mlsanity.com/paper/2511.16081/) (2025)
- [Ftextsuperscript2LP-AP: Fast & Flexible Label Propagation with Adaptive Propagation Kernel](https://mlsanity.com/paper/2604.20736/) (2026)

## Abstract (arXiv)

Graph heterophily, where connected nodes have different labels, has attracted significant interest recently. Most existing works adopt a simplified approach - using low-pass filters for homophilic graphs and high-pass filters for heterophilic graphs. However, we discover that the relationship between graph heterophily and spectral filters is more complex - the optimal filter response varies across frequency components and does not follow a strict monotonic correlation with heterophily degree. This finding challenges conventional fixed filter designs and suggests the need for adaptive filtering to preserve expressiveness in graph embeddings. Formally, natural questions arise: Given a heterophilic graph G, how and to what extent will the varying heterophily degree of G affect the performance of GNNs? How can we design adaptive filters to fit those varying heterophilic connections? Our theoretical analysis reveals that the average frequency response of GNNs and graph heterophily degree do not follow a strict monotonic correlation, necessitating adaptive graph filters to guarantee good generalization performance. Hence, we propose [METHOD NAME], a simple yet powerful GNN, which extracts information across the heterophily spectrum and combines salient representations through adaptive mixing. [METHOD NAME]'s superior performance achieves up to 9.2% accuracy improvement over leading baselines across homophilic and heterophilic graphs.