# Multi-Head Spectral-Adaptive Graph Anomaly Detection

arXiv: https://arxiv.org/abs/2512.22291 · HTML: https://mlsanity.com/paper/2512.22291/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 25 Dec 2025.

## Builds on (most cited first, 27 of 27)

- [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)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [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)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Anti-Money Laundering in Bitcoin: Experimenting with Graph Convolutional Networks for Financial Forensics](https://mlsanity.com/paper/1908.02591/) (2019)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [From Amateurs to Connoisseurs: Modeling the Evolution of User Expertise through Online Reviews](https://mlsanity.com/paper/1303.4402/) (2013)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [Tackling Over-Smoothing for General Graph Convolutional Networks](https://mlsanity.com/paper/2008.09864/) (2020)
- [AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filter](https://mlsanity.com/paper/2104.12840/) (2021)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Analysis of stochastic Lanczos quadrature for spectrum approximation](https://mlsanity.com/paper/2105.06595/) (2021)
- [Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filtering](https://mlsanity.com/paper/2107.04755/) (2021)
- [Spectral-Based Graph Neural Networks for Complementary Item Recommendation](https://mlsanity.com/paper/2401.02130/) (2024)
- [Chi-Square Wavelet Graph Neural Networks for Heterogeneous Graph Anomaly Detection](https://mlsanity.com/paper/2505.18934/) (2025)
- [GRASPED: Graph Anomaly Detection using Autoencoder with Spectral Encoder and Decoder (Full Version)](https://mlsanity.com/paper/2508.15633/) (2025)

## Abstract (arXiv)

Graph anomaly detection technology has broad applications in financial fraud and risk control. However, existing graph anomaly detection methods often face significant challenges when dealing with complex and variable abnormal patterns, as anomalous nodes are often disguised and mixed with normal nodes, leading to the coexistence of homophily and heterophily in the graph domain. Recent spectral graph neural networks have made notable progress in addressing this issue; however, current techniques typically employ fixed, globally shared filters. This 'one-size-fits-all' approach can easily cause over-smoothing, erasing critical high-frequency signals needed for fraud detection, and lacks adaptive capabilities for different graph instances. To solve this problem, we propose a Multi-Head Spectral-Adaptive Graph Neural Network (MHSA-GNN). The core innovation is the design of a lightweight hypernetwork that, conditioned on a 'spectral fingerprint' containing structural statistics and Rayleigh quotient features, dynamically generates Chebyshev filter parameters tailored to each instance. This enables a customized filtering strategy for each node and its local subgraph. Additionally, to prevent mode collapse in the multi-head mechanism, we introduce a novel dual regularization strategy that combines teacher-student contrastive learning (TSC) to ensure representation accuracy and Barlow Twins diversity loss (BTD) to enforce orthogonality among heads. Extensive experiments on four real-world datasets demonstrate that our method effectively preserves high-frequency abnormal signals and significantly outperforms existing state-of-the-art methods, especially showing excellent robustness on highly heterogeneous datasets.