# Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts

arXiv: https://arxiv.org/abs/2403.05026 · HTML: https://mlsanity.com/paper/2403.05026/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 102 references that are in the map.
- First posted on arXiv 8 Mar 2024.

## Builds on (most cited first, 30 of 59)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [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)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Heterogeneous Graph Attention Network](https://mlsanity.com/paper/1903.07293/) (2019)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [A Fourier-based Framework for Domain Generalization](https://mlsanity.com/paper/2105.11120/) (2021)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Self-Supervised Contrastive Pre-Training For Time Series via Time-Frequency Consistency](https://mlsanity.com/paper/2206.08496/) (2022)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [Focal Frequency Loss for Image Reconstruction and Synthesis](https://mlsanity.com/paper/2012.12821/) (2020)
- [Improving Out-of-Distribution Robustness via Selective Augmentation](https://mlsanity.com/paper/2201.00299/) (2022)
- [Inductive Representation Learning in Temporal Networks via Causal Anonymous Walks](https://mlsanity.com/paper/2101.05974/) (2021)
- [Invariant Risk Minimization Games](https://mlsanity.com/paper/2002.04692/) (2020)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Handling Distribution Shifts on Graphs: An Invariance Perspective](https://mlsanity.com/paper/2202.02466/) (2022)

## Built on by (most cited first, 19 of 19)

- [A Comprehensive Survey of Dynamic Graph Neural Networks: Models, Frameworks, Benchmarks, Experiments and Challenges](https://mlsanity.com/paper/2405.00476/) (2024)
- [RealTCD: Temporal Causal Discovery from Interventional Data with Large Language Model](https://mlsanity.com/paper/2404.14786/) (2024)
- [Graph Representation Learning via Causal Diffusion for Out-of-Distribution Recommendation](https://mlsanity.com/paper/2408.00490/) (2024)
- [USBD: Universal Structural Basis Distillation for Source-Free Graph Domain Adaptation](https://mlsanity.com/paper/2602.08431/) (2026)
- [Invariant Link Selector for Spatial-Temporal Out-of-Distribution Problem](https://mlsanity.com/paper/2505.24178/) (2025)
- [Graph Memory Learning: Imitating Lifelong Remembering and Forgetting of Brain Networks](https://mlsanity.com/paper/2407.19183/) (2024)
- [Self-Evolving Agents as Dynamic Graph Transformation: A Survey and New Perspective](https://mlsanity.com/paper/2608.18104/) (2026)
- [A Survey of Out-of-distribution Generalization for Graph Machine Learning from a Causal View](https://mlsanity.com/paper/2409.09858/) (2024)
- [Evolving Graph Learning for Out-of-Distribution Generalization in Non-stationary Environments](https://mlsanity.com/paper/2511.02354/) (2025)
- [Simple yet Effective Node Property Prediction on Edge Streams under Distribution Shifts](https://mlsanity.com/paper/2504.00328/) (2025)
- [Federated Causal Inference in Healthcare: Methods, Challenges, and Applications](https://mlsanity.com/paper/2505.02238/) (2025)
- [Robust Anomaly Detection Under Normality Distribution Shift in Dynamic Graphs](https://mlsanity.com/paper/2509.17400/) (2025)
- [Test-time GNN Model Evaluation on Dynamic Graphs](https://mlsanity.com/paper/2509.23816/) (2025)
- [Towards Single-Source Domain Generalized Object Detection via Causal Visual Prompts](https://mlsanity.com/paper/2510.19487/) (2025)
- [Towards OOD Generalization in Dynamic Graphs via Causal Invariant Learning](https://mlsanity.com/paper/2603.01626/) (2026)
- [Causal-aware Graph Neural Architecture Search under Distribution Shifts](https://mlsanity.com/paper/2405.16489/) (2024)
- [Debugging Tabular Log as Dynamic Graphs](https://mlsanity.com/paper/2512.22903/) (2025)
- [SPR: Toward a Graph Foundation Model for Transferable Graph Cognition via Spectral Patterns and Relational Geometry](https://mlsanity.com/paper/2606.03315/) (2026)
- [Differentiable Koopman Operator for Contrastive Learning on Dynamic Graphs](https://mlsanity.com/paper/2610.02990/) (2026)

## Abstract (arXiv)

Dynamic graph neural networks (DyGNNs) currently struggle with handling distribution shifts that are inherent in dynamic graphs. Existing work on DyGNNs with out-of-distribution settings only focuses on the time domain, failing to handle cases involving distribution shifts in the spectral domain. In this paper, we discover that there exist cases with distribution shifts unobservable in the time domain while observable in the spectral domain, and propose to study distribution shifts on dynamic graphs in the spectral domain for the first time. However, this investigation poses two key challenges: i) it is non-trivial to capture different graph patterns that are driven by various frequency components entangled in the spectral domain; and ii) it remains unclear how to handle distribution shifts with the discovered spectral patterns. To address these challenges, we propose Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts (SILD), which can handle distribution shifts on dynamic graphs by capturing and utilizing invariant and variant spectral patterns. Specifically, we first design a DyGNN with Fourier transform to obtain the ego-graph trajectory spectrums, allowing the mixed dynamic graph patterns to be transformed into separate frequency components. We then develop a disentangled spectrum mask to filter graph dynamics from various frequency components and discover the invariant and variant spectral patterns. Finally, we propose invariant spectral filtering, which encourages the model to rely on invariant patterns for generalization under distribution shifts. Experimental results on synthetic and real-world dynamic graph datasets demonstrate the superiority of our method for both node classification and link prediction tasks under distribution shifts.