# Invariant Link Selector for Spatial-Temporal Out-of-Distribution Problem

arXiv: https://arxiv.org/abs/2505.24178 · HTML: https://mlsanity.com/paper/2505.24178/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 74 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 30 of 40)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [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)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [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)
- [A Survey of Hallucination in Large Foundation Models](https://mlsanity.com/paper/2309.05922/) (2023)
- [Graph Retrieval-Augmented Generation: A Survey](https://mlsanity.com/paper/2408.08921/) (2024)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [Discovering Invariant Rationales for Graph Neural Networks](https://mlsanity.com/paper/2201.12872/) (2022)
- [Interpretable and Generalizable Graph Learning via Stochastic Attention Mechanism](https://mlsanity.com/paper/2201.12987/) (2022)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [Foundational Models Defining a New Era in Vision: A Survey and Outlook](https://mlsanity.com/paper/2307.13721/) (2023)
- [Out-Of-Distribution Generalization on Graphs: A Survey](https://mlsanity.com/paper/2202.07987/) (2022)
- [Position: Graph Foundation Models are Already Here](https://mlsanity.com/paper/2402.02216/) (2024)
- [Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatment](https://mlsanity.com/paper/2309.13378/) (2023)
- [Non-IID Transfer Learning on Graphs](https://mlsanity.com/paper/2212.08174/) (2022)
- [Generalized Out-of-Distribution Detection and Beyond in Vision Language Model Era: A Survey](https://mlsanity.com/paper/2407.21794/) (2024)
- [VCR-Graphormer: A Mini-batch Graph Transformer via Virtual Connections](https://mlsanity.com/paper/2403.16030/) (2024)
- [Environment-Aware Dynamic Graph Learning for Out-of-Distribution Generalization](https://mlsanity.com/paper/2311.11114/) (2023)
- [Graph Neural Bandits](https://mlsanity.com/paper/2308.10808/) (2023)
- [Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts](https://mlsanity.com/paper/2403.05026/) (2024)

## Built on by (most cited first, 5 of 5)

- [Graph4MM: Weaving Multimodal Learning with Structural Information](https://mlsanity.com/paper/2510.16990/) (2025)
- [Learnable Spatial-Temporal Positional Encoding for Link Prediction](https://mlsanity.com/paper/2506.08309/) (2025)
- [HeroFilter: Adaptive Spectral Graph Filter for Varying Heterophilic Relations](https://mlsanity.com/paper/2510.10864/) (2025)
- [OWLEYE: Zero-Shot Learner for Cross-Domain Graph Data Anomaly Detection](https://mlsanity.com/paper/2601.19102/) (2026)
- [Towards OOD Generalization in Dynamic Graphs via Causal Invariant Learning](https://mlsanity.com/paper/2603.01626/) (2026)

## Abstract (arXiv)

In the era of foundation models, Out-of- Distribution (OOD) problems, i.e., the data discrepancy between the training environments and testing environments, hinder AI generalization. Further, relational data like graphs disobeying the Independent and Identically Distributed (IID) condition makes the problem more challenging, especially much harder when it is associated with time. Motivated by this, to realize the robust invariant learning over temporal graphs, we want to investigate what components in temporal graphs are most invariant and representative with respect to labels. With the Information Bottleneck (IB) method, we propose an error-bounded Invariant Link Selector that can distinguish invariant components and variant components during the training process to make the deep learning model generalizable for different testing scenarios. Besides deriving a series of rigorous generalizable optimization functions, we also equip the training with task-specific loss functions, e.g., temporal link prediction, to make pretrained models solve real-world application tasks like citation recommendation and merchandise recommendation, as demonstrated in our experiments with state-of-the-art (SOTA) methods. Our code is available at https://github.com/kthrn22/OOD-Linker.