# A Unified Invariant Learning Framework for Graph Classification

arXiv: https://arxiv.org/abs/2501.12595 · HTML: https://mlsanity.com/paper/2501.12595/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 15 references that are in the map.
- First posted on arXiv 22 Jan 2025.

## Builds on (most cited first, 8 of 8)

- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.06607/) (2021)
- [GOOD: A Graph Out-of-Distribution Benchmark](https://mlsanity.com/paper/2206.08452/) (2022)
- [Causal Attention for Interpretable and Generalizable Graph Classification](https://mlsanity.com/paper/2112.15089/) (2021)
- [Graph Rationalization with Environment-based Augmentations](https://mlsanity.com/paper/2206.02886/) (2022)
- [Learning Graphons via Structured Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2012.05644/) (2020)
- [Dynamic Sparse Learning: A Novel Paradigm for Efficient Recommendation](https://mlsanity.com/paper/2402.02855/) (2024)
- [Exploring Lottery Ticket Hypothesis in Media Recommender Systems](https://mlsanity.com/paper/2108.00944/) (2021)

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

- [Hierarchical Time-Aware Mixture of Experts for Multi-Modal Sequential Recommendation](https://mlsanity.com/paper/2501.14269/) (2025)
- [SimCT: Recovering Lost Supervision for Cross-Tokenizer On-Policy Distillation](https://mlsanity.com/paper/2605.07711/) (2026)
- [Identifying and Correcting Label Noise for Robust GNNs via Influence Contradiction](https://mlsanity.com/paper/2601.17469/) (2026)
- [Transferable Graph Condensation from the Causal Perspective](https://mlsanity.com/paper/2601.21309/) (2026)
- [CGRL: Causal-Guided Representation Learning for Node-Level Out-of-Distribution Generalization](https://mlsanity.com/paper/2603.24304/) (2026)

## Abstract (arXiv)

Invariant learning demonstrates substantial potential for enhancing the generalization of graph neural networks (GNNs) with out-of-distribution (OOD) data. It aims to recognize stable features in graph data for classification, based on the premise that these features causally determine the target label, and their influence is invariant to changes in distribution. Along this line, most studies have attempted to pinpoint these stable features by emphasizing explicit substructures in the graph, such as masked or attentive subgraphs, and primarily enforcing the invariance principle in the semantic space, i.e., graph representations. However, we argue that focusing only on the semantic space may not accurately identify these stable features. To address this, we introduce the Unified Invariant Learning (UIL) framework for graph classification. It provides a unified perspective on invariant graph learning, emphasizing both structural and semantic invariance principles to identify more robust stable features. In the graph space, UIL adheres to the structural invariance principle by reducing the distance between graphons over a set of stable features across different environments. Simultaneously, to confirm semantic invariance, UIL underscores that the acquired graph representations should demonstrate exemplary performance across diverse environments. We present both theoretical and empirical evidence to confirm our method's ability to recognize superior stable features. Moreover, through a series of comprehensive experiments complemented by in-depth analyses, we demonstrate that UIL considerably enhances OOD generalization, surpassing the performance of leading baseline methods. Our codes are available at https://github.com/yongduosui/UIL.