Rethinking Graph Out-Of-Distribution Generalization: A Learnable Random Walk Perspective
Henan Sun, Xunkai Li, Lei Zhu, Junyi Han, Guang Zeng, Ronghua Li, Guoren Wang
TL;DR
This paper introduces a learnable random walk approach for graph out-of-distribution generalization, addressing limitations of existing methods by modeling invariant knowledge through parameterized random walks and mutual information loss.
Contribution
It proposes LRW-OOD, a novel method that uses learnable random walks and KDE-based MI loss to improve graph OOD generalization under distribution shifts.
Findings
Achieves 3.87% accuracy improvement over state-of-the-art methods.
Effectively enhances graph OOD generalization across various distribution shifts.
Demonstrates the effectiveness of learnable random walks in capturing invariant knowledge.
Abstract
Out-Of-Distribution (OOD) generalization has gained increasing attentions for machine learning on graphs, as graph neural networks (GNNs) often exhibit performance degradation under distribution shifts. Existing graph OOD methods tend to follow the basic ideas of invariant risk minimization and structural causal models, interpreting the invariant knowledge across datasets under various distribution shifts as graph topology or graph spectrum. However, these interpretations may be inconsistent with real-world scenarios, as neither invariant topology nor spectrum is assured. In this paper, we advocate the learnable random walk (LRW) perspective as the instantiation of invariant knowledge, and propose LRW-OOD to realize graph OOD generalization learning. Instead of employing fixed probability transition matrix (i.e., degree-normalized adjacency matrix), we parameterize the transition matrix…
Peer Reviews
Decision·Submitted to ICLR 2026
1. The shift from seeking invariant topology/spectrum to learning invariant transition probabilities via random walks is interesting. 2. The paper is theoretically rigorous: rather than relying on heuristics, it formally links the learnable random walk framework to the OOD generalization objective. 3. The evaluation is thorough, covering multiple types of distribution shifts and a wide array of nine competitive baselines
1. While the proposed random walk method effectively extracts invariant knowledge through feature similarity, it appears less capable of capturing invariant subgraphs. This limitation may reduce its effectiveness under strong topological distribution shifts. 2. The ablation study on LRW uses a vanilla random walk GNN. A more informative comparison would include a variant employing a non-random-walk method, which could more clearly highlight the specific contribution of LRW. 3. The paper mentio
The paper addresses an important and timely problem in graph learning OOD generalization under distribution shifts. The proposed idea of viewing invariance through learnable random walks provides an interesting alternative to existing topology- and spectrum-based paradigms. The method is clearly described, with mathematical formulations and theoretical discussions that enhance readability. Experimental evaluations are good, covering multiple datasets and baseline comparisons.
The paper’s conceptual novelty is somewhat limited. The learnable random walk formulation largely reformulates known ideas about adaptive sampling and mutual-information-based regularization, without a fundamentally new theoretical insight. The related work section lacks a full discussion of prior random-walk-based or path-level GNN models, making it unclear how LRW-OOD truly departs from those approaches. Moreover, the experimental baselines, while broad, omit several recent and strong graph OO
Originality: The idea of using learnable random walk (LRW) sequences to capture invariant features across distribution shifts is innovative and interesting, offering a fresh perspective on graph OOD generalization. Theoretical Completeness: The paper provides solid theoretical grounding, demonstrating through rigorous proofs that LRW sequences can effectively capture invariant knowledge and align with OOD principles. Experimental Validation: Extensive experiments on Synthetic Datasets, Cross-d
Clarity and Presentation: Some sections could benefit from additional clarification. For example, the introduction's example is somewhat unclear and could be more straightforward. Additionally, the experimental setup on different datasets, while detailed in the appendix, would be clearer if briefly introduced in the main text. Insufficient Explanation of Random Walk Approach: The paper uses random walk sequences to address the limitations of existing methods, but more detailed explanation or ca
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Taxonomy
TopicsAdvanced Graph Neural Networks · Machine Learning in Healthcare · Graph Theory and Algorithms