Title: Pruning Spurious Subgraphs for Graph Out-of-Distribution Generalization
Venue: NeurIPS 2025
Accepted: yes
Keywords: OOD generalization

invariant learning

graph neural networks
Abstract: Graph Neural Networks (GNNs) often encounter significant performance degradation under distribution shifts between training and test data, hindering their applicability in real-world scenarios. Recent studies have proposed various methods to address the out-of-distribution (OOD) generalization challenge, with many methods in the graph domain focusing on directly identifying an invariant subgraph that is predictive of the target label. However, we argue that identifying the edges from the invariant subgraph directly is challenging and error-prone, especially when some spurious edges exhibit strong correlations with the targets. In this paper, we propose $\texttt{PrunE}$, the first pruning-based graph OOD method that eliminates spurious edges to improve OOD generalizability. By pruning spurious edges, $\texttt{PrunE}$ retains the invariant subgraph more comprehensively, which is critical for OOD generalization. Specifically, $\texttt{PrunE}$ employs two regularization terms to prune spurious edges: 1) _graph size constraint_ to exclude uninformative spurious edges, and 2) _$\epsilon$-probability alignment_ to further suppress the occurrence of spurious edges. Through theoretical analysis and extensive experiments, we show that $\texttt{PrunE}$ achieves superior OOD performance and outperforms previous state-of-the-art methods significantly.


Peer reviews:
comments: SUMMARY:
The paper proposes a graph OOD generalization algorithm via graph pruning. The motivation is that the key of OOD generalization is to identify the invariance parts (subgraphs) but some sprious edges prevent the model find the true invariant subgraphs. Thus, the authors want to prune these edges to let the model better understand the invariances in the graph.

STRENGTHS AND WEAKNESSES:
Strengths:
1. The paper is easy to follow and well-written.
2. The motivation of pruning sprious edges seens to make sense. 
3. The theoretical analysis further reveals the superiority of the method. 

Weaknesses:
1. Despite the authors claim sprious edges is a significant issue in identifying key subgraphs, they do not provide an analysis on how and why it happen. 
2. Following the previous one, the authors also do not clearly answer why the edge pruning could be suitable to handle the issue. Do there have any other strategies?

QUESTIONS:
1. Do the authors can provide an in-depth analysis to show whether the sprious edges would be the key limitation in identifying the invariant subgraphs and why the edge pruning be the most suitable strategy?

LIMITATIONS:
See weaknesses.
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-02

comments: SUMMARY:
The paper introduces PrunE, aiming to improve out-of-distribution (OOD) generalization in Graph Neural Networks (GNNs). Specifically, instead of directly identifying invariant subgraphs, PrunE, focuses on pruning spurious edges from the graph, employing two main regularization terms, i.e., graph size constraint and probability alignment: Forces the lowest K% of edge probabilities toward zero, further reducing the presence of spurious edges. Theoretical analysis and extensive experiments on both synthetic and real-world datasets seem to demonstrate the effectiveness of the proposed method.

STRENGTHS AND WEAKNESSES:
The strengths of this paper can be summarized as follows:

+ PrunE introduces an intuitive and simple learning paradigm for OOD generalization in graphs: rather than directly identifying invariant subgraphs, it prunes spurious edges. The method is conceptually simple, with only two lightweight regularization terms, making it easy to implement and tune.

+ In addition, by operating directly in the input space and pruning explicit edges, PrunE offers clear interpretability: the retained subgraph after pruning highlights the parts of the graph most relevant to the prediction. Additionally, the method is computationally efficient, with runtime and memory overheads comparable to standard ERM and lower than many other OOD methods.

Meanwhile, this paper also has the following weakness:

- It seems counterintuitive to model the edges in the graph independently.

- The simplicity of the method is both a strengths and weakness. The two regularization terms seem ad hoc, where the motivation of combining them together need to be further enhanced in the paper.

QUESTIONS:
Please refer to my summary of weakness.

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-03

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe proposed method, *PrunE* addresses OOD generalization problem in graph representation learning from a novel perspective, graph sparsification. Compared to previous graph OOD methods, *PrunE* adopts a surprisingly simple yet effective prune strategy, which is designed to preserve more invariant substructure, at a cost of slightly increased uninformative edges. The proposed methods demonstrate extraordinary performance in extensive empirical studies.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The authors introduce a novel perspective for addressing the graph OOD problem, graph sparsification. \n2. The proposed method, *PrunE*, demonstrates significant performance improvements over a wide range of baseline methods in various datasets.\n3. The paper is well written, and the motivation is clear.\n\nWeaknesses:\n1. The theory in this paper is very similar to the graph lottery ticket, but the related works are not cited.\n2. Graph sparsification is a large research area. The proposed *PrunE* leverages a very basic method, and according to the basic theory, other graph sparsification methods may also work in an OOD scenario. However, this is not noted in the paper.\n3. There is a typo in Table 2. The reported number is EC50-assay instead of EC50-sca.\n\nQUESTIONS:\nIt seems to me that the *PrunE* method itself is similar to some very old graph sparsification methods[1]. However, such work (as well as the whole graph sparsification domain, e.g., [2]) is not introduced in the paper, and the well-known **lottery ticket theory** is not even mentioned in the paper. Can authors justify or clarify this?\n\n[1] Chen, Tianlong, et al. \"A unified lottery ticket hypothesis for graph neural networks.\" ICML 2021.\n\n[2] Bo Hui and Da Yan and Xiaolong Ma and Wei-Shinn Ku, Rethinking Graph Lottery Tickets: Graph Sparsity Matters, ICLR 2023\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 2, "DATE": "2025-07-03"}

comments: SUMMARY:
The paper improves GNN robustness and generalization by identifying and pruning spurious subgraphs—structures correlated with predictions but not causally relevant. Using a causal framework, it employs counterfactual reasoning to detect these subgraphs and a generative model to create perturbed graphs for comparison. Pruning the spurious parts reduces shortcut learning and enhances out-of-distribution performance.

STRENGTHS AND WEAKNESSES:
Strengths:1.Well-motivated problem: The issue of spurious correlations in GNNs is important and underexplored. The paper provides a strong motivation grounded in causal inference and generalization theory. 2. Novel integration of causality in GNN pruning: While causality has been used in graph learning, this paper’s combination of generative counterfactual modeling and pruning of subgraphs for generalization is novel. 3.Good use of visualizations: Diagrams and figures help illustrate key components like the counterfactual generation and pruning mechanism.

Weaknesses: 1. Overall, this is a solid work. However, "spurious subgraphs are structural patterns in the input graph that are correlated with prediction labels in the training data but are not causally relevant to the true task." Is there any real world example besides the MUTAG dataset that demonstrate this? I am not sure this issue existed for every datasets in the realworld. Therefore not sure how this 

2. Figure 6 and Figure 7's results shows the model successfully find the important subgraphs. It seems this results are similar to a lot of GNN explanation work. For example, if I use GNNExplainer for find the subgraph, will this be very different from yours ?

QUESTIONS:
Same to weakness. Overall I think this is a good paper.

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-04