Title: MultiNet: Adaptive Multi-Viewed Subgraph Convolutional Networks for Graph Classification
Venue: NeurIPS 2025
Accepted: yes
Keywords: Graph Convolutional Networks

Graph Classification

Over-smoothing
Abstract: The problem of over-smoothing has emerged as a fundamental issue for Graph Convolutional Networks (GCNs). While existing efforts primarily focus on enhancing the discriminability of node representations for node classification, they tend to overlook the over-smoothing at the graph level, significantly influencing the performance of graph classification. In this paper, we provide an explanation of the graph-level over-smoothing phenomenon and propose a novel Adaptive Multi-Viewed Subgraph Convolutional Network (MultiNet) to address this challenge. Specifically, the MultiNet introduces a local subgraph convolution module that adaptively divides each input graph into multiple subgraph views. Then a number of subgraph-based view-specific convolution operations are applied to constrain the extent of node information propagation over the original global graph structure, not only mitigating the over-smoothing issue but also generating more discriminative local node representations. Moreover, we develop an alignment-based readout that establishes correspondences between nodes over different graphs, thereby effectively preserving the local node-level structure information and improving the discriminative ability of the resulting graph-level representations. Theoretical analysis and empirical studies show that the MultiNet mitigates the graph-level over-smoothing and achieves excellent performance for graph classification.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper defines a new graph neural network, namely the Adaptive Multi-viewed Subgraph Convolutional Network (MultiNet), for graph classification. Unlike the classical GNNs, the new MultiNet is defined based on the subgraph convolution operation within the substructures. The substructures are divided by assign different attentions on the nodes, and each substructure consists of nodes with higher attention. Therefore, performing the convolution operation on the substructure essentially equals to performing a subgraph convolution, and this strategy can help to reduce the over-smoothing problem. Because, the information passing is limited among different subgraphs. The new MultiNet have better graph classification performance than the classical GNN methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\nAn interesting idea to reduce the over-smoothing for graph classification.\nGood idea to define new subgraph convolution operation with the attention mechanism.   \nOverall, this paper is clearly written and easy to follow.\n\nExcluding the strengths, I still have some major concerns. Please see Questions.\n\nQUESTIONS:\nI think the authors need to answer my following questions, and the paper can be further improved.\n\nFirst, Eq. 4 and Eq. 8 have the same form, what is the difference between them?\n\nSecond, the node-level over-smoothing is always discussed by many works, what is the difference between the node-level and graph-level over-smoothing? \n\nThird, some minor grammar mistakes need to be fixed, such the sentence on row 184, “where the extent to which a node transmits its information to neighbors...”, there are two leading words of subordinate clause (where and which) .\n\nFourth, as I remember the MUTAG and PTC data was well evaluated by many classical methods, including the DGCNN and GIN, why the authors did not include the results？\n\nLIMITATIONS:\nI have listed some limitations in Questions, such as some grammar and statement problems.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces MultiNet, a novel Adaptive Multi-Viewed Subgraph Convolutional Network designed to address graph-level over-smoothing in Graph Convolutional Networks (GCNs). By leveraging local subgraph convolution and alignment-based readout mechanisms, MultiNet enhances graph classification performance through preserving local node features and structural information.\n\nSTRENGTHS AND WEAKNESSES:\nS1. MultiNet adaptively divides graphs into multiple subgraph views, capturing discriminative local node features and mitigating node-level over-smoothing.\n\nS2. Establishes node correspondences across graphs, enabling expressive readout functions that preserve structural information and reduce graph-level over-smoothing.\n\nS3. Demonstrates effectiveness in mitigating over-smoothing and achieving state-of-the-art graph classification performance on benchmark datasets.\n\nW1. The paper claims that solving node-level over-smoothing cannot fully address graph-level over-smoothing due to the permutation invariance of traditional readout functions. However, the authors do not provide sufficient theoretical or experimental evidence to support this claim. Moreover, the proposed model still relies on permutation-invariant aggregation, which raises questions about whether the issue is truly resolved.\n\nW2. The ultimate goal of addressing over-smoothing is to improve model performance. However, the experimental results show that the proposed model primarily mitigates the performance degradation caused by deeper layers, rather than leveraging deeper propagation to achieve better overall performance. This limits the practical benefits of the model.\n\nW3. The paper lacks comparisons with recent graph-level algorithms. Without such comparisons, it is difficult to evaluate the effectiveness of the proposed method in optimizing graph-level representations.\n\nW4. The aggregation process in the proposed model closely resembles matrix factorization, particularly in the use of the node assignment matrix to map node embeddings to cluster-level embeddings. However, the paper does not explicitly discuss this similarity or provide theoretical validation for the effectiveness of this design. Adding a discussion and validation of matrix factorization approximations would strengthen the paper's contributions.\n\nQUESTIONS:\nQ1. How does the paper theoretically or experimentally prove that permutation invariance of traditional readout functions is the primary cause of graph-level over-smoothing?\nQ2. Given that the proposed model still relies on permutation-invariant aggregation, how does it fundamentally address graph-level over-smoothing?\n\nQ3. Does the proposed model leverage deeper propagation to achieve better performance, or does it primarily focus on mitigating performance degradation caused by deeper layers?\n\nQ4. Are there any experiments showing that the model outperforms shallower networks in terms of classification accuracy?\n\nQ5. Why does the paper not include comparisons with state-of-the-art graph-level algorithms? How does the proposed method optimize graph-level representations compared to these recent approaches?\n\nQ6. How does the aggregation process in the proposed model relate to matrix factorization techniques? Can the authors provide theoretical or experimental validation to demonstrate the effectiveness of using matrix factorization-like operations in the model design?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper develops a new Adaptive Multi-Viewed Subgraph Convolutional Network (MultiNet) to solve the over-smoothing problem and improve the graph classification performance. The MultiNet is defined based on the subgraph convolution on divided subgraphs from the original global graph. The experiments on standard datasets confirm the performance of the MultiNet. Overall, this paper is well-written, easy to follow and  and technically sound.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n1. This paper defines an end-to-end framework to adaptively divide the input graph into subgraph views, and perform the local convolution on the subgraphs to limit the information passing among different subgraph views. So, the new MultiNet can avoid the over-smoothing problem. \n2. This paper defines a new local convolution filter on the subgraph view with the attentions of adjacent nodes. The new filter can propagate the node information based on the attention and limit the information of nodes with lower attention.\n3. The authors provide necessary theoretical analysis to confirm the advantages of  the new MultiNet.\n\n**Weaknesses**\n1. The over-smoothing is always a serious problem for node classification, but how the over-smoothing influence the graph classification? More theoretical analysis or descriptions are needed. \n2. Why use the alignment readout, why do not directly use the sum or avg pooing? These operations are widely used for graph neural networks to extract graph representation.\n3. For table 1, the accuracies of some method are missed, why not compare them? \n4. The authors also need to cite some necessary references about graph over-smoothing problem, not only list the references about node over-smoothing.\n\nQUESTIONS:\nSome statements need to be more clear. Some experiments are missed. Some technology details need to be well explained. Please refer my rebuttal weakness for details.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work aims to reduce the effects of the graph-level over-smoothing problem for graph classification, and proposes a novel MultiNet model (a new graph neural network, GNN). This paper first analyze how the over-smoothing influences the graph representation learning through the GNN. Then, this paper proposes to perform the attention-based subgraph convolution on adaptive extracted subgraph based views, that focuses on the information propagation within the subgraph view and naturally reduce the information passing over the global structure. The experiments on benchmark datasets show the superior performance for the proposed MultiNet model.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. An interesting strategy to divide the global graph structure into subgraph-based views, and perform the subgraph convolution to reduce the over-smoothing problem of the convolution operation on the global structure.\n2. Provide mathematical analysis to show how the MultiNet works and limits the over-smoothing over the global structure.\n Weakness:\nIt seems that each subgraph view is not completely isolated from the global graph structure, since the substructure is identified by node attentions. Although the information may be mainly propagated between high attention nodes, the information may still pass between the low attention nodes. The authors did not clearly explain this problem.\n\nQUESTIONS:\n1. I feel a little confused for the symbol P^(j) between the equations (11) and (12), should it be P_j ? It is not consistent to other symbol P_j. Maybe, it is a typos?\n2. For the experiments, why some GNN models are not evaluated on the MUTAG and PTC datasets?\n\nLIMITATIONS:\nI think some theoretical analysis about how the proposed method reduce the graph-level over-smoothing need to be more clear. As I say in the weakness, the information seems still pass between low attention nodes, this may lead to some minor over-smoothing problem.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-01"}