Paper: Graph Representation Learning with Multi-granular Semantic Ensemble (ICLR-2024)

Reviewer comment (Experiments):
The effectiveness of the proposed framework is largely depended by the selection of prototype numbers, which determines the semantic levels learned by student models. However, the selection procedure of this set of hyperparameters is not clearly justified in the current draft.

Author response:
Thank you for your valuable suggestion. We introduce the selection of the $K$ sets prototypes number in page 5 and the default setting in the key hyper-parameters of Appendix E. To illustrate it again, we assign the number of prototypes in each set in descending order, i.e., $D_1 > D_2 > \cdots > D_K > 1$. We highlight the corresponding part with green in the updated paper version. Besides, we conduct experiments to evaluate the impacts of different prototype set numbers in the experiment section (left subplot of Figure 5).  
Upon reviewing the paper of IMP, we find that the known label space ($C$) and annotated support set are prioritized considerations for the Infinite Mixture Prototypes (IMP) in [1]. The learnable prototype numbers (clusters) are inferred based on a specified condition (e.g., $\operatorname{min}_{c} d_ic < \lambda$). It is crucial to note that the priority conditions required by IMP may not be provided in the context of self-supervised Learning (SSL) settings, rendering IMP unsuitable for SSL tasks. Consequently, a direct comparison between the two prototype number selection schemes may not be entirely fair. Our work aims to learn multi-granularity semantic features to adapt to various downstream tasks. In this regard, a SSL-based framework ensures that the extracted features are sufficiently generalizable for subsequent fine-tuning in downstream applications.
Meanwhile, we acknowledge the potential of an adaptive prototype number selection schema tailored for SSL tasks as an intriguing research direction. Designing specific criteria to determine conditions for adjusting prototype numbers in SSL settings could offer valuable insights and warrant exploration in future research endeavors.

[1] Allen, Kelsey, et al. "Infinite mixture prototypes for few-shot learning." International conference on machine learning. PMLR, 2019.

Reviewer comment (Experiments):
It seems that authors use some heuristic methods to determine the prototype numbers for multi-student distillation. Such heuristic method can hardly capture the intrinsic semantic structures underlying the pre-training dataset. By comparison, the prototype number determination scheme explored in [a] can better discover such structure in a learnable way. Can authors justify their prototype number selection scheme against such method with some theoretical or empirical results?

Author response:
Thank you for your valuable suggestion. We introduce the selection of the $K$ sets prototypes number in page 5 and the default setting in the key hyper-parameters of Appendix E. To illustrate it again, we assign the number of prototypes in each set in descending order, i.e., $D_1 > D_2 > \cdots > D_K > 1$. We highlight the corresponding part with green in the updated paper version. Besides, we conduct experiments to evaluate the impacts of different prototype set numbers in the experiment section (left subplot of Figure 5).  
Upon reviewing the paper of IMP, we find that the known label space ($C$) and annotated support set are prioritized considerations for the Infinite Mixture Prototypes (IMP) in [1]. The learnable prototype numbers (clusters) are inferred based on a specified condition (e.g., $\operatorname{min}_{c} d_ic < \lambda$). It is crucial to note that the priority conditions required by IMP may not be provided in the context of self-supervised Learning (SSL) settings, rendering IMP unsuitable for SSL tasks. Consequently, a direct comparison between the two prototype number selection schemes may not be entirely fair. Our work aims to learn multi-granularity semantic features to adapt to various downstream tasks. In this regard, a SSL-based framework ensures that the extracted features are sufficiently generalizable for subsequent fine-tuning in downstream applications.
Meanwhile, we acknowledge the potential of an adaptive prototype number selection schema tailored for SSL tasks as an intriguing research direction. Designing specific criteria to determine conditions for adjusting prototype numbers in SSL settings could offer valuable insights and warrant exploration in future research endeavors.

[1] Allen, Kelsey, et al. "Infinite mixture prototypes for few-shot learning." International conference on machine learning. PMLR, 2019.

Reviewer comment (Evaluation):
Authors are suggested to show the semantic prototypes learned for both molecular graphs and PPI graphs. Such visualization can help to understand the learning mechanism of the proposed method.

Author response:
Thanks for your suggestion. To address your concern, we add a case study to visually illustrate the knowledge learned by student models trained with different granularities, showcasing their effectiveness across different downstream tasks. Due to the constraints of the open review platform, we are unable to directly upload figures. Therefore, we update the case study in Appendix G after the main paper. We kindly invite you to refer to Appendix G for additional details and visualizations.

Reviewer comment (Novelty):
The primary methodology of the paper appears to draw significant inspiration from the ProtoNCE loss, originally from the visual domain, as candidly acknowledged by the authors in “our optimization objective can be an analogy to the ProtoNCE loss to maximize the mutual information at cluster-level”. This brings forth concerns regarding the novelty and distinctiveness of the paper's central contribution. While adapting this approach to the context of GNNs is commendable, it seems that the crux of the innovation might be largely credited to the ProtoNCE loss itself.

Author response:
> Thanks for raising this question. As introduced in the introduction part, the primary motivations of our work are to analyze the generalizability of existing graph self-supervised methods and propose a framework to improve it. Through experiments conducted on multiple well-established datasets across diverse domains, we empirically demonstrate that the promising performance observed in existing methods on one or two datasets often fails to translate into robust generalization across all datasets. Given the sub-optimal generalization ability and the diversified structural indicators in different graph-related tasks, we posit the assumption that **Could multi-granularity graph semantic features further improve the generalization ability of learned representations in different downstream applications?** and propose the corresponding MGSE framework to enable the learning of multi-granularity semantic features.  Though the ProtoNCE loss is not our contribution, we believe that the philosophy of combining multi-granularity graph semantics is the pivotal factor leading to performance improvement, which can taken as the most important contribution of this work. Our assumption is also supported by the comprehensive empirical study in this work, MGSE achieves the best data generalization by comparing with six state-of-the-art competitive baselines with performance improvement of up to 9.2%, facilitated by our proposed multi-granular semantic ensemble that extracts comprehensive representations from input graphs.
While algorithmic and architectural innovations are critical for driving progress in the field, works such as [1, 2, 3] that offer robust and insightful empirical investigations and studies of different aspects of performance (i.e., multi-granular graph representations for stronger generalization) are also essential for advancing our collective understanding of the existing research gaps. Therefore, we believe that our work could be a valuable contribution to the research community.

[1] Knowledge distillation: A good teacher is patient and consistent In CVPR 2022

[2] What Makes for Good Views for Contrastive Learning? In Neurips 2020

[3] Is Homophily a Necessity for Graph Neural Networks? In ICLR 2022

Reviewer comment (Reproducibility):
The structure of the paper, particularly in Section 4, lacks comprehensive detail. With only two pages dedicated to the methodology, certain aspects remain unclear. For instance, the authors mention the construction of "K sets of corresponding trainable prototypes" but do not elucidate how these prototypes are updated. This omission leaves room for ambiguity and confusion.

Author response:
> Thanks for bringing up this question, we briefly illustrate the update mechanism of the K set prototypes at the lower part of page 5 and the upper part of page 6. To avoid confusion, We highlight this part in the updated paper file for reference. Here, we introduce the update mechanism in more detail for illustration. In our proposed MGSE, the teacher model is fixed and the K set trainable prototypes are optimized along with the K student models. Specifically, we compute the probability distributions ($\mathbf{p}^{t}$ and $\mathbf{p}^{s}$) of the teacher model and K student models on the K sets of prototypes as Equation (2), then measure their divergence with negative cross entropy as Equation (3).
The measured divergence will be used to optimize the K sets of prototypes and student models to align $\mathbf{p}^{t}$ and $\mathbf{p}^{s}$ through the same optimizer.
Meanwhile, as introduced on page 5, we add a ME-MAX regularization, i.e., Equation (4), to enforce as many prototypes to be utilized. The ME-MAX regularization along with the sharpen operation will optimize the K sets of prototypes in a meaningful and discriminative manner.

Reviewer comment (Reproducibility):
Could the authors clarify the update mechanism for the "K sets of corresponding trainable prototypes"?

Author response:
> Thanks for bringing up this question, we briefly illustrate the update mechanism of the K set prototypes at the lower part of page 5 and the upper part of page 6. To avoid confusion, We highlight this part in the updated paper file for reference. Here, we introduce the update mechanism in more detail for illustration. In our proposed MGSE, the teacher model is fixed and the K set trainable prototypes are optimized along with the K student models. Specifically, we compute the probability distributions ($\mathbf{p}^{t}$ and $\mathbf{p}^{s}$) of the teacher model and K student models on the K sets of prototypes as Equation (2), then measure their divergence with negative cross entropy as Equation (3).
The measured divergence will be used to optimize the K sets of prototypes and student models to align $\mathbf{p}^{t}$ and $\mathbf{p}^{s}$ through the same optimizer.
Meanwhile, as introduced on page 5, we add a ME-MAX regularization, i.e., Equation (4), to enforce as many prototypes to be utilized. The ME-MAX regularization along with the sharpen operation will optimize the K sets of prototypes in a meaningful and discriminative manner.

Reviewer comment (Experiments):
How does the proposed MGSE method compare with other fine-tuning techniques when applied to one base model?

Author response:
> To clarify, though our proposed MGSE is applied on the base graph SSL methods to diversify knowledge in different granularities, it does not require supervised information during the training phase. Therefore, our method should be categorized as a self-supervised learning framework like all the base methods. During the fine-tuning phase, we follow the same protocol, which is introduced in Appendix E, to finetune our method and all the teacher models with supervised information. 
To the best of our knowledge, there is currently no graph learning framework designed explicitly to leverage the knowledge of a graph self-supervised learning (SSL) model and further enhance its generalization ability in a self-supervised manner.  We consider this aspect to be a novelty and a noteworthy contribution of our proposed framework. We hope our work can offer a distinctive perspective and serve as inspiration for future research endeavors aimed at advancing the study of comprehensive and robust graph representation learning.

Reviewer comment (Experiments):
The paper argues that multiple student models exhibit diverse levels of granularity. So why not choose the best model for the downstream task but use an ensemble? It is essential to consider the possibility that combining models with varying levels of granularity might introduce conflicting or inconsistent information, leading to a negative impact on the overall performance of the downstream task. A thorough analysis and experimentation on the ensemble's potential drawbacks and benefits are warranted to address this concern.

Author response:
> Thanks for raising this question. We acknowledge that the utility of fine-grained versus coarse-grained knowledge may vary across specific downstream tasks, and the selection of the most informative knowledge granularity is task-dependent. However, a central motivation behind our paper is the development of a model that exhibits adaptability across a broad spectrum of downstream tasks. In situations where downstream tasks are not predefined, representations with multi-granularity semantics is more promising to achieve competitive performances across various tasks. This is supported by the observation that our proposed Multi-Granularity Semantic Embeddings (MGSE) consistently enhance the performances of all teacher models across diverse datasets and settings. Additionally, there are instances where a single application(dataset) requires knowledge at different granularities, particularly in multi-task scenarios. Our experimental observations further support this claim by the more substantial performance improvements on multi-label datasets, including Tox21, ToxCast, SIDER, ClinTox, and MUV.
> To further address your concern, we conduct additional experiments w.r.t. the performance of each single student model and the results are shown in the table below. We can observe that each student outperforms the teacher model (GraphCL), showing the effectiveness brought by the knowledge distillation. However, coupled with our proposed multi-granular ensemble mechanism, MGSE achieves the best performance across all variants and baselines.

|                           |      BBBP      |     Tox21      |    ToxCast     |     SIDER      |    ClinTox     |      HIV       |      BACE      |      MUV       |
| :-----------------------: | :------------: | :------------: | :------------: | :------------: | :------------: | :------------: | :------------: | :------------: |
| Teacher |   69.68±0.67   |   73.87±0.66   |   62.40±0.57   |   60.53±0.88   |   75.99±2.65   |   78.47±1.22   |   75.38±1.44   |   69.80±2.66   |
| MGSE (Student #1, K=50) |   71.20±0.92   |   75.33±0.70   |   63.85±0.35   |   60.83±0.65   |   77.37±1.28   |   77.87±1.48   |   77.66±0.64   |   71.06±1.33   |
| MGSE (Student #2, K=21) |   71.68±0.77   |   75.48±0.50   |   62.06±0.30   |   59.78±0.58   |   77.16±1.54   |   78.25±1.08   |   78.26±0.90   |   69.75±1.43   |
| MGSE (Student #3, K=2) |   68.75±0.69   |   72.88±0.70   |   60.29±0.58   |   57.66±0.32   |   74.63±1.06   |   76.84±1.65   |   75.16±0.87   |   68.73±1.25   |
|  MGSE (Average Ensemble 3 students)  | **72.26±0.65** | **75.89±0.33** | **64.57±0.34** | **61.44±0.68** | **78.67±2.89** | **79.07±0.72** | **79.22±0.93** | **71.46±1.45** |

Reviewer comment (Experiments):
Although the authors have designed different student models based on the analysis to capture knowledge at different granularities for solving various downstream tasks, it is important to visually demonstrate the distinct granularities of knowledge captured by each student model, rather than solely asserting that “different prototype sets capture different semantic granularities because we assign different numbers of prototypes to each prototype set in descending order”. The authors should consider adding a case study to provide a better explanation, like the mentioned example in the introduction about which knowledge in amino acids is coarse-grained and which knowledge is fine-grained.

Author response:
> Thanks for your suggestion. To address your concern, we add a case study to visually illustrate the knowledge learned by student models trained with different granularities, showcasing their effectiveness across different downstream tasks. Due to the constraints of the open review platform, we are unable to directly upload figures. Therefore, we update the case study in Appendix G after the main paper. We kindly invite you to refer to Appendix G for additional details and visualizations.

Reviewer comment (Experiments):
If I haven't missed any important details, as far as I know, the model ensemble can also lead to performance improvement. Therefore, it is crucial to determine whether the performance improvement comes from capturing knowledge at different granularities or is simply a result of the model ensemble strategy.

Author response:
> Yes, we have conducted experiments to verify that the performance improvements are not solely gained from the model ensemble and we demonstrate experimental results and corresponding analysis in the right subplot of Figure 3 and page 8. 
In the experiments, we add two other model ensemble variants without multi-granularity semantics learning design in our proposed framework. From the results we can find, that though the two variants based on model ensemble can also boost the teacher model’s performance to some extent, the improvement over MGSE is obviously larger, indicating the effectiveness of considering multiple granularities other than the model ensemble. Meanwhile, it is fair to say that a simple model ensemble strategy can not bring performance improvements as significant as our multi-granularity semantics learning design and we propose a more effective method to learn comprehensive graph knowledge based on the model ensemble.

Reviewer comment (Evaluation):
From the results, it can be observed that the designed framework brings some improvement, but this improvement comes at the cost of ensemble of multiple models. Additionally, although the authors have indicated that the proposed framework's computational complexity is proportional to the existing graph self-supervised models, considering the significant computational complexity of the original graph-based self-supervised models, it is uncertain whether this trade-off is worthwhile.

Author response:
> Thanks for bringing up this question. We admit that learning multi-granularity semantics through our designed framework incurs additional computational costs. However, we think that the trade-off is worthwhile for several reasons. 
> Firstly, GNNs are lightweight models compared to many backbones in other domains such as text and image processing. The computational complexity of our designs is proportional to existing graph self-supervised models, and thus, the scalability bottleneck of current graph SSL methods does not lie in the model size. Consequently, the performance improvements brought by our method do not significantly compromise computational efficiency.
> Secondly, although not the primary focus of this work, our proposed Multi-Granularity Semantic Embeddings (MGSE) demonstrate the potential for model compression. We have conducted experiments to investigate the impact of GNN model depth on final performance, as illustrated in the right subplot of Figure 4. The experimental results indicate that a larger model architecture consistently contributes positively to the final performance. Moreover, our framework has the capacity to approximate or even surpass the performance of over-parameterized teacher models with multiple lighter student models. Consequently, the results illustrate that the additional computation cost incurred by incorporating multiple student models can be mitigated by achieving comparable results with a lighter student model architecture.
> Finally, we respectively argue that a model architecture with sufficient capacity is paramount for enhancing generalization ability. Though our proposed MGSE can not achieve simialr effects to the foundational models in the NLP and CV domains, our goal is to improve the generalization ability of existing graph SSL methods. This enables them to seamlessly adapt to diverse downstream graph-related applications with more competitive performances, which is validated by the comprehensive experiments presented in our paper. Therefore, we believe the increased computation cost is justified in light of the broader goal of advancing model generalization ability.