Scalable Diffusion for Bio-topological Representation Learning on Brain Graphs

• Extensiveness of the experiments (datasets, baseline methods)

• In line 72, the authors claimed that the proposed method addresses ‘authentic’ bio-topological representations. I would like to ask why authors used the term ‘bio-topology’ instead of ‘topology’ and ask how they could capture the authentic bio-topological features. I assume that the bio-topological feature should reflect information derived from biologically meaningful topologies (e.g., brain networks defined on pre-defined atlases), while the topological features might represent features from any arbitrary types of brain parcellations. If this interpretation is correct, multi-scale bio-topology would then correspond to multiple brain networks defined on multiple pre-defined atlases (or other schemes that involve biological meanings). However, in this paper, they are simply set as graphs calculated using a hyperparameter $\lambda$, which may not sufficiently capture biologically meaningful structures.

• In line 755, the authors explained that they identified an ‘optimal’ set of scales $lambda = [0.5, 1.5]$, but it is unclear how they obtained these values. The authors explained that they used the knowledge of brain functional modules to set the scales, but providing much detailed explanation would be helpful. Which knowledge exactly do you used and how you applied it to set the parameter?

• Also, as the number of denoising step was set to 3, I understand that only three scales (i.e., 0.5, 1.0, and 1.5) were used to capture multi-scale features during denoising. I concern that this range of scales may be under-examined, and only using three scales may miss features from other resolution which could reflect critical topological information.

• The reason of setting the key parameters $\tau$ and $K$ to 0.5 and 1.0, respectively, are quite unclear to me. I assume that the maximum values of these parameters are not necessarily to be set as 1, and could be larger than 1. Also, setting the parameters identical across all nodes highly likely limit the flexibility to capture localized variations across nodes. In the appendix B, authors explained that a large $\tau$ may result in complicate community detection, but based on the Fig. 7, a smaller $\tau$ (Fig. 7a) seems resulting in more complicated communities across scales. Also, based on the same figure, the $\tau$ and scales $\lambda$ are dependent each other, which may need to set different $tau$ for different scale.

• Minor weakness: There are many typos, e.g., Vallina (Vanilla is correct) diffusion model in line 115. In line 132, the $i$ and $j$ should range from 1 to $N$ as the number of nodes is $N$. In line 748, ‘Figure 9’ needs to be replaced to ‘Figure 8’. In Table 1, ‘ANDI’ needs to be replaced to ‘ADNI’.

1. Some experiments are missing. How about the classification result of BrainSTORE by using a single modality like SC or FC? The baselines including BrainGNN and BrainGB only use a single modality, so it is hard to show that the better performance of BrainSTORE is due to the method itself or more modalities information.
2. In the visualization of classification results in Fig3, the ADNI has three classes, but the figure only shows two clusters, what does the color represent? HC, MCI, or AD? How about the result in PPMI dataset.
3. Fig4. shows the performance of the model using the scalable learning strategy. How do you replace it with a different algorithm?
4. The result of ADNI in Fig 4 and Fig 5 shows the single accuracy, but it conducts three binary classifications in table 1, do you conduct one vs one classification here? Table 2 should also shows the result of two datasets.
5. In explanation of community detection, the model assigned the nodes to different communities, is there any reference to support that some specific nodes belong to the same or different communities in patients from the clinical perspective?

1. Authors overlooked the difference between BrainSTORE and expressive graph neural networks either for general purposes, e.g. GSN [1] and PathNN [2], or dedicated to brain networks, e.g., NeuroPath [3]. These methods are expressive on high-order structures with various hops, making them multi-scale. What makes BrainSTORE more advanced than those three methods in your research problems?

[1] Bouritsas, Giorgos, et al. "Improving graph neural network expressivity via subgraph isomorphism counting." IEEE Transactions on Pattern Analysis and Machine Intelligence 45.1 (2022): 657-668.

[2] Michel, Gaspard, et al. "Path neural networks: Expressive and accurate graph neural networks." International Conference on Machine Learning. PMLR, 2023.

[3] Wei, Ziquan, et al. "NeuroPath: A Neural Pathway Transformer for Joining the Dots of Human Connectomes." arXiv preprint arXiv:2409.17510 (2024).

2. The motivation of this paper can be improved.

2.1. Limitations were claimed in Sec.1, 2nd paragraph as existing methods are constrained at a single scale, while there are expressive GNNs existing such as I mentioned in Weakness#1 that are not on a single scale. Additionally, BrainGNN reviewed in this work has multiple pooling layers to merge brain regions, which is also a multi-scale method.

2.2. The authors also overlooked their motivations for using diffusion methods in BrainSTORE. Please explain why representation learning methods other than denoising diffusion methods are not better.

3. Bio-topological properties are present multiple times without a specific description. For example, in Sec.2.1, 'these methods often overlook bio-topological properties within multimodal graphs, limiting their expressiveness' is hard to believe without a clear explanation. Do they refer to multi-scale representation? And to prevent misleading readers, does multi-scale in this work refer to various sub-graphs with different hops?

4. Figure 1 is lack of descriptions. What does the color of arrows refer to? Do the colored encoders in the bottom part of Figure 1 refer to $f_{theta}$? What is the definition of those colored decoders? What is the definition of $f_{theta}$ and Tran()? You should call back your figure when you introduce a step of the proposed methods.

5. The sample size of datasets in experiments is limited to hundreds.

6. Resolution parameter $\lambda$ controls how many scales are learned to brain network representation. I suggest authors show the trend of accuracy when altering the range of $\lambda$ to evaluate their ideas.

7. I suggest authors show the ablation studies of multimodal input by solely using SC or FC.