W1, Q1, and Q2: Consistent thresholds are applied across all experiments and t-tests in our manuscript for all models and baselines. Thresholds for FC and SC are consistently set as 0.5 and 0.1, respectively, for all models and datasets, where SC is normalized to [0, 1] before thresholding.

Q3: To show the threshold variation, we adjust the threshold to 0.3 and 0.7 leading to more and fewer edges in the FC graphs for all four datasets, respectively. As listed below, some baselines could be very sensitive to thresholding. Such as BNT, BolT, and Graphormer show significant drops when the FC threshold changes. This pattern is clearly shown in the second row of Fig.S3 in our newly uploaded PDF. In contrast, NeuroPath always shows the best average rank of performance.

W2, and Q4: Thank you for raising the important concern of using an unexplained term in our theoretical analysis. In Sec 3.2, we explored the theoretical foundation of our NeuroPath by using expressive power which appears not the best term. The core of our theoretical analysis is how many neural pathways are allowed to be represented by NeuroPath as we described in the paragraph next to Fact 3.1. However, expressive power refers to the ability of a graph model to distinguish the isomorphism of graph (sub)structure. This technical term is popularly used to prove the expressiveness of a GNN [1]. Since we focus on neural pathways modeling instead of isomorphism of (sub)structure, expressive power does not exactly fit to frame our theory for modeling complex neural interactions. Instead, we will revise Fact 3.1 by replacing the expressive power with the number of the path substructure that can be modeled by NeuroPath. Based on this, in our proof of Fact 3.1, such capacity of modeling half paths of a graph can be easily formulated as Lemma A.1 after expanding Eq (1) as Eq (7). Then, it is easy to follow the proof of Lemma A.1 after we get Eq (9).

[1] 10.1007/978-981-16-6054-2_5

Novelty

1. Although there are previous works utilized transformer and graph transformer, our NeuroPath is the first model to uncover the SC-FC coupling mechanism between (structural) neural pathways and (functional) neural activities under a new design of MHSA framework that can represent the path of graph without any pre-processing.

• As highlighted by the other reviewers, our work introduced a novel comprehensive integration of connectivity matrices coined as topological detour, a novel graph substructure showing a significant contribution to neuroscience research of structure-function coupling. Our NeuroPath method is the first model that can learn the relationship between such detour pathways and brain activity.

• On the other hand, existing frameworks of modeling the path of a graph mainly focus on introducing high-order features [1] or grouping nodes of a path [2]. Our NeuroPath, in contrast, does not require any pre-processing to obtain features or search paths in advance. This makes the pathway modeling implementable since the brain connectome graph is so dense that finding all paths is highly time-consuming as listed in Table below.

Performance

1. In our manuscript, we aim to show comprehensive results that contain all possible training scenarios of brain connectome data to test both accuracy and robustness. This follows the previous benchmarking work [3]. For the sake of clarity, we calculate the average rank of performance to show a comprehensive performance rank of NeuroPath and 8 baselines as below, where NeuroPath shows the best average rank on all four datasets. On the other hand, we shown a more practical downstream task in the manuscript, zero-shot learning, where results also show a significant improvement in performance for all datasets, e.g., more than 16% improvement against the second-place method when training on HCPA and testing on UKB. Moreover, by varying the model size and FC threshold as shown in Fig.S3 in our newly uploaded PDF, NeuroPath still has the best comprehensive performance.

2. The efficiency of our NeuroPath is demonstrated by the parameter number and the actual computing time. The table below shows the average processing time on the UKB dataset.

Questions

1 We thank for these insightful comments. We are fully aware of the importance of functional dynamics in the network neuroscience field. In our current implementation, we use the time series of the BOLD signal as the node feature to learn temporal information in NeuroPath. Although we have not employed sliding window techniques, we specifically evaluate the effect of window size in our deep model. As we showed in the experiment section (ln Sec 4), we have not found statistical significance with respect to window size (from 100 to 500 time points). In this paper, we put the spotlight on the concept of topological detour for SC-FC coupling. Incorporating sliding windows is definitely on our radar for future work.

2 We scale the model size and compare the scalability between NeuroPath and the existing graph transformers and brain transformers that have more layers as listed below and in Fig.S3.

3 There is only one hyperparameter of NeuroPath related to the representation of neural pathways, $H$, the hop # of TD-MHSA. We show the best choice of this hyperparameter in Fig.4 in the manuscript, where the best $H$ is decided by brain region number.

4 In the response of Novelty, we discussed the difference between NeuroPath and existing general graph transformers. The difference between NeuroPath and brain models is mainly the objective of brain connectomes data modeling. As discussed above, we focus on modeling brain activity via neural pathways acquired from structure-function integrated connectivity. In contrast, existing brain models are whether merging [4,5] nodes of a graph to aggregate information of brain subnetworks or fusing [6] dynamic brain time series.

[1] 10.1109/tpami.2022.3154319

[2] 10.48550/arxiv.2306.05955

[3] 10.48550/arxiv.2306.06202

[4] Brain Network Transformer

[5] 10.1016/j.media.2021.102233

[6] 10.1016/j.media.2023.102841

Thanks for the authors' for clarifications and additional details on novelty and performance. And the advantages of not involving preprocessing to extract features, and include structure-function coupling. I have increased my score correspondingly.

Weaknesses

The actual computing time of existing brain models, transformers, and our NeuroPath per graph is shown below. According to this table, the computational time to train the model of every experiment can be calculated along with the data number in Table 5 in our manuscript.

Questions

Yes, we have. Distributions of the subject age are shown in Fig.S1 in our newly uploaded PDF file.

Limitations

In Fig.S2, We run the same $t$-test as in Fig.2 in the main text for the degree of our topological detour across diverse populations by gender. By comparing the detour degree with the FC degree, we can draw the same conclusion as in Sec 2.1. It is worth noting that the male group shows a lower detour degree, i.e., fewer detour pathways, than the female group in the HCPA dataset.

Weaknesses

Equations on line 173 can be rewritten more clearly: a set of learnable parameters $\{ \bar{\mathbf{W}}, \hat{\mathbf{W}} \in \mathbb{R}^{(HC)\times C} \}$ and $\boldsymbol{\bar\alpha}_h, \boldsymbol{\bar\beta}_h, \boldsymbol{\bar\gamma}_h, \boldsymbol{\hat\alpha}_h, \boldsymbol{\hat\beta}_h, \boldsymbol{\hat\gamma}_h \in \mathbb{R}^{C\times C}$ where $h=1,\dots,H$.

Questions

We run more ablation studies on other properties by scaling the model size and varying the threshold of FC graph construction. They are visualized by line plots for a better description as shown in Fig.S3 in our newly uploaded PDF file.