NeuroTree: Hierarchical Functional Brain Pathway Decoding for Mental Health Disorders

C1. Cannabis addicts have stronger FC compared to schizophrenia patients.

We appreciate the reviewer's careful inquiry about this claim! Study [1] found cannabis users show higher baseline functional connectivity in reward circuits than schizophrenia patients. Our Fig 4. (a-2) and (a-3) results predict higher FC numbers in cannabis users across Yeo's seven brain networks, with additional FC degree centrality predictions available at the link:https://anonymous.4open.science/r/anonymous_ICML/anonymous_DC.png.

References: [1]Fischer et al. Journal of Schizophrenia Research, 2014.

M3 & Q2.: Other parcellation schemes methods and robust approaches using NeuroTree.

Thank you for your valuable comment!

1). Other parcellation schemes: The addiction and COBRE atlases contain 90 and 118 ROIs respectively. As shown in section 7 and Fig 4, regardless of which atlas was used, the extracted tree-structured pathways successfully mapped to Yeo's 7 networks, enabling cross-dataset interpretation. Our framework consistently revealed distinct hierarchical structures in psychiatric conditions across both parcellations, demonstrating the stability and generalizability of our tree construction method. In future work, NeuroTree can easily extend to additional parcellations (e.g., AAL, BASC) for different disease research problems.

1). The robust of NeuroTree: As described in Section 6.1 and shown in Table 1 with SOTA performance, despite differences in parcellation schemes, we can improve stability through training the NeuroTree framework to obtain nodes (regions) prediction and weighted paths. This indicates that the hierarchical brain tree structures constructed by NEUROTREE are robust to the choice of ROI definitions. According to Definition 3.5, Kruskal's algorithm ensures tree decomposition with the shortest paths.

E1 & E3 & M2: NeuroTree uses the CMFS loss model performance and the biological significance of k-hop using spectral norm

We appreciate the reviewer’s insightful question! 1). Loss ablation: According to the experiment w/o CMFS loss in Table 1, we found that adding CMFS loss can make the overall (+ CE loss) loss more robust in our tensorboard plot at link:https://anonymous.4open.science/r/anonymous_ICML/anonymous_loss_comparison.png.

2.) K-hop convergence: The intuition for analyzing the rate of spectral norm decay with increasing k-hop allows us to examine how rapidly information from distant nodes attenuates across the dynamic brain network structure. A faster decay in spectral norm indicates more localized brain interactions as higher-order information becomes less influential. Conversely, slower decay preserves longer-range dependencies in the FC network. Higher k-values incorporate more distant neural connections, potentially reflecting the brain's long-distance functional integration processes.

M2 & Q1 & Q4:How does the inclusion of age as an input during training affect the model's ability to predict age groups in Table 2? Was age also provided as an input during prediction?

We appreciate your thoughtful review. 1.) Effectiveness of including age variable in the model: Recent research [2,3] shows incorporating demographic data (especially age) into GNN for fMRI enables more precise learning of subject differences. NeuroTree's ODE design uses age to regulate features during message passing, enhancing graph classification through age-aware GCN. This approach accounts for individual fMRI differences, demonstrating how personal features like age can stabilize dynamic graph convolutional neural network performance.

References:

[2]Zhang, Hao, et al. IEEE TMI, 2022

[3]Wang, Xuesong, et al. MICCAI, 2022.

2.) Effects of age and CMFS loss on tree structure: According to our supplementary figure at link https://anonymous.4open.science/r/anonymous_ICML/anonymous.png, without parameter $\theta$ and CMFC loss, the tree branches appear disorganized and fragmented, with paths lacking anatomical continuity and interpretability. However, with parameter $\theta$ that dynamically regulates functional connectivity based on individual age, it presents more coherent branches and clearer hierarchical structure.

3.) Is age included as a prediction in Table 2?: The advantage of NeuroTree is that it is age-aware GCN to learn the influence of age on dynamic FC patterns. We follow the currently existing literature [2,3] conventional practices, incorporating age information as part of the model input for feature learning. We input age during the training phase, but to avoid data leakage, we do not include age in the prediction phase.

We supplement that the complete results of Table 2 the NeuroTree can also be used in the training and testing process without including age at the link:https://anonymous.4open.science/r/anonymous_ICML/anonymous_table.png.

Thank you for your thoughtful review. We've addressed each question as fully as possible within the word limit.

We thank the reviewer for valuable suggestions and insightful comments, and we have clarified a few things about accuray and brain age so that our contribution can be better understood.

Q1. About the terminology of 'interpretability' and 'causal' modeling.

1.) The three meanings of interpretability in NeuroTree:

• In this work, we integrate the deep learning model concept from the literature [1,2,3] to enhance brain disorders classification. We define "interpretable variables" as observable latent factors in our model, not only providing an fMRI modeling but also showing the level of variations. We have corrected our terminology to "demographics" in the revised manuscript.

• In section 3.1, we integrate age as parameter $\theta$ into ODE-GCN and predict disease-relevant regions, visualized through node importance scores (brain regions) in tree explanations, enhancing model interpretability (Fig. 4).

• NeuroTree can completely perform model training to hierarchically decompose the fMRI brain network into a tree structure, with each level showing significant brain regions on the tree path to help explain brain disease, which provides further interpretability.

2.) Statistical Interpretation: We will conduct hypothesis testing through alation study, comparing our framework with ODEs and without ODEs to show the statistical significance of using causal network analysis.

3.) The definition of 'causal' modeling: We clarify that our use of the term "Causal" originates from explanations in deep learning literature [4,5]. For example, dynamic causal graph learning in [4] enables neural networks to automatically learn "time-varying causal graphs" or causal structures from traffic data. In Section 3.1, NeuroTree employs the ODE model form Eq (1) to simulate influences between brain regions, reflecting a continuous-time causal dynamic relationship. Although we have not yet used traditional Granger causality or dynamic causal modeling to directly present a directed graph node method, the time-varying graphs (dynamic FC) derived from ODE provide a framework that approximates causal relationships. We appreciate the reviewer's perspective and we have revised the manuscript to remove the "causal" word to make our paper more clear.

[1]Zheng, et al. "Brainib: Interpretable brain network-based psychiatric diagnosis with graph information bottleneck." IEEE TNNLS, 2024.

[2]Cui, et al. "Interpretable graph neural networks for connectome-based brain disorder analysis." MICCAI, 2022.

[3]Chen, et al. "Learnable subdivision graph neural network for functional brain network analysis and interpretable cognitive disorder diagnosis." MICCAI, 2023.

[4]Lin, et al. "Dynamic causal graph convolutional network for traffic prediction." IEEE CASE. 2023.

[5]Wein, et al. "A graph neural network framework for causal inference in brain networks." Scientific reports, 2021.

Q2. About model accuracy in brain network classification and comparison of models.

We clarify this from two perspectives:

Our model NeuroTree combines achieved the state-of-the-art performance using dynamic fMRI compared to similar models like PathNNs, BrainGNN, etc., given the variance in the individual fMRI data [8,9]. However, we believe this is an important yet essential step to predict the patients with mental disorders, especially since we also achieved an AUC of 0.71 on the public COBRE dataset. In the future, NeuroTree can integrate with other modalities (e.g., DTI, genetic information), allowing us to examine the connection alterations among patients.

[8]Zhao,et al. "Enhancing major depressive disorder diagnosis with dynamic-static fusion graph neural networks." IEEE JBHI, 2024.

[9]Peng, et al. "Gate: Graph CCA for temporal self-supervised learning for label-efficient fmri analysis." IEEE TMI, 2022.

Q3. About 'Chronological Brain Age Prediction' terminology definition problems and model prediction usefulness.

1. Clarification of definition and interpretation: In our work, chronological age refers to the subject’s actual age, which is used as a regulatory parameter to model age-related changes in FC. Specifically, in our AGE-GCN, we incorporate the age parameter $\theta$ to learn how FC strength evolves over time, thus enhancing the interpretability of aging patterns in mental disorders (See Eq. (3)–(12)).

2. The utility of predicting actual age in disease populations: We fully agree with the reviewer that the difference between chronological age and brain age is a clinically meaningful biomarker. However, NeoroTree is not solely designed to predict age accurately. Instead, it uses age as a modulation variable to explore how FC patterns vary with age across different clinical groups (e.g., cannabis users, schizophrenia patients).

3. In the revised version, we conduct the prediction of brain ages among healthy controls, while comparing the prediction accuracy from patients with addictive disorders.

M1 & W2: The study's evaluation is limited by using only two datasets, including disorder representation, dataset heterogeneity, and demographic diversity.

We thank the reviewer concern for data diversity! Due to data privacy concerns and the limited availability of public fMRI data for individuals with mental disorders that also include demographic information. We believe our proposed NeuroTree method's contributions are beneficial not only for decoding specific disease fMRI datasets but also extend to broader research applications such as EEG in neuroscience.

M2: Summary statistics of demographics in two datasets and sample size. We thank the reviewer for taking the time to review our work. Due to page limitations, we have placed the demographic statistics details for both datasets in Appendix H. Dataset. The total Cannabis sample size is 323 and COBRE is 142.

W1: Model computational cost and complexity, and the scalability for future studies.

We appreciate for pointing out this issue. 1).Computational cost: We have additionally supplemented experiments conducted for 100 epochs including a comparative table of computational costs with and without parameters ($\theta$,$\Gamma$,$\lambda$) across two datasets. To facilitate comparison of computational costs, we have included a Graph Transformer-based module with higher computational cost for comparison in the table below:

2). Code Implementation: In addition, the model we designed can be easily trained on a personal computer (include GPU, Google Colab Jupyter Notebook), the related environment setting can be found in our paper Appendix G Table 4. Compared to Graph Transformer modules with their extensive matrix calculations, NeuroTree significantly reduces computational demands through strategic parameter configurations. Additionally, NeuroTree enables researchers to observe parameter effects, enhancing model interpretability in alignment with specific research objectives.

W3: Low reproducibility: No code/models are provided. Thank you very much for the reviewer's discussion on the reproducibility of our research!

1). Code acquisition: We will release the complete code (including tree plot) and processed fMRI data on GitHub at the camera-ready stage when the paper is accepted.

2). Reproducible: We demonstrate relevant links to the training and testing process in Tensorboard according to the reviewer's (gVcG) suggestion for your reference:https://anonymous.4open.science/r/anonymous_ICML/anonymous_loss_comparison.png

O1: Redundant Sentence Correction. We appreciate your careful review and corrections! We express our sincere apologies regarding the extra sentence mistake. We have corrected the English grammar expression to maintain logic. However, current approaches face two fundamental limitations. First, .. Second,..

O2 & O3: Consider (1) clearly distinguishing between matrix and scalar values in equations, and (2) specifying the dimensions of each matrix. We thank the reviewer for the detailed review of our work! We have added explanations for $\sigma$ being the sigmoid function in Eq (1) and $\eta, \rho \in \mathbb{R}^+$ for the scalar values in Eq (2) of the paper. We clarify that the external input vector $u(t) \in \mathbb{R}^{v}$ interacts with the external stimulus encoding matrix $C \in \mathbb{R}^{v \times v}$, while both the static adjacency matrix $A^{s} \in \mathbb{R}^{v \times v}$ and the time-dependent dynamic adjacency matrix $A^{d}(t) \in \mathbb{R}^{v \times v}$ contribute to the overall network connectivity at time $t$, and $D^{-\frac{1}{2}} A D^{-\frac{1}{2}} H^{(l-1)} W^{(l-1)} \in \mathbb{R}^{v \times d_{\text{out}}}$ with output $d$ dimension.