$\textit{NeuroPath}$: A Neural Pathway Transformer for Joining the Dots of Human Connectomes
Authors: Ziquan Wei
Tingting Dan
Jiaqi Ding
Guorong Wu
Venue: NeurIPS 2024 poster (2024)
Keywords: Graph transformer
Brain newtork
Neural pathway
Topological detour
structure-function coupling
fMRI
DWI
Cognition classification
Alzheimer's disease diagnosis
Primary area: neuroscience_and_cognitive_science
TL;DR: We propose NeuroPath, a graph Transformer that can express neural pathways by a novel multivariate structure-function coupling of human connectome and apply on supervised or zero-shot learning of neural activity classification and disease diagnosis.

Abstract: Although modern imaging technologies allow us to study connectivity between two distinct brain regions $\textit{in-vivo}$, an in-depth understanding of how anatomical structure supports brain function and how spontaneous functional fluctuations emerge remarkable cognition is still elusive. Meanwhile, tremendous efforts have been made in the realm of machine learning to establish the nonlinear mapping between neuroimaging data and phenotypic traits. However, the absence of neuroscience insight in the current approaches poses significant challenges in understanding cognitive behavior from transient neural activities. 
To address this challenge, we put the spotlight on the coupling mechanism of structural connectivity (SC) and functional connectivity (FC) by formulating such network neuroscience question into an expressive graph representation learning problem for high-order topology. Specifically, we introduce the concept of $\textit{topological detour}$ to characterize how a ubiquitous instance of FC (direct link) is supported by neural pathways (detour) physically wired by SC, which forms a cyclic loop interacted by brain structure and function. In the clich\'e of machine learning, the multi-hop detour pathway underlying SC-FC coupling allows us to devise a novel multi-head self-attention mechanism within Transformer to capture multi-modal feature representation from paired graphs of SC and FC. Taken together, we propose a biological-inspired deep model, coined as $\textit{NeuroPath}$, to find putative connectomic feature representations from the unprecedented amount of neuroimages, which can be plugged into various downstream applications such as task recognition and disease diagnosis. 
We have evaluated $\textit{NeuroPath}$ on large-scale public datasets including Human Connectome Project (HCP) and UK Biobank (UKB) under different experiment settings of supervised and zero-shot learning, where the state-of-the-art performance by our $\textit{NeuroPath}$ indicates great potential in network neuroscience.

NeuroPath, A Neural Pathway Transformer for Joining the Dots of Human Connectomes
Ziquan Wei
Tingting Dan
University of North Carolina at Chapel Hill
University of North Carolina at Chapel Hill Chapel Hill, NC 27599
Chapel Hill, NC 27599
zi riquanw@eamil unc. edu
dan@med wnc. edu
Jiaqi Ding
Guorong Wu
University of North Carolina at Chapel Hill
University of North Carolina at Chapel Hill Chapel Hill, NC 27599 guorong_ wu@med. wnc.unc... edu
Chapel Hill, NC 27599 jiaqid@cs. unc edu
Abstract
Although modern imaging technologies allow us to study connectivity between two distinct brain regions in-vivo, in-depth understanding of how anatomical struc- ture supports brain function and how spontaneous functional fluctuations emerge remarkable cognition is still elusive. Meanwhile, tremendous efforts have been made in the realm of machine learning to establish the nonlinear mapping between neuroimaging data and phenotypic traits. However, the absence of neuroscience insight in the current approaches poses significant challenges in understanding cognitive behavior from transient neural activities. To address this challenge, we put the spotlight on the coupling mechanism of structural connectivity (SC) and functional connectivity (FC) by formulating such network neuroscience question into an expressive graph representation learning problem for high-order topology. Specifically, we introduce the concept of topological detour to characterize how a ubiquitous instance of FC (direct link) is supported by neural pathways (dctour) physically wired by SC, which forms a cyclic loop interacted by brain structure and function. In the cliché of machine learning, the multi-hop detour pathway underlying SC-FC coupling allows us to devise a novel multi-hest self-attention mechanism within Transformer to capture multi-moda feature representation from paired graphs of SC and FC. Taken together, we propose a biological mooloical-inspired deep model, coined NeuroPath, find putative connectomic feature representations from the unprecedented amount of neuroimages, which can be plugged into various downstream applications such task recognition and disease diagnosis. We have evaluated NeuroPath on large-scale public datasets including Human Connectome Project (HCP) and UK Biobank (UKB) under different experiment settings of supervised and zero-shot learning, where the state-of-the-a performance by our NeuroPath indicates great potential in network neuroscience.
Introduction
The seek of meaningful feature representations for graph topology has been extensively investigated [4 228 34), with widespread applications in reasoning path [16] and cycle basis [61] for knowledge graph, well as neural fingerprint [17]. junction tree autoencoder 29] and cellular Weisfeiler Leman (WL) testing [ for molecular substructure encoding. Moreover, graph data in the realm of neuroscience research demands feature representation bearing additional neuroscience insight
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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which is supposed to underline particular neurobiological mechanisms of interest. For example, substructure embedding [36 31 and snapshot embedding [53] B] have been proposed to characterize the phenotypic traits from structural connectivity (SC), which is static graph and physically wired by neuronal fibers, and functional connectivity (FC) in the brain, which is a dynamic graph and supported by neural circuit overlaid on SC topology (2]. Nevertheless, the graph learning approach of physical neural pathways of SC coupled with FC is rare in related works [4] 13 39].
The advancement of diffusion-weighted imaging (DWI) technology enables the in-vivo measurement of physical region-to-regio connections through neuronal fibers (aka. SC). Multiple lines of neuro- science finding suggest that high-level cognition and behavior emerge from the remarkable SC-FC coupling mechanism, making the in-depth understanding of the interplay between SC and FC become
the gateway to reverse engineering human mind [52 [5] To that end, a plethora of computational models have been proposed over the past decade, including biophysical models 25 58
graph harmonics [4 38), network communications [19]. multivariate statistical technique 41 and deep
learning-basse based cemeture-function mapping [10 49 45 However, the complex relationship between
structural and functional connectivity is still clusive [14], particularly evidenced by the lack of direct
physical pathways (formed by SC in Fig. [ orange box) between two brain regions that exhibit functional co-activation (indicated by FC in Fig. [ [green box) 124 42 [6 Although the topology of SC does not necessarily always aligned with the counterpart of FC motivating previous related works, there is converging consensus that each FC instance is supported by sub- sub-graph of SC, as shown in Fig. I orange box, where blue links constructing a path sub- wub-graph represent the neural pathway that physically supports the red link.
We strike on this outstanding neuroscience question by lifting the concept of univariate coupling, which is limited to the correspondence between a direct link of SC and another direct link of FC, to a new paradigm of multivariate SC-FC coupling mechanism that models how the ubiquitous FC instance is associated with the detour pathway on SC topology. As shown in green box of Fig. [ the red line represents the direct FC link between region #1 and #2 while the collection of blue lines indicates the corresponding detour pathway of SC. Although the whole-brain topology remains unchanged as brain function evolves, the functional co- co-activation over time is dynamically supported by different neural pathways of SC. Note, the direct FC link and SC detour form cyclic loop inherited from both SC and FC topology. Such conceptualization is supported by various neuroscience findings that synchronization of neural activity between two brain regions is fundamentally supported by the
underlying neural circuitry established by structural connectivities 23 24 21).
In the perspective of machine learning, shown in the middle of Fig. [ the overarching goal is to establish a mapping function between neuroimaging data (SC only, FC only, or both) to the phenotypic traits (such as cognitive tasks). Due to the complex nature of human cognition, however, current deep models encounter several significant challenges. First, it is less common to use the static SC only for the prediction of evolving cognitive states, largely due to the ill- ill-posed setting which boils down to a one-to-many mapping [50]. Alternatively, tremendous efforts have been made to predict cognitive states based on time series of neural activity (3] and FC topology 4. However, it has been frequently reported that massive inter-subject variations of FC often predominate the intrinsic task-relevant patterns, such variations in real-world data are demonstrated in Sec. 2.1 Thus, current seaminng-based approaches have difficulties in scaling up to large-size population data. Furthermore, limiting consideration to either SC or FC alone fails capture the holistic nature of the brain as dynamic system, resulting in existing approaches having limited power to uncover new insight of complex relationship between SC and FC 39 In this regard, it is natural to combine the information of SC and FC in a multi-modality learning scenario [51] 30 (7). In general, current research focuses on information fusion at node or link level. Few attention has been paid to integrating SC and FC by combining the power of machine learning and insight of cognitive neuroscience.
Taken together, we propose a novel deep model, coined NeuroPath, to (1) enhance the machine performance of predicting cognitive status using both SC and FC information and (2) uncover new neuroscience underpinning of SC-FC coupling mechanism. In nutshell, conceptualize that the effective way to advance our current understanding of cognitive neuroscience is to characterize the latent SC-FC coupling mechanism from neuroimaging data. To land this conceptualization into an end-to-end deep model, we put the spotlight on devising a new multi-head self-attention (MHSA) component by capitalizing on the multivariate SC-FC coupling mechanism. As shown in Fig. grey box, nodes of multiple paths detouring an FC link on SC are transformed respectively by multiple heads of self-attention in one layer. On top of this, we learn putative feature representations from

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Legends
Noural pathway (detour) FC
Cognitive
Rol
SC link
tasks
#4
#5
#2
Vision
-Attention
Aclf-Attentionn
Machine Learning
Mult-
#7
#2
#3
head Self-
HLP
MLP
O
attention
concatenate
MLP
033
layer2
Memory
layer
1-hop
hitering
2-nop
head2 heads
hop
+5
Detour
Mult-head
adjacency
self-attention
Structural
Motor
NeuroPath Transformer
Connectivity
SC-FC
Functional
(SC)
Coupling
Connectivity (FC)
Figure 1: Planting a novel multivariate SC-FC coupling mechanism to explainable deep model. Orange box: The structural connectivity (SC) denoted by grey links represents the strength of neurological fiber that physically connects two brain regions. SC is relatively static given the neural activities are transient, e.g. cognitive tasks. Green box: The functional connectivity (FC) is commonly considered the brain network topology [48] since SC is static for different cognitive tasks. The overlapping area orange and green boxes: the multivariate SC-FC coupling mechanism, where neural pathway (detour) is constructed by multiple SC links to support one FC link. Grey box: NeuroPath Transformer using a new MHSA module filtered by adjacency matrices emits the representation of multi-hop detours.
the cyclic loop capturing complete information on how the underlying functional fluctuations are supported by the neural pathway (aka. SC detour) with different lengths.
Our major contribution has three folds. First, we present novel multivariate SC-FC coupling mechanism that allows us to develop explainable deep model with great neuroscience insight and guarantee from graph theory. Second, we present Transformer- based deep model that is scalable to utilize existing large population of neuroimaging data. Third, we have validated our NeuroPath on large-scale public datasets with a total 10,886 fMRI scans including Human Connectome Project (HCP), UK Biobank (UKB), Alzheimer's Disease Neuroimaging Initiative (ADNI), and Open Access Series of Imaging Studies (OASIS). We have evaluated (1) the accuracy for predicting phenotypic traits (cognitive status in healthy brains and disease risk for aging brains) (2) model interpretability in identifying latent neural pathways, and (3) the clinical value of our model in terms robustness and zero-shot learning, where promising results suggests potential application in computational neuroscience field.
2 Preliminaries
2.1
Motivations
Massive inter-subject variations of FC often predominate the intrinsic task-relevant patterns. Take the HCP data 99] example in which the data heterogeneity issue has been harmonized by using standardized imaging protocol. As shown in Fig. -
we first identify a set of brain regions which exhibit significant difference between resting stage and VISMOTOR tasking in paired 1-test using detour degree and FC degred") respectively, where the identified regions are colored based on p-values. Next, we examine the location of these regions in each functional sub-networks (manually defined using neuroscience domain knowledge). For comparison, we display the overlap ratio (y-axis) between the number identified regions and the total number of regions in each sub- network (x-axis) at the bottom of Fig. 2 Current neuroscience findings suggest that resting state relevant to default mode network (red circle) while VISMOTOR task associated with visual (orange circle) and sensorimotor areas (green circle). In this regard, the detour degree achieves
Detailed steps of paired i-tests be found in Appendix.

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overall higher discrimination power than FC to the extent that most of identified regions are aligned with neuroscience finding with much less false positives in other non-relevant regions. The same findings are observed on diverse populations by gender in Appendix Fig. [ The evidence shown in Fig. 2 underscores the importance of including SC detour in finding putative functional biomarkers, prompting us to further integrate the SC-FC coupling mechanism into the design of NeuroPath.
2.2 Relevant Machine Learning Work for Brain Connectomes
Tremendous efforts have been made to perform graph learning on human connectome data. The most representative work includes graph convolu-
Detour degree
tional network (GCN 333 36]) and transformer- based deep models K
31 Recently, most of pop-
ular GNN models and their application in neuro- science have been reviewed in [4].
p-velue 00
FC degree
Inspired by the great success of Transform [56 in
Functional sub-nntworr
NLP and CV, various graph transformer models have been proposed in graph learning. For example, GraphGPS [47] and TokenGT [32 models use ei- ther a structure encoding or token of graph elements as the initial graph feature representations. Further- more, self-attention gating mechanism is proposed in [26] using an additional branch of edge embed- ding to implement the augmentation of self-attention. By integrating original node features and structural embeddings into augmented self-attention mod- ule, Graphormer [62] shows the same expressibil- ity conventional graph neural networks (GNN), which has been proved in [63] that such augmented self-attention is strictly more expressive than low- order WL for distinguishing non-isomorphic graphs present our NeuroPath
Default Made
C Visual C Sensorimotor
Over- ratio
Detour degree
FC degree
Sub-networks
Figure 2: Motivation of integrating SC-FC
coupling in neural networks. Top: Brain re- gions manifesting significant resting state vs VISMOTOR difference using detour degree and FC degree. Color indicate the p-values (0 S < 0.05) in paired r-test. Bottom: The overlap ratio (y-axis) between the number of identified significant regions and the total num- ber of brain regions in each pre-defined func- tional sub-networks (x-axis). Specifically, we examine the identified regions in default mode (red circle/box), visual (orange circle/box), and sensorimotor (green circle/box) networks since they are closely associated with resting stage vs VISMOTOR difference.
43.. In the following, where the novel biological-inspred self-attention mechanism yields more expressive power of graph representation than Graphormer [62].
3 Neuro - A Biosogecal-Inspiree Transformer for Human Connectomes
Problem formulation Given that the detour degree can profile nodes highly associated with functional sub-networks, the problem in this work is formulated as how to plant this neuroscience insight of topological detour from SC-FC coupling into deep neural networks.
Notations, Assume SC and FC are denoted by adjacency matrices A E N and A E RNNN,
respectively, where AL) is the connectivity between 7th and jth region (i. 1,..,,,N) N). SC and FC are calculated by the subject-wise normalized water matter (WM) fiber counts and the Pearson's 's correlation coefficient of neural signals, respectively. Furthermore, we use A (-) to denote the binary adjacency matrix after high-pas: pass filtering and adding lelf-loop for either SC or FC. Node attribute is denoted by X E xxC where C' is the feature dimension.
In practice,
Definition of detour in the context of SC-FC coupling. To capture multi-scale topology, employ random walk on graph of SC, yielding set of multi-hop detour adjacency matrices as follows:
Definition 3.1 (Detour adjacency matrix). Dd binary matrix shapes of N x N and stores if a link of FC is associated with a h-hop topological detour, where a 1-hop detour equivalent to an edge.
is obtained by element- wise production between binary matrices D* := ((AS)* > 0). (A
where 1 < h < H, and H is the maximum length of detour.

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Legends
Tratning rendout
Teatink readout
Topological
Concatenate
Unleamsble
Functional connectivity (shared)
detour (hop-by-hon hop)
TD-MHSA
Lingan
Lincor
FC-MHSA
Heeds
Heads
0a
Jmask
Fressh
PAUIIA
A
L.THar
Node features
Figure 3: Framework of twin branch, topological detour filtered multi-head self-attention (TD- MHSA) and functional connectivity filtered multi-head self-attention (FC-MHSA), for node feature transformation in NeuroPath, where training/testing readout indicates different branch is used for training/testing stage.
Note that D avoids finding all simple paths by our model, it significantly reduces computational costs with sufficient power for the neural pathways representation as discussed in Sec. 3.2
3.1 Network Architecture of NeuroPath
NeuroPath is designed with twin branch as shown in Figure where two branches in the model have identical frameworks of the multi-head self-attention (MHSA) from the Transformer encoder [56]. This twin branch is designed for feature representation to fuse SC and FC information by being consistent between FC link representation and SC detour representation. Given a set of learnable parameters W, W E (HC)xC and ãh, , Tp. âi,, 3r, 4%. E RCxC where h = 1...., H, H is head number of MHSA, and C' denotes feature dimension, the branch TD-MHSA is then defined as
(xD(X) = Concat (X1,...,X,, X.), W,
(1)
where X₁, Softmax (Xār) fmask (D*)) (X7r). Similarly, the FC-MHSA branch is defined as
(xc Concat (XI....,Xe Xz) w.
(2)
Smack (AF) (Xfr). Adding masks to attention maps is a mature approach for only involving interested nodes in the self-attention mechanism. To achieve this, fmask here defined filling negative infinities false slots and zeros true slots of the binary adjacency matrix so that Sof tmax can ignore false slots in both branches.
where X, Soft (Xx))
Loss function during training is set the downstream application objective along with the consistency constraint loss LTD, which defined as
LTD (X) fFC (X)]l
Taking classification as an example, the final loss CELoSS (label, Y) + LTD, where the logits = p AF frD (X)@ with learnable parameters gCxn, n is class number and p is degree of brain network adjacency A
3.2 Neural Pathway Representation by NeuroPath
TD-MHSA strictly follows the pathway of topological detour after SC-FC coupling to produce node features hop-by-hop corresponding to each head of self-attention. representation, frD (X),, is the weighted sum of nodes among half of the neural pathways in the range of H- Hooop after expanding Eq. Detailed proof can found in Appendix.
fact, the i-th node feature
Fact 3.1. The top pathway representations are obtained by arg maxj,k ( Ejep Siy3 Wine) where S denotes the softmax of self-attention p C Pl is a set of node index of a path and P is the node collection of neural pathways within H H-hop starting at i-th node.
Fact indicates the power of our NeuroPath for high-order graph substructure. PathNN 40 models all simple paths has HH computational complexity by sorting all paths in advance. In contrast,
5

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NeuroPath can model important paths using only O(N²) computational complexity and does not require any pre-computation of high-order topology.
Regarding the neuroscience knowledge that FC is relatively denser than SC with the evidence of significant indirect SC links [39) FC adjacency is also denser than the TD adjacency according to the Def. 3.1] Meanwhile, the consistency constraint LTD cooperates with the twin branch so that FC-MHSA produces the expressive node feature representation well. Consequently, existing states of FC-MHSA can hold the same power of TD-MHSA by consistent feature representation, and hence benefit the prediction by this SC-FC coupling.
4 Experimental Results
The experiments are designed for the following four Research Questions (RQ), RQ1: How is performance on neural activity recognition and cognition disordering disease diagnosis compared to state-of-the-art (SOTA) brain models and graph transformers? RQ2: Can the brain network representation by NeuroPath being consistent on zero-shot learning experiments? RQ3: Does performance enhancement by NeuroPath align with intuitions by ablations of model framework and neural pathway length? RQ4: What is the pattern of neural pathways contributing to prediction? To thoroughly answer those questions, four public datasets are used in our experiments. Detailed data preprocessing and profiles can be found in Appendix.
The Lifespan Human Connectome Project Aging (HCPA) dataset is instrumental in task recognition research, offering a comprehensive view of the aging process. It includes data from 717 subjects, encompassing both fMRI (1=4,863) and DWI (n=716). includes data from three brain tasks associated with memory and sensory-motor: VISMOTOR, CARIT, and FACENAME, and the resting state. In the related experiments, these tasks are treated as (1) four-class classification problem and (2) resting/tasking classification for zero-shot learning. We partition brain regions using AAL atlas 55 in experiments except for ablation studies using Gordon atlas (20)
United Kingdoms Biobank (UKB) dataset is large-scale dataset with MRI data. There are fMRI (n=5,483) and DWI (n=3,162) preprocessed by the same algorithm as HCPA. includes data from one brain task that engages cognitive and sensory-motor [22] 37). Data is treated as a two-class classification in the following experiments. Brain regions are partitioned by Gordon atlas 200]
Alzheimer's 's Disease Neuroimaging Initiative (ADNI) dataset 55 serves as an invaluable resource, featuring collection of pre-processed fMRI (n=138) and DWI (n=135) with AAL parcellation in our experiment. Additionally, ADNI includes clinical diagnostic labels, encompassing a spectrum of cognitive states: Cognitive Normal (CN), Subjective Memory Complaints (SMC), Early-Stage Mild Cognitive Impairment (EMCI), Late-Stage Mild Cognitive Impairment (LMCI), and Alzheimer's Disease (AD). Considering the data balance issue, we simplified these categories into two broad groups based on disease severity: we combined CN, SMC, and EMCI into 'CN' group, while LMCI and AD were grouped as the 'AD' group.
Open Access Series of Imaging Studies (OASIS) dataset 35 presents a substantial collection of
data from 924 subjects, comprising 3,322 fMRI sessions in total. Among the dataset, fMRI (n=402) and DWI (n=362) are pre- pre-processed with Destrieux parcellation [13. Our experiment focused on binary classification: subjects in preclinical stages of AD those manifesting dementia-related conditions are under the 'AD' group, while healthy individuals are under the 'CN' group.
All datasets are split as train/validation in a 5-fold cross validatii according to the subject index to prevent data leakage. Node attributes of brain network setting as Blood-Oxye -xyygnn Level Dependent (BOLD) signal or correlation (CORR) between BOLD signals are performing vary different datasets 48 Furthermore, the deep model performance is also affected by using a short-length or full-length BOLD which is considered dynamic static brain network, respectively (48). To evaluate NeuroPath under all situations, four combinations of CORR/BOLD and static/dynamic are all tested in our experiments.
Competitive methods, two baselines (MLP and GCN), three SOTA brain models (BrainGNN (66] BNT 31, and BolT ()) and two SOTA general graph transformers (Graphormer 62) and NAG- phormer 12) are chosen for comparison with NeuroPath, where MI.P and GCN both have one layer of the vanilla framework followed by batch normalization and activation for feature representation

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Table Performance comparison on HCPA and UKB datasets. Colored numbers indicate ranking in the first, second, and third place.
HCPA CORR
HCPA BOLD
UKB CORR
UKB BOLD
static
dynamic
static
dynamic
static
dynamic
static
dynamic
Accuracy
MLP
96.01 +0.50
92.57=0.32
93.42+a..s
83.64
+9.00
99.05=0.44 97.70
96.42200.00
GCN
90.85 91.95=0.45
92.94+0.n8
84.60+0.45
99.00+0.22
97.54
99.31 =0.33
93.39
BrainGNN
90.85 86.0612.64
89.38 1..88
12,62.3333
97. 97.54.0.52
95.32
90.33
86.11
BNT
97.92+0.65 -4.15
92.57
98.71 86.55+0.37
+0.34
97.15
98 =0.0.
95.98=0044
BolT
96,40+0.41
91.68
95.78
91.92=0.00
99.13
g0.61
=0.29
98.22=0.31
Graphormer
78.80
78.73
59.63
65.01 +3.84
92.76+11..0
99.8.
86.82
55.56.-21.08
NAGphormer
93.67 40.96 90.96 90.73
94.76+1.15
82.02
0..7
96.83
99.22 0.33
92.90=00.9
NeuroPath
96.6910.54 92.7620.52
95.0311193
87.54 99.22.10.4
27.77
99.59
94.12.0.75
Fl score
MLP
96.01 92.5220.35
93.42+0.55 58 82.86+1.68
99.00.0.15
97.69=0.32
99.05-0.49
96.42=0.60
GCN
95.85
91.9020.41
92.98+0.0 60 83.95
99.00g0.22
97.53
99.31 =0.83
93.36g0.71
BrainGNN
90.92+1.41 85.43+3.37
89.38
64.40
97.54+0.s2
95.30#1.71
90.35
86.09
BNT
97.9210.06
94. 14.162
02.57+1.22
86.45
98.71
97.15
98.64_0.18
95.97
BolT
96.3810.43
91.6610.39
95.7810.87
91.76.1.78
99.1310.34
97.60
99.29_0.26
98.22.0.31
Graphormer
77.29 75.26_2.66
53.05 17.04+1.46
92. 67 200.25
80.19
86.54_13.03
50.12=27.56
NAGipormmer
93.69+0.95
90.64
94.76+1.16
$1.0622.08
98. 00.5
96.8220035
99 99.22-0.55
92.88=0.68
NeuroPath
96.70.0.54 54 92.7220.54 95.0921.86 1.66 27.03
99 29.22220.24
97.77=0.21
99.59=0.21
94.11 20.75
Table 2: Performance comparison on ADNI and OASIS datasets. Colored numbers indicate ranking
in the first, second, and third place.
ADNI CORR
ADNI BOLD
OASIS CORR
OASIS BOLD
static
dynamic
static
dynamic
static
dynamic
static
dynamic
Accuracy
MI.P
79.26.10.34
82.68
80.6747.26
82.93
89.28=3.58
89.32+3.18
88, 88.9943.52
89.02+3325
GCN
86.22
83.30 6
80.67
17.26
83.53
88.80 2.88
88.30
88.27 1.4.8
88,49133.6
BrainGNN
$2.07.6.88
83.30 42
82.07
83.42226.05
89.65 49.29_4475
87.76
89.27
BNT
82.81 16.47
83.30 30
40.67
84.33
99
89.02
89.98
88.7544436
89.57.33.0
BolT
82,0013.55
80.3412.82 62
81.41
80.80
88.30
88.97
87.5414.62
88.5013.35
Graphormer
82.7445.89
83,28
83,48
81.28+6.58
88.55=4.22
88.57+3.18
87.49+5.19
88.9843.26
NAGphormer
82.74
82.79
81.3316.09
82.17
89.53.3.3
88.6413.4
89.02
89.21 13.44
NeuroPath
85.5644.97
83.82
83.48
83.68
90.01 +3.42
89.49
89.02.+3.48
89.21 43.44
Fl score
MLP
74.72.8.er
77.9815.19
74.9619.17
76.75.7706
87.05
86.7414481
85,27
85, 85.02.15.03
GCN
78.5349.76
76.95
76.1948.50
77.87+6.66
84.75
85.71
85.56
85.8643.97
BrainGiNN
76.57 110.01
79.1418.00
75. 75.11 19.69
16.99
86.07
15.71
85.12
14.9415.22
84.50)
BNT
79.68
78.71
80.164s.01
80.5048.40
86.07 13.19
86.73
85.32
85.6744.04
BolT
79.6444.33
76.89+7.75
76.68
77.92+4.62
85,49
84.91
4-4.78
84,70+4..39
Graphormer
78.1416603
78.29 22
77.78
76. 76
84.77=5.24
85.67
85,4414.73
84.40.14.17
NAGphormer 76.57 16.67
76.46
15.40
17.80
85.61 14.79
84.76
83.87.1..0
84.48.14.58
NeuroPath
83.29+4.45
79.93
77.35
78.05
86.37=5.03
86.26
87.02+43.77
85.01+4.48
Table 3: Conclusion of performance: Average rank of methods on different scenarios and evaluation metrics. 'Bold' and 'underline' denote the first and the second place, respectively.
MI.P
GCN
BrainGiNN
BNT
BoFT
Graphormer NAGphormer NeuroPath
HCPA 4.0
4.5
7.0
2.8
2.5
8.0
5.3
2.0
UKB 3.0
3.75
7,0
5.0
2.3
8.0
5.3
1.8
ADNI 6.9
4,4
4.1
2.1
5.8
4.6
5.8
1.6
OASIS
3.3
5.3
4.4
2.8
6.5
6.4
5.0
2.5
and one layer of graph convolution for graph prediction, All train/validate settings such as random seed and learning rate set as the same.
7

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4.1 Performance of Neural Activity Classification
Performance on datasets HCPA and UKB is listed in Table Except for UKB BOLD dynamic. NeuroPath can rank in the top two places under all data settings on the accuracy and the weighted FI score. The highest accuracy of neural activity classification on all settings of UKB can be achieved by NeuroPath as 99.59%, while the best by other models, 99.31% %. is achieved by the GCN rather than other faney models implying they are rarely capturing features from neuroscience senses. Regarding HCPA dataset, SOTA brain models have more than double the number of parameters than our model as listed in Appendix. Nonetheless, we can hold the second place for all data settings in HCPA since NeuroPath learn from the physical neural pathways, while the general graph transformers can be even worse than the vanilla MLP and GCN since they do not involve neuroscience knowledge.
4.2 Performance of Cognition Disordering Diagnosis
The performance of AD/CN classification on datasets ADNI and OASIS is listed in Table NeuroPath has the top three performance among all datasets with four different data settings except for the Fl score on dynamic OASIS BOLD. The neuroscience insight of SC-FC coupling benefits NeuroPath achieved the best aceuracy on 5/8 cases and the best F1 score on 3/8 cases. It is worth noting that NeuroPath is the only one that has over 90% accuracy in these experiments. Class unbalance in ADNI and OASIS datasets makes the F1 score lower than accuracy. Nevertheless, NeuroPath has top scores on both two datasets, 83.29% and 87.02% respectively, under all data settings. Given the challenges of more neural pathways present dynamic graphs that have a higher degree as listed in Appendix, our performance slightly drops to against others. In summary, NeuroPath shows superior performance than existing SOTA models on static graphs of various data with the benefit of our novel multivariate SC-FC coupling.
Table 4: Zero-shot learning between four datasets using BOLD as node attributes under different data settings, where resting/tasking state classification is tested for HCPA and UKB datasets, Fl scores are listed, and 'bold' and 'underline" denote the first and the second rank, respectively.
4.3 Zero-shot Learning
Despite neural activity classification and cognitive disordering diagnosis are two types of experiments usually tested in computational neuroscience research, zero-shot learning by train- ing and validating the model on one dataset and testing on another dataset is rarely present in the field. Since for both resting/tasking and AD/CN clas- sification, we all have two datasets, it is feasible to test our explainable deep model by zero-shot learning show the clinical value. The experimental setting is consistent as above with 5-fold cross validatioo to choose the best model state the train-val dataset, and then test it validating set of the corresponding fold of another dataset.
OASIS +ADNI
ADNI -OASIS
static
dynamic
static
dynamic
Graphormer NAGphormer 13.19
77.63
77.24 77.24
79.69
83.55 90
78.0917.24
69.63
78.0917.06
NeuroPath
79.7813.58
81.57
80.03 50
19.6516.35
HCPA-+UBB
UKB HCPA
static
dynamic
static
dynamic
Graphormer 39.09 14
50.97
57.78
64.36
NAGphormer 74.4924.01
70.17
89.77
10.44
NewroPath
91.29
72.0812.14
90.61 13.65
75.62
Given that the three SOTA brain models are all sensitive to the node number of the graph, they are not compatible with zero-shot learning. Therefore, Fl scores are listed in Table 4 in comparison against two general graph transformers, which are designed for various vertex-cardinality. It is worth highlighting that our model outperforms all competitors under different data settings except for ADNI->OASIS dynamic. Specifically, NeuroPath can surpass the best of others with 16.8 score for HCPA->UK static. Although the performance of zero-shot learning by NeuroPath still has an observable gap to the fully supervised version listed in T and
2 results here show that the neural pathway pattern learned by NewroPath is more consistent than FC pattern across datasets.
4.4 Ablation of Hyperparameter
Since the length of the neural pathway is limited by the head number of two branches in NeuroPath, the ablation of the head number in MHSA leads to various performances of our model. As shown in Fig. 4 we set head number H from to 8 keeping all other settings remain the same. The green
8

---

Table 5: Ablation of none branch (a vanilla Transformer), single branch, and twin branch of NeuroPart on four datasets with static BOLD as node attributes, where 'bold' and 'underline" denote the first and the second rank, respectively.
ADNI
OASIS
HCPA
UKB
Accuracy
score
Accuracy
F1 score
Accuracy
Fl score
Accuracy
Fl score
None
82,42.5.95
78.65
18.52
86.1913.81
97.53
99.53 97.53
99.53
w/ TD-MHSA
82.7447.88
77.51
89.05+3.00
86. 44.52
97.33+0.44
97.3444043
99.10=0.13
99.10+0.13
w/ FC-MHSA
81.9343.25
80.97
89.31
97.72.0.34 86,58
97.72.0.51
99 99.25
99.25
w/ both 85.5614.97
83.29
90.01
86.37
98.23
98.23
20.59
19.5910.21
curves shown in Fig. demonstrate clear peaks at 7 on datasets HCPA and UKB that are processed with a finer parcellation of 333 regions. In comparison, for the atlas used on datasets ADNI and OASIS has no more than 200 regions, the peak disappeared with a flat trend of F1 score suggesting longer pathways are less contributing the prediction under fewer regions. This is aligned with the nature of more hops needed to construct the same neural pathway where regions are more but smaller on HCPA and UKB than ADNI and OASIS.
HCPA
UKB
4.5 Ablation of Model Architecture
F1 score
98.0
99.4 -
97.5
99.2 -
Twin branch is a core design of Neu- roPath plant the insight of SC-FC coupling to deep model. The ablation of using none illustrate the effectiveness of our de- sign. As listed in 5 NeuroPath with twin branch has the best perfor- mance on all datasets except for the Fl score on OASIS. Despite TD-MHSA using the detour adjacency that can de- tect brain communities as mentioned in Sec. 2.1 SC-FC fused feature rep- resentation by using the consistency constraint LTD for twin branch has more contribution to the performance.
97.0
333 regions
333 regions
96.5
single branch can
F1 score
90-
ADNI
92.5
OASIS
900
87.5-
75
116 regions
85.0-
160 regions
Pathway length
Pathway length
Figure 4: Ablation study of various lengths of the neural pathway that is visible to NeuroPath. Static BOLD set as node attributes in this experiment. The blue shade is the range of error bars and the green lines are average Fl scores.
Table 6: Fl scores by models with different layer numbers on four datasets. 'Bold' and 'underline' denote the first and the second place of the average rank, respectively.
4.6 Ablation of Model Depth
HCPA
UKB
Rank
Rank
Performance comparison between models with different layer numbers listed in Table [6] Most of compet- ing models dropped on performance when increasing the layer number to 16, e.g., Graphormer dropped under 50 on HCPA and UKB datasets. In contrast, NeuroPath is more stable than others and has the best average ranking.
Layer #
4
8
16
4
8
16
BNT
91.81
93.41
93.28
3.67
88.63
96.32
97.45
3.00
BolT
97.01
97.81
88.23
2.33
81.36
89.20
89.84
4.00
Graphormer
64.08
47.01
50.84
5.00
43.42
43.44
59.46
5.00
NAGphormer
96.89
97.26
97.22
2.33
99.24
98.95
99.20
2.00
NeuroPath
97.76
97.72
96.60
1.67
99.59
99.61
99.44
1.00
ADNI
Rank
OASIS
Rank
BNT BolT Graphormer
76.39
75.91
77.28
3.67
85.32
85.96
85.21
3.33
75.93
78.67
78.23
2.67
85.30
84.55
85.55
3.67
78.58
74.12
74.12
4.00
84.45
83.87
83.87
5.00
NAGphormer
75.86
77.15
78.44
3.00
86.05
86.49
85.78 1.67
4.7 Ablation of Graph Building
NeuroPath
78.93
78.42
78.32
1.67
86.16
86.77 85.78 1.00
Performance comparison between models with different edge threshold to construct brain network is listed in Table Similarly, existing methods dropped on performance when graph is too dense or too sparse as the threshold of Pearson coefficient changed, which is an empirical hyperparameter. NeuroPath can keep the best average ranking in this case.
4.8 Pattern of Neural Pathway Contributing to Prediction
As we introduced in Sec. 3.2 NeuroPath in fact weighting neural pathways to obtain the feature representation of the brain network. Therefore, the neural pathways can be sorted by their weights

---

produced by our model. As shown in Fig. 5 we visualized three pathways corresponding to the same three functionally connected node pairs (blue nodes in Fig. where links that have the same color are members of the same pathway. To show the neural pathway pattern of diseased brain topology, the three functionally connected node pairs are selected from FC links that exhibit significant difference (p S 0.05) between AD and CN subjects from the OASIS dataset in f-test. We exclude the influence of inter-subject variations FC mentioned in Sec. 2.1 narrowing FC links in the r-test solely be- tween regions of the subcortical, entorhinal cortex, occipital lobe, and parietal lobe, where those brain structures are associated with the progression of AD 660 I.. In comparison of pathway visualization in Fig. [5] it is obvious that the AD subject demands longer SC detour to support the same direct FC link than CN subjects which only need shorter pathways (within two hops). This observation suggests diseased human connectome might need longer detour to support normal brain function since the brain network could rewire neurological fibers from other normal regions to fetch up lesion regions Therefore, this visualization is neuroscience evidence of the interpretability of NeuroPath.
8
Table 7:
Fl scores by models with different FC thresholds to build brain networks. 'Bold' and 'underline' denote the first and the second place the average rank, respectively.
4.9 Computational Costs
The computational costs can be indi- cated by the practical running time and the learnable parameter amount
HCPA
UKB
Rank
Rank
FC threshold
0.3
0.5
0.7
0.3
0.5
0.7
as listed in Table 8 Although Graphormer and NAGphormer are two models with lower parameter numbers than NeuroPath, they have slower training and testing than Neu- roPath with prepprocsssing leading to more computing time. This demon- strates the efficiency of NeuroPath.
BNT
95.73 92.57
84.51
4.00
76.41
98.64
94.46
4.33
BolT
87.02 95.78 94.68
3.00
86.98
99.29
87.04 3.67
Graphormer
90.41
53.05
88.43
4.33
97.76
86.54
96.73
3.67
NAGphormer
96.08
94.76 96.85
2.33
97.80
99.22
98.78
2.33
NeumPaath
97.57 95.09 97.32
1.33
99.27
99.59
99.15
1.00
ADNI
Rank
OASIS
Rank
BNT
77.74 80.16
77.92
1.67
85.
85.32
86.05
3.67
BolT Graphormer
74.33 76.68 76.53
4.00
84.98
84.91 84.67 4.67
75.82 77.78 75.17
3.33
86.23
85.44 87.15 2.00
NAGphormer
72.55
75.40
77.29
4.67
86.32
83.87
85.78 3.67
Conclusion
NeuroPath
78.36 77.35
79.49
1.67
86.59
87.02
86.13 1.33
In this work, we propose NeuroPath, a graph transformer to model the physical neural pathway by our novel multivariate SC-FC coupling mechanism and learn the relationship between neural pathways and brain functions. The framework of NeuroPath driven by the neuroscience insight can effectively produce SC-FC coupled feature representation of multi-hop neural pathways from the twin branch design. Compared to SOTA brain models and graph transformers on large-scale datasets including HCP and UKB under various data settings, our experiments have not only demonstrated the superior performance of NeuroPath in neural activity classification and cognitive disordering diagnosis but also provided great interpretability. Planting the proposed multivariate SC-FC coupling into the design of NeuroPath enables it to be not only applicable for zero-shot learning on unseen datasets but also better performance than general SOTA models on resting/tasking classification and AD diagnosis. By visualizing the top-1 neural pathway contributing to the prediction by NeuroPath, more interpretability is brought our performance on AD diagnosis, and the observation of visualization agrees with the hypothesis that it needs longer structural detour to support a functional but diseased human connectome. Modeling neural pathways shows us clue of fundamental neuroscience models to decipher the relationship between brain structural and functional topology.
Table 8: Computational complexity in experiments, where computing time the average on UKB dataset with unit the millisecond per graph data.
Param # Preproc. Train Test
BrainGNN
7.30M
7.24
2.61
BNT
1.57M
1.82
0.64
AD
CN
BolT
1.58M
3.83
1.83
Figure 5: The visualization of the top-1 neural pathway
Graphormer
0.30M
270
2.79
0.90
that corresponds a significant FC link contributing
NAGphormer
0.26M
3.92
1.85
NeumoPth
0.69M
1.61
0.67
the prediction by NeuroPath on OASIS dataset.
10

---

6 Acknowledgments
Thanks to the Foundation of Hope and NIH grant AG068399.
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[62] Chengxuan Ying, Tianle Cai, Shengjie Luo, Shuxin Zheng, Guolin Ke, Di He, Yanming Shen, and Tie- Yan Liu. Do transformers really perform badly for graph representation? Advances in neural information processing systems, 04:28877-28888 2021.
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A Appendix
A.1
Accessibility
All data can be accessible via internet (HCPA) UKB ADN OASIS The licenses to obtain those data can also be accessed on the websites. The preprocessing algorithm is introduced in the next section. The codes and data split settings can be acquired via this code repository
A.2 Data Preprocessing
The neuroimage processing consists of the following major steps:
We segment the Tl-weighted image into white matter, gray matter, and cerebral spinal fluid using FSL software [27]. On top of the tissue segmentation Fig. 6 we parcellate the cortical surface of IMRI into cortical regions according to the different atlas regional signal of timeseries in Fig. 6 where FC, in the end, the Pearson correlation coefficient between regional timeseries. Additionally, convert each DWI scan to diffusion tensor images (DTI) (44 in this step.
We apply surface seed-based probabilistic fiber tractography producing an anatomical connectivity matrix (SC in Fig. 6 the anatomical connectivity is defined by the number of fibers linking two brain regions normalized by the total number of fibers in the whole brain.
18 using the DTI data, thus
Note that the weight of
Constructions of SC and FC Networks
TIw MRI
Brain extraction, tissue segmentation. brain mask refinement,
FC SC
IMRI
Head-motion estimation, slice time correction, confounds estimation,
Workflow
DWI
Image gradient, template construction, .... tractography.c ....
Figure 6: General workflows for processing Tl-weighted image (Tlw MRT), functional MRI (fMRI) and diffusion-weightee image (DWI). The output is shown at the right, including two brain networks of FC and SC.
httpps//www.hhmsaccueettttm.teee
http:://ww.uubb.bbnk.cc.
www.looii.uuucccc.. https://adni..oni..o use. udw.
15

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A.3 Data Profiles
Data profiles of four datasets are listed in this section. As listed in Table the graph number of static data could be larger than the subject number in the corresponding dataset introduced in the main text since few subjects have multiple runs/sessions in datasets, where the time gap between runs/sessions is large so they are preprocessed as independent data. Dynamic data is split from the full scan of one subject into 100-length slices causing more graphs and different connectivity.
One major phenotype of brain networks is the age of the subject as shown in Fig. Accordingly, our experiments are setup with wide range of ages.
Table 9: Data profiles, where |G' denotes the number of graphs, and aeg(D) (D) denotes the average degree of brain networks.
|C denotes the number of classes,
HCPA static
UKB
ADNI static
OASIS static
dynamic
static
dynamic
dynamic
dynamic
Gl [C) avg(D)
4,863
18,306
5,890
22,600
138
294
402
1,678
4
2
2
2
2
2
2
6.53
13.52
12.85
36.07
44.44
43.89
56.47
59.36
HCPA: Age in month
ADNI: Age in year
120
60
100
80
40
60
40
20
20
10
1432 6086)
7281
6541
(508, 680)
(728, 802]
1802 8788)
(850, 1024)
1876, (sa)
(1004, tona))
(1172, 1280)
(1096, 1177)
(664,
(580,
(70.6,74.5)
(66.7, (6.7770.6)
78.478.41
(62.8 68.73.0.71
(7844
82:3)
62.8]
50:21
58.9)
(en. s0.10.11 11
(88.8,
(82.3.
1SS,
Figure 7: The age distribution of HCPA and ADNI datasets, where blue bars are histograms of age, and orange curves denote the data percentage accumulation.
A.4 Detailed Steps of Paired r-test
A paired f-test is run for the topological detour degree found by the depth-first algorithm with radius of 6 for every parcel per subject between resting and tasking groups, where there are 716 subjects in total from the HCPA dataset. The vector of parcel from all subjects in the same group is the input to 1-test algorithm, where subjects of two groups are strictly paired. In comparison, the degree of FC is calculated by the total number of FC links for every parcel and tested in the same way using 1-test algorithm. After (-test, significant parcels are obtained by filtering the p-value smaller than 0.05. Gordon parcellation has fine partition (n=330) of the brain and has 12 pre-defined sub-networks relevant to brain functions. The overlap ratio calculated by Nawn; where Nsign: is the number of parcels of i-th community have 0.05 and Nnet, is the total number of parcels in i-th sub-network.
Nuet,
A.5 Paired 1-test on diverse populations by gender on HCPA dataset
As shown in 8 detour across diverse populations by gender. By comparing the detour degree with the FC degree, we draw the same conclusion in Sec 2.1. It is worth noting that the male group shows lower detour degree, i.e., fewer detour pathways, than the female group in the HCPA dataset.
the same I-test in F in the main text for the degree of our topological
A.6 Proof of Fact
Wins). where The top pathway representations are obtained by arg maxj.1 ( CyEp SSiT
Fact 3.1
denotes the softmax of self-attention, p C P a set of node index of a path and P the node collection of neural pathways within H-hop starting at i-th node.
16

---

Female group in HCPA
Male group in HCPA
Detour degree
Detour degree
p-PoluP 0.99
FC degree
p-ralce 6M5
FC degree
Functional sub-networks
Functional sub-networks
C
Default Mode
Visual
C Sensorimator
Default Mode
Visual
( Sensorimotor
Over-
Detour degree
Over-
Detour degree
tap ratio
FC degree
FC degree
Sub-networks
Sub-networks
Figure 8: The same I-test as Fig.2 in the main text runs on two diverse populations by gender among
HCPA dataset.
Proof. The first is to expand Eq. by using definitions mentioned in Section 3.
(TD(X) Concat (X)...., XH) W
H
(4)
Σ X, W i -h- (A-1)=C.j==h+)
where Wing is slice of weights W with entries, and we have
X, Softmax (X + mmakk (D*)) (X²x)
(5)
In plain words, Sof tmax in the above equation the standard softmax operation that only involves h- hop connected columns and applies every row, then it produces a self-attention matrix S E NNN where
Sof tmax (Iz), if argtrue 1,1
S
(6)
otherwise.
where x denotes the term inside Sof tmax in Eq.
Then
frD(X):
Σ Σ
Sn Wenj-
(7)
h=1 jEargtrue
Herein, this proof is transformed to representing node sets of all pathways by D /. ie., the following Lemma
Th- lh.......
Lemma A.1. The node collection of half of the neural pathways within H Hohop started the i-th node can be sorted as P E {argtrue D Jh=1,...,, where 'collection' denotes a set allowing repeated members.
To prove this Lemma, there is an easy fact that can be seen. If Vi the degree D; 0, then
A S S++2 0, vh > 0
(8)
This is true since V1 < N, (Å $ 0. Then, given that D ((AS))>
(AF) and F
remains unchanged with various h, we can have the same deduction on detour adjacency matrix
D - D h+ 0, vh
(9)

---

9 bD > 0, the j-th node will present accumulated on every other hop adjacency matrix, 0 if k = + and E Ø Thus, the node index j as a member multiple/single pathways with at least length of h appears (H - h) + times.
Given Eq.
i.e., A Dx
Assuming path sub-graph starts at i-th node ends at ft-hop and has the node index collection {i 1++1,++ ., t1, ,. + h} regardless of the starting node, then this case,
P = { + t] -)//2 1))
(10)
where [:] means repeating elements times in a collection. Since the entire node index collection
of one path is {li + t| (h -1 + 1)]==,,.-. ,A, Pf can be sorted as exactly the half of all simple
paths this path sub-graph if it contains even number of nodes, or half + the number is odd.
Consequently, we can make a deduction from one path to all non-overlap paths started at i-th node, where the definition of neural pathway in our work the non-overlap paths.
Taking Eq. 7 and Lemma A.1 together, fTD(X) [); weights all nodes of half of the neural pathways by sorting results P. By assigning each node with the learnable weights S. Wijj since S.y is a scalar that can be moved aside to matrices, each path weights is thus represented by this weight consists of learnable parameters and can be extracted explain the contribution by neural pathways to any downstream application. This can finish the proof.
A.7 Hardwares
local platform that has dual Intel(R) Xeon(R) Gold 6448Y CPUs and four NVIDIA RTX 6000 Ada GPUs. All SOTA models in our experiments used the default hyperparameters except for Graphormer which is implemented by us. Detailed settings can be found in the released codes.
Our experiments
A.8 Limitations and Discussions
The limitations of NeuroPath
folds. First, the top path representation limited on the half number of neural pathways in theory. This limitation is amplified in dynamic data that has a higher degree of connections leading more pathways, where the performance is relatively lower than in static data as listed in the tables of our experiments. Although our detour adjacency matrix avoids finding all simple paths terms of computational complexity, modeling brain network with all neural pathways could make NeuroPath more fundamental. Second is the limited size of disease datasets used in the experiments.
A.9 Societal Impact
Our major contribution to the machine learning field a novel graph transformer framework that has sufficient expressive power for the neural pathway of human connectome with much lower computational complexity than previous path neural networks. This allows us to develop new deep model with novel multivariate SC-FC coupling mechanism. Furthermore, zero-shot learning experiments to demonstrate the potential of our model to be a fundamental neuroscience model. From the application perspective, the new deep model for uncovering the physical neural pathway supporting the in-vivo functional connection has great potential to establish a new underpinning of the relationship between brain structure and function topology.
have provided
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Reviews:
[{"review_id": "JgRtTzN61t", "reviewer": "Reviewer_4uWQ", "summary": "This paper introduces a transformer model that integrate both structural connectivity (SC) and functional connectivity (FC). It formulates a graph representation learning framework to extract feature from the brain connectome data. The model has two branches to encode SC and FC data separately, and later training to align the two modalities with consistency constrain loss. The learned representations could be further applied into multiple downstream tasks, including neural activity classification, cognition disordering diagnosis, etc. It also demonstrates its performance on zero-shot learning.", "questions": "1. How is the temporal information and complex dynamics of functional connectivity modeled in the framework? What is the limitation for the window size for the dynamics to be captured?\n2. What is the scalability of the proposed model?\n3. Discuss choices for hyperparameters?\n4. Discuss major differences in the developed method with compared baselines?", "limitations": "The paper does not have potential negative societal impact. The limitation of modeling dynamical data and limited data size has been thoroughly discussed. Justifications for 9, 11, 13, 14, 15 are missing in checklists.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "**Motivation**\n1. The paper is well motivated to integrate both functional connectivity and structural connectivity in brain connectome data to improve the performance in the downstream tasks.\n\n**Method**\n1. This model has focused to develop an efficient model with half of the expressive power of PathNN, and also provided with a theoretical proof. \n2. The pattern of neural pathway to help interpret the model's prediction adds more strengths to the proposed method. \n\n**Evaluation**\n1. This work did extensive evaluation on multiple benchmarks and multiple baselines, and performed ablation studies to demonstrate the effectiveness of the having two branches of NeuroPath model. \n2. The demonstration of model's capability on zero-shot learning is interesting.", "weaknesses": "**Novelty**\n1. The model has limited novelty compared to existing SOTA models using transformer, and graph transformer model on brain connectome data.\n\n**Peformance**\n1. The model also has limited improvement on the model performance. The accuracy is on par or worse than SOTA baseline in multiple downstream tasks. \n2. Though the authors highlight the efficiency of model designs, while the proposed model's size (0.69M) is larger than some baselines including Graphormer (0.3M), NAGphormer (0.26M) which achieved comparable performance.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Novelty\n1. 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.\n\n - 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.\n\n - 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. \n\n|     | PathNN  | Graphormer  | NAGphormer | *NeuroPath* |\n| - | - | - | - | - |\n| Pre-process type         | All simple paths        | Shortest distance | Graph diffusion | None      |\n| Pre-process time / graph | 5.23s ($H=4$), 650s ($H=5$) | 270ms             | 40ms            | \\-        |\n\n\n## Performance\n1. 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.\n\n|  | HCPA | UKB  | ADNI | OASIS |\n| - | - | - | - | - |\n| MLP   | 4.0  | 3.0  | 6.9  | 3.3   |\n| GCN   | 4.5  | 3.75 | 4.4  | 5.3   |\n| BrainGNN   | 7.0  | 7.0  | 4.1  | 4.4   |\n| BNT   | 2.8  | 5.0  | 2.1  | 2.8   |\n| BolT  | 2.5  | 2.25 | 5.8  | 6.5   |\n| Graphormer   | 8.0  | 8.0  | 4.6  | 6.4   |\n| NAGphormer   | 5.3  | 5.3  | 5.8  | 5.0   |\n| *NeuroPath*    | **2.0**  | **1.8**  | **1.6**  | **2.5**   |\n\n2. 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.\n\n|   | Param # | Pre-proc time / graph | Train / graph | Test / graph |\n| - | - | - | - | - |\n| Graphormer | 0.30M   | 270ms   | 2.79ms        | 0.90ms       |\n| NAGphormer | 0.26M   | 40ms     | 3.92ms        | 1.85ms       |\n| *NeuroPath*  | 0.69M   | \\-     | **1.61ms**        | **0.67ms**       |\n\n## Questions\n**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.\n\n**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.\n\n|Model     |HCPA |     |     |Rank|UKB  |     |     |Rank|\n|-|-|-|-|-|-|-|-|-|\n|Layer #   |4    |8    |16   |    |4    |8    |16   |    |\n|BNT |91.81|93.41|93.28|3.67|88.63|96.32|97.45|3.00|\n|BolT    |97.01|97.81|88.23|2.33|81.36|89.20|89.84|4.00|\n|Graphormer|64.08|47.01|50.84|5.00|43.42|43.44|59.46|5.00|\n|NAGphormer|96.89|97.26|97.22|2.33|99.24|98.95|99.20|2.00|\n|*NeuroPath* |97.76|97.72|96.60|**1.67**|99.59|99.61|99.44|**1.00**|\n\n| |ADNI |     |     |Rank|OASIS  |     |     |Rank|\n|-|-|-|-|-|-|-|-|-|\n|BNT  |76.39|75.91|77.28|3.67|85.32|85.96|85.21|3.33|\n|BolT |75.93|78.67|78.23|2.67|85.30|84.55|85.55|3.67|\n|Graphormer|78.58|74.12|74.12|4.00|84.45|83.87|83.87|5.00|\n|NAGphormer|75.86|77.15|78.44|3.00|86.05|86.49|85.78|1.67|\n|*NeuroPath* |78.93|78.42|78.32|**1.67**|86.16|86.77|85.78|**1.00**|\n\n**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.\n\n**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.\n\n[1] 10.1109/tpami.2022.3154319\n\n[2] 10.48550/arxiv.2306.05955\n\n[3] 10.48550/arxiv.2306.06202\n\n[4] Brain Network Transformer\n\n[5] 10.1016/j.media.2021.102233\n\n[6] 10.1016/j.media.2023.102841", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "sd5fqOkAot", "reviewer": "Reviewer_Qyot", "summary": "This paper introduces a novel way of predicting brain diseases with the help of structural and functional brain connectivity. It couples structural as well as functional connectivity from human neuroimaging studies. It comprehensively studies the performance of the new method on a large variety of datasets. In all, the study is quite comprehensive in terms of experiments.", "questions": "The ablation studies would be better described with visual information and other properties.", "limitations": "See weaknesses", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "There are a lot of experiments on a variety of different datasets and hence this makes it a very robust method for mentioning structural and functional connectivity. Most results are also statistically significant with p < 0.05. the model structure is also well mathematically described.", "weaknesses": "Some mathematical details are not very understandable Framework of twin branch, FC-MHSA etc. Equations on line 173 are not easy to understand. The results of the ablation studies are not presented in a very comprehensive manner.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Weaknesses\n\nEquations 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 $h=1,\\dots,H$.\n\n## Questions\n\nWe 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.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ZAOFQl630y", "reviewer": "Reviewer_6veV", "summary": "Authors propose NeuroPath, a transformer-inspired model that leverages a multi-head self-attention mechanism to capture multi-modal feature representations from SC (structural connectivity) and FC (functional connectivity) graphs. The model is evaluated on well-known large-scale public datasets OASIS, ADNI, UK Biobank, and HCPA. One of the main novelties of the paper is the use of coupled SC and FC graphs.", "questions": "Would you have more information on the demographics of the datasets included in the paper?", "limitations": "While the model aims to handle inter-subject variations, it's unclear how well it accounts for individual differences in brain structure and function across diverse populations. It would be nice if the authors could include a discussion about that.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "This paper introduces the concept of *topological detour* to characterize how functional connectivity (FC) is supported by neural pathways in structural connectivity (SC). This approach goes beyond the traditional univariate coupling, allowing the model to capture complex, multi-hop pathways that support functional connectivity. The proposed model architecture uses a *twin-branch approach* to accommodate the SC-FC pairing.", "weaknesses": "While the authors do include a table with the number of learnable parameters, it would be nice to include explicit information about the training procedures and the necessary time to train the model.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## Weaknesses\nThe 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.\n\n|          |Param #|Pre-proc time / graph|Train / graph|Test / graph|\n|----------|-------|---------------------|-------------|------------|\n|BrainGNN  |7.30M  |\\-                   |7.24ms       |2.61ms      |\n|BNT       |1.57M  |\\-                   |1.82ms       |0.64ms      |\n|BolT      |1.58M  |\\-                   |3.83ms       |1.83ms      |\n|Graphormer|0.30M  |270ms                |2.79ms       |0.90ms      |\n|NAGphormer|0.26M  |40ms                 |3.92ms       |1.85ms      |\n|NeuroPath |0.69M  |\\-                   |1.61ms       |0.67ms      |\n\n## Questions\n\nYes, we have. Distributions of the subject age are shown **in Fig.S1** in our newly uploaded PDF file. \n\n## Limitations\n\n**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.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "IBPE0KbOco", "reviewer": "Reviewer_g82y", "summary": "In this work, the authors propose NeuroPath, a graph transformer acting on structural (SC) and functional (FC) connectivity matrices. NeuroPath aims to learn the relationship between these pathways and brain functions. The framework uses a twin-branch design to generate coupled features of multi-hop neural pathways. \n\nExperimental results on large datasets such as HCP and UKB show that NeuroPath outperforms state-of-the-art (SOTA) brain models and graph transformers in tasks like neural activity classification and cognitive disorder diagnosis. It offers superior performance in resting/tasking classification and Alzheimer's Disease (AD) diagnosis, showing promise for zero-shot learning on unseen datasets. \n\nThe model's interpretability is enhanced by visualizing the top neural pathways contributing to its predictions.", "questions": "-\tClarification on Thresholding Methodology: What specific thresholding techniques were used to derive the structural and functional connectivity matrices? Could you provide details on the criteria and process for selecting these thresholds?\n-\tConsistency Across Models: Were identical thresholds applied to the connectivity matrices across all models tested in your experiments? If different thresholds were used, please elaborate on the reasoning behind this choice and the potential impact on the results.\n-\tImpact of Threshold Variation: Is there a possibility that adjusting the thresholds applied to the connectivity matrices could result in other models outperforming NeuroPath in predictive performance? Have you conducted any experiments to explore the sensitivity of the results to different threshold levels?\n-\tDefinition of Model's Expressive Power: How do the authors specifically define the \"expressive power\" of the model in the context of your study? Could you provide a clearer explanation of this concept and how it relates to the model’s ability to capture and represent complex neural interactions?\n-\tLine 129: \"Transform\"-> \"Transformer\"\n-\tLine 163: \"Production\"-> \"Product\"", "limitations": "Yes, the authors included short sections in the appendix covering the Limitations and societal impact of their work.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "-\tComprehensive Integration of Connectivity Matrices: incorporates multi-hop structural and functional connectivity matrices, enabling to investigate the interplay between these two types of neural interactions. This approach addresses a significant gap in understanding brain function, as the relationship between structural and functional connectivity remains a complex and open research problem in neuroscience.\n-\tExtensive Experimental Evaluation: NeuroPath's effectiveness is demonstrated through extensive experiments on large-scale datasets, including thorough comparisons with state-of-the-art (SOTA) and traditional models. The results consistently show that NeuroPath achieves superior performance, highlighting its potential to advance the field of neural activity classification and cognitive disorder diagnosis.", "weaknesses": "-\tThresholding Ambiguity: Structural Connectivity (SC) and Functional Connectivity (FC) matrices are significantly influenced by the thresholding applied to filter their entries. The paper lacks clarity on how this thresholding process was implemented and whether a consistent threshold was applied across all models tested. This omission raises concerns about the comparability and validity of the experimental results.\n-\tLack of Clarity on Theoretical Foundations: Fact 3.1 is insufficiently explained, and its proof in the Appendix is difficult to follow. The paper does not clearly define the \"expressive power\" of the model, leaving readers without a solid understanding of this key concept and its implications for the model’s performance. This lack of clarity diminishes the strength of the theoretical contributions and the overall comprehensibility of the work.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**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.\n\n**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.\n\n|Model       |HCPA |     |     |Rank|UKB  |     |     |Rank|\n|------------|-----|-----|-----|----|-----|-----|-----|----|\n|FC threshold|0.3  |0.5 |0.7  |    |0.3  |0.5|0.7  |    |\n|BNT         |95.73|92.57|84.51|4.00|76.41|98.64|94.46|4.33|\n|BolT        |87.02|95.78|94.68|3.00|86.98|99.29|87.04|3.67|\n|Graphormer  |90.41|53.05|88.43|4.33|97.76|86.54|96.73|3.67|\n|NAGphormer  |96.08|94.76|96.85|2.33|97.80|99.22|98.78|2.33|\n|NeuroPath   |97.57|95.09|97.32|**1.33**|99.27|99.59|99.15|**1.00**|\n\n|       |ADNI |     |     |Rank|OASIS  |     |     |Rank|\n|------------|-----|-----|-----|----|-----|-----|-----|----|\n|BNT         |77.74|80.16|77.92|1.67|85.14|85.32|86.05|3.67|\n|BolT        |74.33|76.68|76.53|4.00|84.98|84.91|84.67|4.67|\n|Graphormer  |75.82|77.78|75.17|3.33|86.23|85.44|87.15|2.00|\n|NAGphormer  |72.55|75.40|77.29|4.67|86.32|83.87|85.78|3.67|\n|NeuroPath   |78.36|77.35|79.49|**1.67**|86.59|87.02|86.13|**1.33**|\n\n\n**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).\n\n[1] 10.1007/978-981-16-6054-2_5", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
# Thank for the insightful comments from all reviewers. 

## Performance concern

Since we aim to comprehensively test various scenarios of modeling brain activities, we run baselines and our NeuroPath using multiple experimental settings on each dataset. However, we simply list all numbers to show the model performance in the manuscript confusing readers to get a conclusion. We will revise the final version by adding the average rank of every method as one comprehensive performance rank on each dataset. 

## Additionally, there are three new experiments and three new figures in the newly uploaded PDF to support our response. 

 - Exp1: Model size scalability comparison between baselines and our *NeuroPath* that have more layers than in the manuscript.

 - Exp2: Performance stability comparison between baselines and our *NeuroPath* on all datasets with different FC thresholds.

 - Exp3: The same $t$-test as in Sec 2.1 runs on diverse populations by gender among the HCPA dataset to compare the inter-subject variations between the FC degree and our **detour** degree.

 - FigS1: Demographics of datasets.

 - FigS2: Results of Exp3

 - FigS3: Results of Exp1 and Exp2 are shown in line plots

We will include new results into the final version by adding to Tables 1, 2, and the Appendix.

Meta-review: This submission generated interest from the reviewers. They appreciated the solid and extensive empirical evaluation of the contributed model, that couples structural and functional connectivity. In addition, the reviewers saw benefits in the zero-shot capabilities, and decreased preprocessing needs. The limited improvement in model performance was noted.
Decision: Accept (poster)