Local-Global Coupling Spiking Graph Transformer  for Brain Disorders Diagnosis from Two Perspectives
Authors: Geng Zhang
Jiangrong Shen
Kaizhong Zheng
Liangjun Chen
Badong Chen
Venue: NeurIPS 2025 poster ()
Keywords: Spiking neural networks
brain-inspired computational model
Primary area: neuroscience_and_cognitive_science
TL;DR: A novel local-global coupling spiking graph transformer, enabling dual-perspective analysis for improved brain disorder diagnosis and interpretable biomarker discovery.

Abstract: Brain disorders have been consistently associated with abnormalities in specific brain regions or neural circuits. Identifying key brain regional activities and functional connectivity patterns is essential for discovering more precise neurobiological biomarkers. However, previous studies have primarily emphasized alterations in functional connectivity while overlooking abnormal neuronal population activity within brain regions. To bridge this gap, we propose a novel Local-Global Coupling Spiking Graph Transformer (LGC-SGT) that jointly models both inter-regional connectivity differences and deviations in neuronal population firing rates within brain regions, enabling a dual-perspective neuropathological analysis. The global pathway leverages spike-based computation in LGC-SGT to model biologically plausible aberrant neural firing dynamics, while the local pathway adaptively captures abnormal graph-based representations of brain connectivity learned by local plasticity in the liquid state machine module.  Furthermore, we design a shortcut-enhanced output strategy in LGC-SGT with the hybrid loss function to suppress outlier interference caused by inter-individual and inter-center variability, enabling a more robust decision boundary. Extensive experiments on three brain disorder datasets demonstrate that our model consistently outperforms state-of-the-art graph methods in brain disorder diagnosis. Moreover, it facilitates the extraction of interpretable neurobiological biomarkers by jointly analyzing regional neural activity and functional connectivity, offering a more comprehensive framework for brain disorder understanding and diagnosis.

Local-Global Coupling Spiking Graph Transformer for Brain Disorders Diagnosis from Two Perspectives
Geng Zhangl:2: Jiangrong Shen 1.2.4; Kaizhong Zheng
Liangjun Chen 12.3, Badong Chen 1,2,3
National Key Laboratory of Human-Machine Hybrid Augmented Intelligence
National Engineering Research Center for Visual Information and Applications Innttittte of Artificial Intelligence and Robotics, Xi'an an Jiaotong University *Faculty of Electronic and Information Engineering, Xi' an Jiaotong University
Abstract
Brain disorders have been consistently associated with abnormalities in specific brain regions or neural circuits. Identifying key brain regional activities and func- tional connectivity patterns essential for discovering more precise neurobiological biomarkers. However, previous studies have primarily emphasized alterations in functional connectivity while overlooking abnormal neuronal population activity within brain regions. To bridge this gap, propose novel Local-Globa. Coupling Spiking Graph Transformer (LGC-SGT) that jointly models both inter-regional connectivity differences and deviations in neuronal population firing rates within brain regions, enabling a dual-perspeetivv neuropathological analysis. The global pathway leverages spike-based computation in LGC-SGT to model biologically plausible aberrant neural firing dynamics, while the local pathway adaptively cap- tures abnormal graph-based representations of brain connectivity learned by local plasticity in the liquid state machine module. Furthermore, we design a shortcut- enhanced output strategy in LGC-SGT with the hybrid loss function suppress outlier interference caused by inter-individual and inter-center variability, enabling a more robust decision boundary. Extensive experiments on three brain disorder datasets demonstrate that our model consistently outperforms state-of-the methods in brain disorder diagnosis. Moreover, it facilitates the extraction inter- pretable neurobiological biomarkers by jointly analyzing regional neural activity and functional connectivity, offering a more comprehensive framework for brain disorder understanding and diagnosis.
graph
Introduction
Brain disorders are complex, multi-level conditions characterized by alterations at both the neuronal and network levels [ Evidence suggests that excessive neuronal activity in the hippocampus and amygdala, along with reorganization of functional connections within the prefrontal cortex and the default mode network, likely contributes to cognitive impairments (2]. Connectivity patterns within these regions are particularly crucial, they mediate the integration of neural circuits that underpin cognitive function 3 Moreover, stress-relas related disorders, such as major depressive disorder (MDD) and schizophrenia, have been shown to be associated with neural activity in the amygdala 4.. Thus, abnormal activity in specific neuronal populations can disrupt neural oscillations, also leading cognitive dysfunction [5). Spiking neural networks (SNNs), which biologically model neuronal firing behaviors in a biologically plausible manner, offer a unique opportunity to integrate
*Corresponding author; jrshen @ www..zuuccccm.. ehenbd mji..xjtu.edu.co
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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connectivity analysis with population-level neural dynamics. Therefore, this study aims to distinguish patients from healthy individuals using SNNs, considering both neuronal activity and connectivity reorganization at the network level.
Recent advances in SNNs have demonstrated their capability characterize static functional connec- tivity p . Building on this foundation, recent studies have extended SNN frameworks to However, their analytical paradigms are limited to functional connectivity changes between brain regions, overlooking the representation of neuronal dynamics within brain regions. This limits their completeness in modeling brains. For example, Alzheimer's 's pathological changes often begin with micro- dincro-dsssuptionss in synaptic plasticity within the hippocampus, while abnormalities macro-level functional connectivity may not become apparent for several years [T]. Therefore, by modeling the dynamic characteristics of neuronal clusters within brain regions alongside functional connectivity differences, we can capture brain changes from both microscopic and macroscopic perspectives, providing more accurate biomarkers. However, existing SNN frameworks seldom integrate these two perspectives, i.e. network topology and neuronal population responses, within a single computational model, limiting their ability to disentangle multi-scale biomarkers.
model dynamic functional and structural connectivity 8 g
To bridge this gap, we propose Local-Global Coupling Spiking Graph Transformer (LGC-SGT) that jointly models inter-regional connectivity discrepancies and neuronal population firing rate deviations across brain areas, enabling a dual-perspece
analysis of neuropathology. Two critical perspectives are provided by our model: 1) disorder-sensitive alterations in inter-regional connectivity strength and topology, and 2) abnormal firing rate responses of neuronal populations within specific brain regions. Therefore, our framework dynamically links macroscale connectivity patterns with microscale- inspired spiking population dynamics. Our spike-based transformer integrates the local-global coupling module, the spiking transformer feature extraction block, and the shortcut-enhanced output strategy with a hybrid loss function. The local-global coupling module captures the spatiotemporal interactions of both aberrant firing rate and abnormal brain connectivity. The local liquid state machine (LSM) pathway guided by functional magnetic resonance imaging (fMRI) initializes region-specific neuronal populations with random connectivity, then updates synaptic weights via spike-timing dependent plasticity (STDP) to emulate local plasticity, constructing the functional connection pattern. The global adaptive spiking graph convolution pathway refines inter-regional connectivity weights via Backpropagation and integrates global information capture the neural firing dynamics. Besides, the
output module with the hybrid loss function is designed to obtain a more robust decision boundary by suppressing the interference caused by the outliers since the differences between inter-individual and inter-center.
The contributions of our paper could be summarized as follows:
We propose the globall coupling spiking graph transformer framework for brain disorder diagnosis. The spike- based transformer integrates local and global pathways, attending to spatiotemporal interactions of both aberrant firing rate dynamics and abnormal brain connectivity.
The chortcut-enhanced output strategy with the hybrid loss function is designed to obtain a more robust decision boundary by suppressing the interference caused by the outliers since the variety of inter-individual and inter-center.
The experiments on three brain disorder datasets show that the proposed LGC-SGT model outperforms existing methods and provides the duallpperspectvv biomarker discovery of interregional connectivity discrepancies and neuronal population firing rate deviations.
2 Related Work
2.1 Function-based Brain Networks Analysis
With the rapid advancement of neuroimaging technologies, researchers have progressively established systematic neuroimaging baasndiinn---eddddie paradigm for investigating brain networks [I]], with fMRI emerging as a crucial data foundation for constructing brain networks through its unique integration of whole- brain coverage and high spatial resolution [2]. The complexity of modeling the brain's 'ss topological relationships has sparked researchers' interest, leading to the development of methods using Graph Neural Networks (GNN) for brain network analysis [13. Additionally, approaches such adaptive

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X2
AMRI
ROI
Input Graph
Local-Global Coupling Block
Spiking Transformer Block xL
Output Block
Local Pathway
Levenablle
Mapping
Connectivvty
sylugs (1 slg!l -3)
Bacipropagction
LSM
Ligad State Nadhinn
-Ale N?
5
Gola
Global Pathway
Neuronal
SSA
Bolking Adtoninn
Dynamic
EN
Butch Narm
Figure 1: The overall framework of the proposed LGC-SGT model.
brain region discrimination 14 information-theore theory-driven connectivity selection 15, and long-
range dependency modeling [6 have been proposed. However, these methods typically focus on modeling functional connectivity relationships and often overlook the representation of neuronal population dynamics within the brain.
SNN-based Brain Networks Analysis
Recent years have seen growing applications of SNNs in diverse fields [1719]. owing to their biological plausibility and low-power characteristies [20]. In brain cognitive modeling, SNNs enable hiologically-base brain network modeling by simulating the dynamic processes of biological neurons. Three-dimensional spiking neural network architectures facilitate the analysis of spatiotemporal neural data through biomimetic topological design [21]. By spatio-temporal associative memories in SNNs, Kasabov et al. [22] achieved brain disorder classification based on 1MRI data. The biologically- inspired characteristics of SNNs reveal how mindfulness training reorganizes brain networks (23 and allow for data analysis the coupling between brain structure and functional connectivity [ Additionally, SNNs constrained by fMRI topology uncover auditory coding mechanisms from the perspective of information transfer efficiency [24]. Anatomically guided spiking networks leverage brain anatomical features to guide SNNs in autonomously learning brain network characteristics [25] Despite these advancements, current SNN frameworks still have limitations in brain network modeling, particularly in their lack of collaborative modeling that integrates inter-region network topology with the responses of neuronal populations within brain regions.
Method
3.1 Problem Definition
In brain network analysis, the core objective of our model is to predict the presence of a brain disorder or discover new biomarkers. Here, the network constructed based on graph-structured data derived from resting-state fMRI data. Formally, we derive set of graph-structured samples {g).... ,.N) for N participants and n ROIS, where each sample G (A', "'','" X',y²) denotes the functional architecture of the i-th objects. In each functional graph of G A E {0, ]] is the graph adjacency matrix that represents the functional connection relationship between brain ROIs. X' E _ denotes the node feature matrix that captures functional activity intensity of the brain ROIS, with the corresponding label of y" that distinguishes brain disorders or healthy controls (HCs). Our following model aims to learn map [(A X²) + y² and discover the biomarkers in the process.
3.2 Local-Global Coupling Spiking Graph Transformer
As shown in Fig. D our LGC-SGT framework contains the local-global coupling module, the spiking transformer feature extraction block, and the shorteut-enhanced output module with hybrid loss

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function. The model begins by constructing a graph embedding that transforms graph-structured brain ROIs feature matrices and functional connectivity matrices into feature embeddings. Establish a map- ping of elementary connection patterns to higher-order pathological features. Specifically, we propose a local-global coupling block that synergistically integrates locally constrained biologically inspired features with globally optimized graph convolutional representations. This integration facilitates precise localization of abnormal brain regions and identification of pathology-relewe Next, we construct the spiking transformer block to effectively capture dependencies among features while strengthening their interactive relationships through dynamic attention weighting. The features processed through spike layer, after which the model combines the features before the spike layer with the binarized features from the spike layer to enhance the output used for binary classification between HCs and patients with brain disorders.
biomarkers.
Local-Global Coupling Module. Building upon the multiple level learning plasticity in the human brain, we propose a local-global coupling (LGC) module designed to simultaneously capture local and global features brain networks. Specifically, the LGC module integrates two parallel pathways: (1) local pathway learned by unsupervised learning via STDP, and (2) global pathway via supervised learning by backpropagation. This dual- autl-path architecture enables synergistic fusion of neuronal dynamics and network organization.
Local Pathway. This pathway mainly consists of three components: an input layer, a reservoir network, and a readout layer. The input layer encodes external signals into spike trains for the reservoir network. The liquid state machine layer comprises spiking neurons with sparse random connectivity, maintaining biologically plausible excitatory-to-iniibiie the cortical microcircuit organization [26]. The readout layer, typically implemented as a linear layer, decodes the states of neurons within the reservoir network. The calculation process of LSM can be described as follows:
ratio of 4:1, which mimics
v(t) ((L
(1)
where x is input of LSM, L is the nonlinear dynamic system (reservoir network), fM is the readout function (readout layer), and y(t) is the output of the readout layer time t. The nonlinear dynamic system L M here is realized with LIF neurons (all spiking neurons in this paper are LIF neurons), given by
u ()) pre = (t) + Wo',u(0 = (1) pre (1-0(1).
{
if fu(l))pre pre > Vih otherwise.
0
where (t). pre is the pre-synaptic input at time step f, r is the leaky factor, W is the weight parameter, Vin is the firing threshold, and (f is the spike output. The STDP rule is only used in the local pathway forward propagation, which can be mathematically represented follows:
ALTP e TIF,
if >t>0 0
AW
(4)
AL -LLDD e CLTDD
Af < 0
where AW represents the change in synaptic weight, At is the time interval between the pre-synaptic and post-synaptic spikes, ALTP and ALTD are control constants of long-term potentiation and long-term depression, respectively, and TLTP and TLTD are time constants.
Global Pathway. The local pathways may lead to the loss of original graph structural details. To mitigate this information loss, we introduce global pathway designed to preserve holistic network attributes. This global pathway employs spiking graph convolutional network with backpropagation to capture whole-bran brain dynamics, formally defined by the following equation:
H = D 1 A OGtobal = SN (BN (BN(eaaarr)()) + H,
(6)
where À - A + 7 is the adjacent matrix with self-connection, Ø is the degree matrix of A, H is the new node representation with connected aggregation, and Octobat the output of the global pathway. SN represents the spiking layer and BN represents the Batch Norm layer.

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Spiking Transformer Blocks. We employ spiking transformer [27] as the backbone network for learning features. The core of the spiking transformer spiking self-attention (SSA). Specifically, given the feature, it first computes the SSA, given by
Q(X) SN SN (Limmear,(X)) (X) = SN (Lineary (X)),,aarr()))))))))))))),)) ((X) SN (L(inacar((X))) (7)
SSA(X) M LP(((X) SN (X) V(X))).
After determining the attention, shortcut message aggregation scheme is applied from the features to the attention, followed by another SNN-enhanced MLP block with the shortcut. The following equations can describe the overall calculation process:
Attn' = SSA(X') + x -1.1=11... L.
(9)
O MMLP(SN(Attr' ))) + Attn', 1...LL L.
(10)
Shorteut-enhanced Output Strategy. Due to the discrete spike firing mechanism employed by SNNs, the step function is non-differentiable. Currently, surrogate gradient methods are widely adopted to address this challenge. However, the network depth increases, employing surrogate gradients inevitably leads to approximation errors and gradient vanishing. Typically, shortcuts can be introduced alleviate gradient vanishing and reduce the information loss (28), but this causes a conflict between the real-valued features intermediate layers and the binarization of SNNs. To address this, researchers have proposed placing spiking activation functions at the beginning of each block to maintain local binarization (29), while enforcing a final spiking layer at the end of the network to achieve global binarization, thus ensuring the network remains purely event-driven. However, binary spike outputs result in information loss. To mitigate the information loss caused by binarization, particularly its impact on classification performance, we propose a shortcut-enhanced output strategy by mixing the features before the spiking layer with their subsequent binarized features for the final output:
Ofnal = O' - SNNaa (O'),
(11)
where O'represents the continuous features before the spiking layer, and S Snnint(O') converts the continuous features into spiking features. The final output is obtained by multiplying the two, where the spiking signals represent important features, and the real-valued coefficients determine the intensity of the features.
3.3 Minimum Error Entropy Criterion
Significant individual differences exist between patients and HCs, and inter-site variability caused by differences in equipment and operational procedures further complicates the data. Traditional loss functions based on cross-entropy (CE) may lack robustness when dealing with such complex data distributions. To address this limitation, we introduce minimum error entropy (MEE) 30) as the extra optimization objective of the model. By minimizing the information entropy of the classification errors, MEE effectively suppresses the interference caused by outliers arising from individual and site differences while reducing reliance on assumptions about specific data distributions.
In cross-entropy loss, the optimization objective essentially measures the difference between two probability distributions, with the optimization performed independently on point-by-point basis. In contrast, MEE takes into account the statistical dependencies among the eтror samples. The error information e can be measured by Rényi's entropy [31]
1
(e)e) 1 log (e),
(12)
where error أ y between target ÿ and model output y, a is the order of entropy, usually = for the convenience of calculation, and Ve(e) is the information potential, given by
Vs(e) = (p())
1
G. ez).
(13)
N2
N
(-c²)
6²
p(x) = N Σ
Gz et), Go = exp
(14)
20
5

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where G. is Gaussian kemne with bandwidth o, and p(:) is the probability density function of error Obviously, minimizing the error entropy criterion (e(e) the same as maximum information potential (e)... Hereby, we define the MEE-Loss as:
[MEE H2((e) = log( N2
Σ
Gale; - ez))
(15)
Then the overall loss can be calculated follows:
LTtta LCR + ALMEE.
(16)
Theoretical Analysis To validate the robustness of MEE-loss, we conducted a theoretical analysis focusing on gradient perturbations caused by outliers. The CE-loss is defined as follows:
e e - f(x;0).
LCB = Σ p:loggi qi
(17)
ΣS=1
where p; is the target distribution, qi is the predict distribution, f is the network mapping. 2; is the network output for category i, x is input data, 0 is the learnable network parameter. Next, we compute the gradient:
C dCCE
VoLCE Σ
Vozi
Σ i=1
(p: - 9:) Vozi.
(18)
Oz,
Similarly, the gradient of MEE-loss is given by:
N
N
VEJUER = -lo(( N2
ΣΣ ==
Go (ei eei (Voe: Voez)).
(19)
If there are outliers in the input, the corresponding network will produce abnormal outputs. The gradient of CE is linearly related 2,, such that Voz, as |2s| f. As outliers increase, their influence on parameter updates grows linearly, directly affecting the gradient update. In contrast, for MEE, the Gaussian kernel mapping results in decrease the contribution of the kernel function as outliers increase: G" (e: Ej) 4 as les eşl This leads to the contribution of outliers to the gradient approaching zero.
4 Experiments
In this section, analyze the following aspects to demonstrate the effectiveness of our proposed
LGC-SGT model and dual-perseective biomarker discovery capability.
Q1. How does the performance of the model compare to other state-of-the-art baseline models?
Q2. Does the model detect abnormal firing rate responses of specific neuronal populations?
Q3. Does the model identify the functional connectivity changes in disorder-sensitive regions?
4.1 Experimental Settings
Datasets, Data Preprocessing, and Implementation Details. We evaluate the proposed LGC-SGT model using three brain network analysis-related fMRI datasets. (1) The ABIDE dataset [ which contains 528 patients with autism spectrum disorder (ASD) and 571 HCs. (2) The REST-meta-MDD
datase 2 which contains 848 patients with MDD and 794 HCs. (3) The SRPBS datase which contains 92 patients with schizophrenia and 92 HCs. The details of datasets, data preprocessing, and experimental implementation can be found in Appendix
http://appppeessl..cccccccossspp htt.eettt.rr//bidd//eeee httpe://rfmri.org//me
https://bicttresouusee jtt.stpsppp//pp///////ttt

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The selected baselines correspond to two categories, The first category is ANNs, including generalized graph networks and specialized brain networks. Specifically, these include GAT 33
Baseline Models.
GCN
34 SIB [35], DIR-GNN [36], ProtGNN [37. BrainGNN [3], IBGNN CI-GNN [39,, BrainIB [5). ContrastPool 14,, and ALTER [6]. The second category the
32
GIN
38.
SNNs. including SpikingGCN
40) MSG [1]. SiGNN 42). and SpikingGTT [27].
4.2
Performance Comparison (Q1)
Tenfold Cross-Validations Table I presents comparison between the proposed LGC-SGT model and the baseline models. The LGC-SGT significantly outperforms both categories of baseline methods across all three datasets. (a) Compared to ANNs. For generalized graph networks, our model demonstrates notable improvements the accuracy metric, achieving 6.2% increase the REST-meta-MDD dataset, 5.15 increase on the ABIDE dataset, and 9.2% increase on the SRPBS dataset. For specialized brain networks, we also observe superior performance, with ACC improvements of 0.9%, 2.5%, and 3.2% on REST-meta-MDD Compared SNNs. Our model achieves improvements of 4.9%, 4.3%, and 4.8% on REST-meta- MDD, ABIDE, and SRPBS datasets, respectively. These experimental results indicate that LGC-SGT consistently outperforms the existing baseline methods across all evaluated datasets.
ABIDE, and SRPBS, respectively. (b)
Table 1:
Tenfold cross-validation performance with ANNs and SNNs on three datasets (REST-meta-MDDD, ABIDE, and SRPBS) (%). The best results marked in bold.
Category
Methods
REST-meta-MDD
ABIDE
SRPBS
GCN
12
60.8 = 1.3
64.4 3.8
82.7 + 8.6
GAT
64.7 :
67.9
84.2 8.1
GIN
65.4 3.2
1.5
84.3 1 8.2
Generalized
SIB 35
57.7 3.2
6.77
81.1
DIR-GNN
64.4
6.70
83.9
ProtGNN
37
61.0 +: 2.1
6.1
84.3
ANN
BrainGNN
13
60.2 + 3.0
6.17
82.2 8.5
IBGNN
38
63.0 1.0+20 2.7
6.10
84.8
CI-GNN 39
66.8 4.0
6.35
87.5
Specialized
Brain
15
70,0 + 2.2
7..2
9.66
ContrastPooL
14
65.1 1.9
2.7
3.4
ALTER
65.8 3.3
70.5
89.5 19.5
SpikeGCN 40
66.0 2.1
68.7 1.6
86.5 2.5
MSG 41
60.4 2.4
81.9 1.9
Generalized
SNN
SiGNN 42
66.2 2.5
69.1 1 1.8
1.8
87.6 1 7.2
SpikeGT
61.8 3.5
65.8 1.4
88.7 3.6
Specialized
LGC-SGT (Ours)
70.9 + 1.7
73.0 - 2.6
93.5 = 3.0
Table Leave-one-site-out cross- validation performance on REST-meta-MDD and ABIDE dataset (%).
Dataset Methods
S1
S2
$3
S4
S5
S6
S7
S8
$9
S10 S11 S12 S13 S14 S15 S16 S17 Mean
CI-GNN 63.3 83.0 85.2 76.3
70.0
68.8
75.4 73.2 72.2 68.3 81.1 62.3 67.3 63.2 68.3 75.2 64.4 71.6
REST- BrainIB 63.3 73.0
85.4 77.8 71.3
68.8
73.2
75.7
80.6 72.0 82.1 67.1 69.4 63.2 70.1
71.1 68.9
72.5
MDD
meta-
SpikeGT 55,5 56.7
75.6 62.5
70.1
62,5
70.4
62.2 61.1 65.6
73.1 57.3 63.3
58.1 63.9
68.4
64.4
64.2
LGC-SGT 63.7 70.0 85.4 77.8 74.7 68.4 76.1 78.4 80.6 75.3
82.1 62.2 69.4 60.4 70.8
68.9
78.9
73.1
CL-GNN
71.1 67.8 64.3 67.9 77.8 78.1 69.2 75.0
63.4
75.1
71.0
BrainIB
72.7 73.4
70.1 67.9 77.8
83.3
74.7
64.8
73.1
ABIDE
SpikeGT
72.7 67.2 69.0
53.6 72.2
70.0 72.2
68.7 63.5
68.0
LGC-SGT 87.5 76.3 70.9 73.4 73.7 70.1 64.3 80.6 70.2 73.3 77.8 72.5 73.5 74.8 67.6 75.3 85.7 74.6
Leave-One-Site-Ont Cross- Validation. conduct save-one-site-out crossvalidation.
To further assess the performance of our model, we ABIDE and REST-meta-MDD datasets contain 17

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OLEL
FoOG.L
FOUNL
120
Number of spkkes
Number of spikee
202
Number
50
100
200
BSA
YCOL
PreCS
CAUL
MOG
POLI
DCGLL
CALL
POUNL
(b)
(C)
Figure Comparison brain region activity of HCs and patients on schizophrenia, ASD, and MDD. The top 5 different regions are shown. The two-sample 1-test with Welch's s correction was employed evaluate the significance of intergroup differences. Statistical significance was defined as p < 0.05. (a) Schizophrenia. (b) ASD. (c) MDD.
independent sites. In detail, divide each dataset into the training (16 sites of 17 sites) to train the model and the testing set (remaining site out 17 sites) for testing the model. We compared our model with CI-GNN, BrainIB, and SpikeGT. CI-GNN and BrainIB were chosen due to their performance better in tenfold cross-validation compared to other models, while SpikeGT represents typical transformer-based SNN model. The experimental results are summarized in Table 2 Compared the baselines, our model achieved the highest site-average accuracy, reaching 73.1% and 74.6% on REST- meta-MDD and ABIDE datasets, respectively. Moreover, demonstrates significant improvements across most sites, in- dicating that the strength of our model lies ability to generalize well across completely different multi-site datasets despite site-specific differences.
Table 3: Ablation study for the modules we design.
Dataset
Method
Accuracy
Baseline
70.94%
REST- meta-
MEE
70.77%
MDD
wo LGC
69.99%
w/o SEO
69.83%
Bascline 73.03%
Ablation Study. To rigorously evaluate the contribution of each proposed component to model's performance, conduct comprehensive ablation studies across three bench- mark datasets. The experimental design systematically isolates three critical elements: (i) the MEE-loss function, (ii) the LGC module, and (iii) the shorteut-enhanced output strategy (SEO). As shown in Table the LGC-SGT achieves the highest clas- sification accuracy three brain disorders classification tasks, demonstrating the effectiveness of the proposed modules.
ABIDE
w/o MEE
72.91%
w/o LGC
72.55%
w/o SEO
71.73%
Baseline
93.51
MEF
90.50%
SRPBS
w/o LGC
89.77%
w/o SEO
89.74%
In-depth Analysis of brain neuronal population dynamics (Q2)
To analyze the neuronal population dynamics of our model, we conducted rigorous statistical compar- isons. The results show that the differences in spiking activity between patients with brain disorders and HCs are statistically significant. Fig. illlssraates the five ROIs exhibiting maximal inter-group differences for each disorder, accompanied by their neuroanatomical schematics. Schizophrenia: Patients demonstrated aberrant activity in several brain regions, including the PreCG.L, MFG.L, PCL.L, CAU.R, and MOG.L. These findings align with prior studies (43|45) that abnormal activity in

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(a)
(b)
(c)
(d)
(e)
(f)
Figure 3: Comparison of brain functional connections of HCs and patients with schizophrenia. In the anatomical brain map, the thickness of the connections represents the strength of functional connectivity; in the circular layout chord diagram, blue lines indicate shared functional connections between the patient and HCs, while red lines represent connections unique to either the patient or HCs. (a) Patients with schizophrenia. ASD. (e) Patients with MDD. (f) HCs of MDD.
(b) HCs of schizophrenia. (c) Patients with ASD. (d) HCs of
these regions serves as potential cause of schizophrenia. These regions are primarily involved the maintenance of working memory, conflict monitoring, and the regulation of goal-directed behavior. ASD: significant activity differences emerge in the OLF.L, INS.R, DCG.L, CAU.L, and MTG.R. Supporting literature 446 further suggests that abnormalities in these regions are closely related to the core symptoms characteristic of ASD. These regions are responsible for detecting internal sensory signals and coordinating the allocation of attentional resources. MDD: patients showed significant activity alterations in the PCG.L, CAL.L, PoCG.L, PCUN.L, and CAU.L. Consistent with these observations, previous studies [49 50] have confirmed that abnormal activity in these brain regions may underlie the development of major depressive disorder. Abnormalitics in these brain regions may lead bias in the processing of negative information.
Comparative analysis across three brain disorders revealed distinct neural activity patterns of aberrant brain regions when contrasted with HCs. These results indicate that our model effectively simulates brain activity and identifies regions exhibiting abnormal neural activity in patients compared HCs. Clinical and neuroimaging results also validate the rationale of the biomarkers we discovered. The detailed experimental setting can be found in Appendix B.T
In-depth Analysis of brain functional connectivity (Q3)
To analyze the functional pattern under different brain disorders, we visualize functional connectivity. The results show that the functional connectivity between patients with brain disorders and HCs

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is significantly different. As shown in Fig. our model learned distinct connectivity patterns for schizophrenia patients and HCs, and obtained some functional connections that could distinguish patients from HCs. Schizophrenia: functional connectivity was significantly increased between the MFG.R and IFGrriang.H (frontoparietal network). This finding is consistent with previous studies [5] reporting that the connectivity between the sensorimotor network and the frontoparietal network enhanced in schizophrenia. ASD: the increased connectivity pointing to the HIP.L region, which aligns with prior research indicating functional abnormalities of the hippocampus in ASD [52]. MDD; connectivity between the THA.R R and HIP.L has been increased, consistent with findings from [53 that connectivity change in these regions is part of the pathophysiology of MDD.
The experimental results demonstrate that our model accurately reproduces the abnormal functional connectivity patterns observed clinically, effectively simulates the physiological mechanisms un- derlying brain functional connectivity, and reveals distinct connectivity patterns characteristic of brain disorders. Clinical and neuroimaging results also validate the rationale of the biomarkers we discovered. The detail of the experiment provided in the Appendix B.2
7 Conclusion and Discussions
summary, we propose the LGC-SGT model that jointly models inter-regional connectivity discrepancies and neuronal population firing rate deviations, enabling dual-perspective analysis of neuropathology. By integrating a shorteut-enhanced output strategy with a hybrid loss function, our framework achieves robust decision boundaries for brain disorder diagnosis. Extensive experiments on three brain disorder datasets demonstrate that the LGC-SGT model consistently outperforms existing graph learning methods, successfully identifying dual- perssectttee biomarkers from both inter-regional connectivity and neuronal firing rate abnormalities. This approach offers novel insights for clinical research and therapeutic strategies.
Conclusion.
Limitations. Although current work effectively simulates brain functional states using resting- state fMRI data, incorporating multimodal data, such as diffusion tensor imaging (DTT) for structural connectivity and electroencephalogran (EEG) for neural oscillations, would provide additional anatomical constraints and temporal resolution, enabling more accurate brain modeling grounded in biological and clinical relevance.
Acknowledgments
This work supported by the National Natural Science Foundation of China (Grant No. 62436005, U21 A20485, 62306274), China Postdoctoral Science Foundation under Grant Num- ber (No. GZB20250394), Young Talent Fund of Xi'an an Association for Science and Technology (0959202513037).
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A Datasets and Implementation Details
A.1 Datasets and Data Preprocessing
In the construction of brain connectomes, we first preprocessed the raw resting-state fMRI data using Statistical Parametric Mapping (SPM) software, including slice timing correction and head motion correction. Subsequently, the resting-state fMRI images were normalized to a standard space using deformation parameters that map the fMRI images to the Montreal Neurological Institute (MNI) template. In addition, a Gaussian filter with a half maximum width of 6 mm is used to smooth the functional images. The resulting fMRI images are filtered with a bandpass filter (0.01-0.08 Hz). After preprocessing, the average time series for each participant is extracted from each ROIs using the AAL atlas, which comprises 90 cerebral regions and 26 cerebellar regions. Then, functional connectivity was computed between all ROIs pairs using Pearson's 's correlation coefficient, followed by Fisher's s r-to-z transformation, resulting in 116 x 116 symmetric matrix representing the brain network. Their demographic information is summarized in Table
Table 4: Description of datasets. Demographic and clinical characteristics.
Characteristic
ABIDE
Rest-meta-MDD
SRPBS
ASD
HC
MDD
HC
Schizophrenia
HC
Sample Size
528
571
828
776
92
92
Age
8.4
7.7
34.3
13.0
39.6
12.4
Gender(M/FF)
464/64
471/100
301/527
318/458
47/45
60/32
A.2 Implementation Details
In the proposed LGC-SGT model, we had the following hyperparameters and the range of them in T And all experiments were performed single NVIDIA RTX 3090 GPU.
Table 5: Ranges of different hyperparameters.
Parameter
Rest-meta-
ABIDE
SRPBS
number of spiking transformer blocks
2
timesteps
lambda
0.1
0.2
0.2
MEE kernel
0.1
0.2
batch size
32
learning rate
le
4
weight decay
le
4
attention heads
embedding dimension
116
B Two Perspective Biomarker Discovery
The differences the association mechanisms between abnormal activity in brain regions and abnormal functional connectivity in pathological contexts primarily reflect their impact different levels of neural networks: the former focuses more on the activity levels of local brain regions, while the latter emphasizes the functional connectivity relationships between brain regions.
B.1 Brain Neuronal Population Dynamics
The analysis employs the Automated Anatomical Labeling (AAL) atlas as the criteria for brain region division, establishing precise one-to-one mapping between 116 spiking neurons and neuroanatomical regions (90 cerebral and 26 cerebellar).
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B.2 Brain Functional Connectivity
To analyze brain functional connectivity under different brain disorders, we performed separate STDP training of the model's 's local pathways using samples from each disorder group and the HCs. To further investigate disorder-specifee differences in functional connectivity patterns, we conducted the following analyses on the trained networks for each group: first, we established a mapping between the model's reservoir layer neurons and specific brain regions; second, we constructed functional connectivity maps based on the synaptic weight matrices obtained after training, quantifying the interaction strength between different brain regions; finally, by comparing network characteristics between patient and HCs, we identified abnormal connectivity patterns specific to each disorder, which may help elucidate the underlying neural circuit mechanisms of brain disorders. For visualization, we selected the top 100 edges with the highest weights along with their connected nodes.
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Reviews:
[{"review_id": "QHXBDttvHM", "reviewer": "Reviewer_TFUH", "summary": "This paper proposes a novel framework, LGC-SGT (Local-Global Coupling Spiking Graph Transformer), for brain disorder diagnosis by jointly modeling individual temporal dynamics and population-level brain network topology. It integrates spiking neural networks to capture biologically plausible local time-series patterns and graph transformers to learn global inter-subject connectivity. Experiments on ABIDE, ADHD-200, and REST-meta-MDD datasets demonstrate that LGC-SGT achieves state-of-the-art performance, highlighting its effectiveness and generalizability in brain disorder classification.", "questions": "see weaknesses", "limitations": "yes", "rating": 2, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1.\tThis paper proposes the local-global coupling spiking graph transformer framework for brain disorder diagnosis and achieve good performance.\n2.\tThe problem of brain disorder diagnosis is important and the solution of LGC-SGT is complete.\n\n\nWeakness:\n\n1.\tWhile the proposed LGC-SGT framework aims to jointly model intra-regional neuronal firing dynamics and inter-regional connectivity patterns, the rationale for integrating both local and global perspectives is not fully justified. If the core pathological mechanism lies in abnormal spiking behavior within specific brain regions, it is unclear why modeling the global topology of brain connectivity is necessary, especially when such connectivity changes may be secondary consequences of local neuronal dysfunction. The paper lacks a clear explanation of how the fusion of local spiking dynamics and global connectivity contributes synergistically to improved diagnosis, or under what circumstances the global patterns provide non-redundant or complementary information beyond what is captured at the local level. This leaves the motivation for combining both scales insufficiently supported from a neuroscientific perspective.\n2.\tThe LGC-SGT framework utilizes two distinct types of information to separately model local and global brain characteristics: the local pathway leverages fMRI time series within individual brain regions to capture neuronal population firing dynamics via spiking neural networks (LSM and STDP), while the global pathway uses functional connectivity matrices derived from inter-regional correlations to model macro-scale network topology via adaptive spiking graph convolution. However, the baseline methods used for comparison typically rely on only one type of information, without combining both. This creates an unfair experimental setup, as LGC-SGT benefits from access to a richer and more comprehensive feature space, which may partially account for its superior performance. The paper does not adequately address this discrepancy, raising concerns about the fairness and rigor of the experimental comparison.\n3.\tThe paper does not provide a thorough ablation study to evaluate the individual contributions of the local and global pathways. Specifically, it remains unclear how effective the model would be if it relied solely on local information (neuronal firing dynamics) or global information (inter-regional connectivity). Without such analysis, the importance of integrating both perspectives in LGC-SGT is not well justified. This lack of experimental evidence weakens the claim that the fusion of local and global features is essential for improved brain disorder diagnosis.", "was_revised": true, "final_justification": "The authors have not addressed my concerns about the motivation for applying the local and global coupling module.", "rebuttal": "We are grateful for the reviewers’ insightful comments. Please find our detailed responses below. We trust they resolve the raised concerns and welcome any further questions.\n\n**W1. About the integration between intra-regional neuronal firing dynamics and inter-regional connectivity patterns.**\n\nWe agree that a clear explanation of the integration between local spiking dynamics and global connectivity contributes to improved diagnosis. \n\nFrom a neuroscience perspective, there is a deeply coupled bidirectional interaction between the local spiking dynamics and global connectivity. This coupling makes it difficult to decouple the pathological origins, for instance, in the case of autism spectrum disorder (ASD), there remains no consensus on which neural changes are primary rather than secondary or compensatory [1]. In major depressive disorder (MDD), its pathophysiology involves interactions across multiple pathways, including abnormal neural activity, connectivity dysfunction, neuroinflammation, and dysregulation of neurotrophic factors [2]. In the aforementioned scenarios, a single-angle analysis is difficult to be effective [3].  Consequently, our method is capable of simultaneously considering regional activity and connectivity patterns, which is well-supported by the deeply coupled bidirectional interaction phenomenon from a neuroscientific perspective. \n\nFrom a clinical perspective, abnormal neuronal firing in specific brain regions often serves as the direct neural basis of core disorder phenotypes [4], making it one of the key biomarkers for neuromodulatory interventions. Meanwhile, brain function fundamentally relies on the coordinated interaction of multiple brain regions, and the activity of a single brain region must be interpreted within the context of its network topology to gain complete significance [5]. For instance, in MDD treatment, repetitive transcranial magnetic stimulation (rTMS) primarily targets the left dorsolateral prefrontal cortex (lDLPFC) [6]. Yet, its antidepressant effects stem not only from the modulation of local activity but also involve functional optimization of downstream regions such as the orbitofrontal cortex (OFC) and hippocampus (HPC) [7], as well as indirect regulation through the OFC-HPC circuit [8]. This process demonstrates that the modulation of local neuronal dynamics must rely on the global functional connectivity network to achieve optimal therapeutic effects, further underscoring the importance of integrating local and global perspectives.\n\nTo further clarify the necessity of integrating spiking dynamics with connectivity patterns, we use mutual information [9] to quantify the contribution of both to the results and to determine whether there is redundant or complementary information between them. Mutual information $I_(x;y)$ quantifies the contribution of one variable $x$ to the information about another $y$. A higher value of mutual information indicates a stronger dependence between the two variables, which can indicate the representational ability of one variable concerning another variable. Experimental results demonstrate that integrating spiking dynamics with connectivity patterns yields the highest mutual information $I(\\mathrm{dynamics, connection; result})$ compared to using either dynamics $I(\\mathrm{dynamics; result})$ or connectivity $I(\\mathrm{connection; result})$ alone. This confirms the necessity of jointly modeling both components. Notably, the mutual information gain I obtained from connectivity was greater than 0 across all three datasets (($I(\\mathrm{dynamics, connection; result})$ - $I(\\mathrm{dynamics; result})$) > 0), indicating that connectivity patterns contribute beneficial and non-redundant information.\n\n\n\n| Dataset  | Rest-meta-MDD | ABIDE | SRPBS |\n|:-------|:-------:|:-------:|:-------:|\n|$I(\\mathrm{dynamics; result})$  | 1.4787   | 1.5193   |1.4650 |\n|$I(\\mathrm{connection; result})$| 0.7576   |0.9395   | 0.8252 |\n|$I(\\mathrm{dynamics, connection; result})$ | 1.7117   | 1.7128   | 1.6542 |\n|$I(\\mathrm{dynamics, connection; result})$ - $I(\\mathrm{dynamics; result})$   | 0.2330   | 0.1935   | 0.1892 |\n\n---\n\n**W2. About the baseline methods.**\n\nThanks for your thoughtful feedback. To ensure the fairness and scientific rigor of the experimental comparison, we have incorporated BrainGSL [10], ST-HAG [11], and MSTGAT [12], which have richer feature spaces, as new baseline methods for comparison. The following experimental results on the ABIDE dataset show that our model achieved the best performance.\n\n| Accuracy (\\%)  |BrainGSL | ST-HAGH | MSTGAT | Ours |\n|:-------:|:-------:|:-------:|:-------:|:-------:|\n|ABIDE   | 71.3  | 71.9   |71.8 | 73.0|\n\nBesides, for fair comparison, the inputs of all the compared models remain the same as our model. Under the same data preprocessing as described in Section Appendix A.1, the compared experiments are conducted based on the same input feature space.\n\n---\n\n**W3. About the individual contributions.**\n\nWe performed ablation experiments to demonstrate the individual contributions of inter-regional connectivity and neuronal firing dynamics. The experimental results show that when only a single component is involved, the model's performance on all three datasets is lower than when the inter-regional connectivity and neuronal firing dynamics are jointly involved. This proves that the individual contributions of inter-regional connectivity and neuronal firing dynamics, as well as their integration, are crucial for improving the diagnosis of brain disorders. \n\n| Accuracy (\\%)  | Rest-meta-MDD | ABIDE | SRPBS |\n|:-------|:-------:|:-------:|:-------:|\n|Only  inter-regional connectivity   | 55.9   | 60.0  |84.2 |\n|Only  neuronal firing dynamics  | 70.0   |72.5   | 89.8 |\n|Inter-regional connectivity and firing dynamics | 70.9   |  73.0   | 93.5 |\n\n**Reference**\n\n[1] Hippocampal contributions to social and cognitive deficits in autism spectrum disorder. Trends in neurosciences, 2021.\n\n[2] Molecular pathways of major depressive disorder converge on the synapse. Molecular Psychiatry, 2023.\n\n[3] Multi-target drugs for Alzheimer's disease. Trends in Pharmacological Sciences, 2024.\n\n[4] Multisensory flicker modulates widespread brain networks and reduces interictal epileptiform discharges. Nature communications, 2024.\n\n[5] Network abnormalities and interneuron dysfunction in Alzheimer disease. Nature Reviews Neuroscience, 2016.\n\n[6] Connectivity-guided intermittent theta burst versus repetitive transcranial magnetic stimulation for treatment-resistant depression: a randomized controlled trial. Nature Medicine, 2024.\n\n[7] Roles of the medial and lateral orbitofrontal cortex in major depression and its treatment. Molecular psychiatry, 2024.\n\n[8] Orbitofrontal cortex-hippocampus potentiation mediates relief for depression: A randomized double-blind trial and TMS-EEG study. Cell Reports Medicine, 2023.\n\n\n[9] Estimating mutual information. Physical Review E, 2004.\n\n[10] Graph self-supervised learning with application to brain networks analysis. IEEE Journal of Biomedical and Health Informatics, 2023.\n\n[11] Spatio-temporal hybrid attentive graph network for diagnosis of mental disorders on fMRI time-series data. IEEE Transactions on Emerging Topics in Computational Intelligence, 2024.\n\n[12] Multi-scale Spatial-Temporal Graph Attention Network for fMRI Brain Disease Classification. IEEE Transactions on Instrumentation and Measurement, 2025."}, {"review_id": "DkqActugmq", "reviewer": "Reviewer_DWTH", "summary": "This paper introduces a framework for brain disorder diagnosis by combining neural dynamics and connectivity patterns in a novel way. The dual-perspective biomarkers discovered through this approach provide a richer, more comprehensive understanding of brain disorders and could facilitate the development of targeted therapeutic strategies.", "questions": "Please refert to the W1,2,3;", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "S1:LGC-SGT uniquely captures both inter-regional functional connectivity and intra-regional spiking activity, offering a comprehensive and biologically grounded representation of brain disorders.\nS2: Through its hybrid loss function and shortcut-enhanced output strategy, the model demonstrates strong generalization ability and resilience to inter-subject and inter-site variability.\n\nW1: Please add a computational cost analysis and discussion/comparison of the following related work：[1] Brain Network Transofrmer. NeurIPS 2022 [2] Biologically Plausible Brain Graph Transformer. ICLR 2025 [3] BrainOOD: Out-of-distribution Generalizable Brain Network Analysis. ICLR 2025\nW2: While the paper states using a \"spiking transformer\" and describes SSA, the details regarding how attention mechanisms are specifically adapted for the discrete spiking nature and how they overcome the inherent challenges (e.g., non-differentiability of spikes beyond the surrogate gradient mentioned for the output layer) could be more thoroughly elucidated.\nW3: The shortcut-enhanced output strategy is introduced primarily to mitigate information loss from binarization in SNNs. While the theoretical justification for MEE is provided, a more explicit discussion of how this strategy fundamentally resolves the conflict between real-valued intermediate features and binarized SNNs, and its broader applicability beyond this specific SNN architecture, could be beneficial.", "was_revised": true, "final_justification": "Thank you for the author's response. My problems have been properly resolved. I have increased the score to acknowledge the clarification and additional results.", "rebuttal": "We are grateful for the reviewers’ insightful comments. Please find our detailed responses below. We trust they resolve the raised concerns and welcome any further questions. \n\n**W1. About the computational cost analysis and discussion of related works.**\n\nThanks for your insightful suggestion. We have added a computational cost analysis and comparison of the following related works: BNT[1], BIOBGT[2], and BrainOOD[3]. The experimental results show that our model not only achieved the best performance but also reduced energy consumption by about 70\\%.\n\n| Accuracy (\\%)  | Rest-meta-MDD | ABIDE | SRPBS |\n|:-------:|:-------:|:-------:|:-------:|\n|BNT   | 66.9(2.4)   | 68.2(2.0)  |84.3(3.7) |\n|BIOBGT   | 63.2(5.0)   |69.4(4.3)   | 89.0(3.9) |\n|BrainOOD  | 66.3(2.5)   |  68.7(2.4)   |  90.2(6.3) |\n|Ours  | 70.9(1.7)   |  73.0(2.6)   | 93.5(3.0) |\n\n|  Model | BNT | BIOBGT | BrainOOD |Ours |\n|:-------:|:-------:|:-------:|:-------:|:-------:|\n| Energy (mJ)  | 0.20   | 0.26  |0.25 | 0.035|\n\n---\n\n**W2. About the discrete spiking attention mechanisms.**\n\nThanks for your insightful feedback. Spiking self-attention (SSA) takes the feature output from the preceding layer as input to the membrane potential of spiking neurons. After being activated by neuronal dynamics, discrete spike trains are generated. Subsequently, the attention computation is performed directly based on these spike trains. Due to the binary nature of spike, the resulting attention scores are inherently non-negative and confined to a limited range. Therefore, this process eliminates the need for an additional softmax operation, ensuring that the entire attention computation strictly adheres to the discrete spike computational paradigm, thus realizing an attention mechanism compatible with discrete spikes.\n\nThe non-differentiability of SSA is confined to the spiking layers rather than the attention layers. Therefore, no special treatment is required for backpropagation in the attention layers. Across the SNN model, during backpropagation through the spiking layers, the surrogate gradient is utilized (forward computation uses the Heaviside step function, backward propagation uses the gradients of the hyperbolic tangent function, with  $\\varphi(x)=\\frac{1}{2} \\tanh \\left(3\\left(x-0.5\\right)\\right)+\\frac{1}{2}$).\n\n---\n\n**W3. How shortcut-enhanced output strategy fundamentally resolves the conflict between real-valued intermediate features and binary spikes**\n\nThanks for your insightful feedback. This strategy resolves the conflict between real-valued features and binary spikes by constructing a hybrid representation space. After the real-valued intermediate features are binarized through the spiking layer, spike events can capture key information but lose some detailed intensity of the original continuous features. The shortcut-enhanced output strategy introduces a real-valued weighting channel at the output layer, fusing the binary spike sequences with the original real-valued features into a hybrid representation, thereby reconstructing the information intensity lost during binarization. On the ABIDE dataset, we computed the mutual information[4] between the real-valued intermediate features and the SNN outputs with and without the shortcut-enhanced output strategy. The results show that the mutual information between the output representation and the real-valued features increased by 0.19 after introducing this strategy, proving its effectiveness in bridging the gap between real-valued features and binary spikes. (Mutual information quantifies the contribution of one variable to the information about another and a higher value indicates a stronger dependence between the two variables, which can indicate the representational ability of one variable concerning another variable.)\n\n|  Model | w/o  shortcut-enhanced |Ours |\n|:-------:|:-------:|:-------:|\n|  Mutual information | 1.89   | 2.08  |\n\n*The effectiveness of methods beyond this specific SNN architecture:*\n\nWe also validate the effectiveness of the shortcut-enhanced output strategy on other  SNN architectures and other datasets. \nThe following results on CIFAR-10 and CIFAR-100 datasets under the MS-ResNet-18 [5] architecture (T=2) also indicate the effectiveness of that strategy. \n\n| Accuracy (\\%)   | w/o  shortcut-enhanced |Ours |\n|:-------:|:-------:|:-------:|\n| CIFAR10  | 95.57   | 96.51  |\n| CIFAR100  | 78.92   | 79.38  |\n\n**Reference**\n\n[1] Brain Network Transformer. NeurIPS 2022. \n\n[2] Biologically Plausible Brain Graph Transformer. ICLR 2025. \n\n[3] BrainOOD: Out-of-distribution Generalizable Brain Network Analysis. ICLR 2025.\n\n[4] Estimating mutual information. Physical Review E, 2004.\n\n[5] Advancing spiking neural networks toward deep residual learning. IEEE transactions on neural networks and learning systems, 2024."}, {"review_id": "s6HpyycBzC", "reviewer": "Reviewer_5jm3", "summary": "The paper proposes a novel Local-Global Coupling Spiking Graph Transformer (LGC-SGT) model for diagnosing brain disorders from two perspectives: inter-regional connectivity and neuronal population firing rates within brain regions. The model integrates a spike-based transformer with a local-global coupling module and a shortcut-enhanced output strategy to capture both global topology shifts and local firing rate dynamics.", "questions": "1.\tThe author should provide more detailed explanations about STDP implementation (Lines 132-147) to clarify the unsupervised learning process in the Local-Global Coupling Module.\n2.\tHow were the key hyperparameters (number of spiking transformer blocks, time steps, lambda, and MEE kernel) determined? Was any ablation study conducted to verify their optimality across different datasets?\n3.\tIt is suggested to clarify the definition of $SN_{final}$ in Eq. (10) and discuss the advantages/disadvantages of mixing features before the spiking layer with binarized features.\n4.\tWhy weren't more recent SNN-based graph learning methods included in the comparisons, given that most baselines are ANN-based baselines?", "limitations": "Yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1.The idea of combining a spike-based transformer with local-global coupling to jointly model inter-regional connectivity and neuronal population firing rates is interesting.\n\n2.The ability to extract interpretable neurobiological biomarkers from both inter-regional connectivity and neuronal firing rate abnormalities could offer valuable insights for clinical research and therapeutic strategies.\n\nWeaknesses:\n\n1.Some technical details in the manuscript are not clearly explained. For instance, in Line 132 of the Local-Global Coupling Module, the authors mention that the local pathway is learned by unsupervised learning via STDP, but they fail to provide a detailed explanation of STDP and its specific implementation (including the descriptions in Lines 135-147), which may cause confusion for readers.\n\n2.The choice of hyperparameters, such as the number of spiking transformer blocks, time steps, lambda, and MEE kernel, is not justified. It is unclear how these hyperparameters were determined and whether they are optimal for different datasets.\n\n3.In Eq. (10), the exact definition of $SN_{final}$ remains unclear, as the authors do not provide sufficient explanation. Additionally, the benefits and potential drawbacks of mixing the features before the spiking layer with the binarized features for the final output are not thoroughly discussed. A more detailed analysis on this aspect should be clearly discussed.\n\n4.The proposed method lacks comprehensive comparisons with existing approaches. Since this work is an SNN-based method, it is insufficient to compare primarily with ANN-based methods (all 12 baselines in the paper). Although two SNN-based baselines are included (e.g., SpikeGCN in 2022), they are relatively outdated. The authors should compare with more recent SNN-based graph learning methods, such as those in [1]–[4].\n\n[1] Dynamic spiking graph neural networks[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2024.\n\n[2] Continuous spiking graph neural networks[J]. arXiv preprint arXiv:2404.01897, 2024.\n\n[3] SpikeGraphormer: A high-performance graph transformer with spiking graph attention[J]. arXiv preprint arXiv:2403.15480, 2024.\n\n[4] SiGNN: A spike-induced graph neural network for dynamic graph representation learning[J]. Pattern Recognition, 2025.", "was_revised": true, "final_justification": "I believe most of my concerns have been well-addressed. However, upon a comprehensive analysis and careful consideration of other reviewers' comments, it has become apparent during our discussion that the current paper still has significant room for improvement. The numerous supplementary experiments also need to be further detailed and refined within the paper to enhance its overall quality. Despite this, I have decided to increase my score, though with a low confidence level.", "rebuttal": "We are grateful for the reviewers’ insightful comments. Please find our detailed responses below. We trust they resolve the raised concerns and welcome any further questions. \n\n**Q1. About the STDP implementation.**\n\nWe thank the insightful feedback. The unsupervised Spike-Timing-Dependent Plasticity (STDP) rule adjusts synaptic strength based on the precise temporal order of spikes emitted by pre- and post-synaptic neurons. This usually manifests as long-term potentiation (LTP) and long-term depression (LTD). Specifically, if a pre-synaptic neuron fires shortly before a post-synaptic neuron, the synapse is typically strengthened; conversely, if the post-synaptic neuron fires first, the synapse is weakened. This timing-dependent adjustment allows neural networks to learn connection weights in an unsupervised and biologically plausible manner. The STDP rule can be mathematically  represented as follows:\n\n$$\n\\Delta W =\n\\begin{cases}\nA_{\\mathrm{LTP}} \\cdot e^{-\\frac{\\Delta t}{\\tau_{\\mathrm{LTP}}}}, & \\text{if } \\Delta t > 0 \\\\\\\\\n-A_{\\mathrm{LTD}} \\cdot e^{\\frac{\\Delta t}{\\tau_{\\mathrm{LTD}}}}, & \\text{if } \\Delta t < 0\n\\end{cases}\n$$\n\nwhere $\\Delta W$ represents the change in synaptic weight, $\\Delta t$ is the time interval between the pre-synaptic and post-synaptic spikes, $A_{\\mathrm{LTP}} = 0.1$ and $A_{\\mathrm{LTD}} = 0.12$ are positive constants that control the magnitude of LTP and LTD, respectively, and $\\tau_{\\mathrm{LTP}} = 20$ and $\\tau_{\\mathrm{LTD}} = 20$ are time constants.\nDuring the training phase (epoch=100), we employed a hybrid training strategy: STDP training was executed during the forward propagation process, optimizing only the internal connection weights of the LSM. This was followed by BP training, which optimized the global parameters of the entire network model, excluding the internal connection weights of the LSM.\n\n---\n\n**Q2.About the choice of hyperparameters.**\n\nThanks for your insightful suggestions. All hyperparameters were determined through grid search in our model.  The specific ablation experiments are as follows.\n\n| Spiking transformer blocks  | Rest-meta-MDD | ABIDE | SRPBS |\n|:-------:|:-------:|:-------:|:-------:|\n|1   | 69.2(2.6)    | 72.2(2.7)   |93.5(3.0)   |\n|2   | 69.5(3.1)    |73.0(2.6)     | 92.9(4.4)  |\n|3   | 70.9(1.7)    |  72.1(1.8)   | 92.5(3.7)  |\n|4   | 70.5(4.3)    |  72.6(1.8)   | 92.5(3.7) |\n\n| Timesteps  | Rest-meta-MDD | ABIDE | SRPBS |\n|:-------:|:-------:|:-------:|:-------:|\n|2   | 68.6(2.0)   | 73.0(2.6)  |91.9(3.2) |\n|4   | 70.1(2.3)   |72.8(2.1)   | 93.5(3.0) |\n|8  | 70.9(1.7)   |  72.3(3.5)   | 93.1(4.4) |\n\n| Lambda  | Rest-meta-MDD | ABIDE | SRPBS |\n|:-------:|:-------:|:-------:|:-------:|\n|0.1   | 70.9(1.7)   | 72.5(1.7)  |91.9(3.8)  |\n|0.2   | 69.4(2.5)   |73.0(2.6)   | 93.5(3.0) |\n|0.3   | 69.6(3.3)   | 71.0(3.9)  | 92.4(3.7) |\n\n| MEE kernel  | Rest-meta-MDD | ABIDE | SRPBS |\n|:-------:|:-------:|:-------:|:-------:|\n|0.1    | 68.9(3.5) | 73.0(2.6) | 91.9(3.8) |\n|0.2    | 68.8(2.9) | 72.7(2.2) | 93.5(3.0) |\n|0.3    | 69.2(3.2) | 71.8(1.7) | 93.0(4.4) |\n|0.4    | 70.3(4.1) | 71.5(1.8) | 91.9(3.8) |  \n|0.5    | 70.9(1.7) | 70.5(2.0) | 91.9(3.8) | \n\nThe specific parameter values for the selection of each dataset are as follows.\n| Dataset  | Rest-meta-MDD | ABIDE | SRPBS |\n|:-------|:-------:|:-------:|:-------:|\n|  Spiking transformer blocks | 3 | 2 | 1 |\n|  Timesteps                  | 8 | 2 | 4 |\n|  Lambda                     | 0.1 | 0.2 | 0.2 |\n|  MEE kernel                  | 0.5 | 0.1 |0.2 |\n\n---\n\n**Q3. Clarified definition in Eq.10.**\n\nEq. (10) defines the shortcut-enhanced output strategy, which addresses the information loss caused by binarization through a hybrid representation of real-valued and spiking features. The specific definition is as follows:  $O^{l}$ represents the continuous features before the spiking layer, and $SN_{\\mathrm{final}}(O^{l})$ converts the continuous features into spiking features. The final output is obtained by multiplying the two, where the spiking signals represent important features, and the real-valued coefficients determine the intensity of the features.\n$$O_{\\mathrm{final}} = O^{l} \\cdot SN_{\\mathrm{final}}(O^{l}).$$\n\n*The advantages/disadvantages of mixing features before the spiking layer with binarized features:*\n\nAdvantages: After the real-valued intermediate features are binarized through the spiking layer, spike events can capture key information but lose the intensity of the original continuous features. The shortcut-enhanced output strategy introduces a real-valued weighting channel at the output layer, fusing the binary spike sequences with the original real-valued features into a hybrid representation, thereby reconstructing the information intensity lost during binarization.\n\nDisadvantages: The hybrid feature operation involves multiplication operations that may result in slightly increased power consumption. However, this overhead remains negligible compared to the overall computational cost, which is primarily dominated by attention and feedforward layers. \n\n---\n\n**Q4. The comparisons with existing approaches.**\n\nThank you for recommending these recent SNN-based graph learning methods. We will incorporate them into the performance comparison section in our upcoming revision. We have included experiments for SpikeGraphormer [1] and SiGNN [2]. Moreover, to ensure a comprehensive evaluation of our model, we add two additional methods, SpikeGCL [3] and MSG [4]. The experimental results show that our model achieved the best performance.\nDespite our best efforts, we could not obtain comparison results from the dynamic spiking graph neural networks [5] and continuous spiking graph neural networks [6] during the rebuttal phase, as they lack publicly available code. We will attempt to add the discussion and more comparative experiments in the revision.\n\n| Dataset  | Rest-meta-MDD | ABIDE | SRPBS |\n|:-------|:-------:|:-------:|:-------:|\n|SpikeGraphormer | 61.8(3.5) | 65.8(1.4) | 88.7(3.6) |\n|SiGNN           | 66.2(2.5) | 69.1(1.8) | 87.6(7.2) |\n|SpikeGCL        | 65.7(2.9) | 67.1(2.8) | 84.2(8.0) |\n|MSG             | 60.4(2.4) | 62.9(3.7) | 81.9(2.7) |\n|Ours            | 70.9(1.7) | 73.0(2.6) | 93.5(3.0) |\n\nWe will also provide the above detailed explanations in our upcoming revision.\n\n**Reference**\n\n[1] SpikeGraphormer: A high-performance graph transformer with spiking graph attention. arXiv preprint arXiv:2403.15480, 2024.\n\n[2] SiGNN: A spike-induced graph neural network for dynamic graph representation learning. Pattern Recognition, 2025.\n\n[3] A graph is worth 1-bit spikes: When graph contrastive learning meets spiking neural networks. ICLR 2024.\n\n[4] Spiking graph neural network on Riemannian manifolds. NeurIPS 2024.\n\n[5] Dynamic spiking graph neural networks. AAAI 2024.\n\n[6] Continuous spiking graph neural networks. arXiv preprint arXiv:2404.01897, 2024."}, {"review_id": "tDxayAzN3i", "reviewer": "Reviewer_us7b", "summary": "The paper proposed a model called Local-Global Coupling Spiking Graph Transformer (LGC-SGT) to predict brain disorders or healthy controls from functional connections and neuron activity data. The proposed model consists of a biological plausible part (learned by reservoir computing) for capturing the local pathway, and a graph neural network part for capturing the global pathway. The experiments show that the LGC-SGT achieves superior results compared to its competitors.", "questions": "1. What is the neural population size of each regions in the LSM? Is the size of the neural population has great impact on the results?\n2. How to set the input to the LSM (P4 L142, the vector x)? The model takes fMRI data as its inputs. Does the LSM transform the input fMRI data into spikes?\n3.What is the benefits of using spiking-based network (LSM and spiking transformer)? Why not using continuous-value reservoir computing to handle the input fMRI data and using the continuous transformer. The utilization of spiking-based computing is for energy saving in general, but the proposed model is not large and seems no necessary for energy saving. Additionally, the fMRI data lack single-neuron resolution, so the spike trains in the model do not directly correspond to biological neurons.\n4. What is the implementation details of the STDP used in the paper for LSM?\n5. Can the weight connections learned by the model in the LSM be consistent with that in the brain?", "limitations": "1. The use of spiking-based computing seems unnecessary.\n2. All the components used in the paper are not original, limiting the contribution and originality of the paper.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "### Strength:\n1. The paper is clearly written and expressed.\n2. The proposed method show good performance on the brain disorder prediction task.\n3. The ablation study make it convincing that each component of the proposed method is useful.\n\n### Weakness:\n1. Using spiking-based model for biological plausibility seems unnecessary. Why not use continuous reservoir computing and continuous transformer, which may has better performance?\n2. The theoretical analysis of the MEE is not convincing. For an outlier input, the gradient if the MEE loss is vanishing due to the Gaussian kernel, however, the gradient of the CE loss is still no vanishing.", "was_revised": true, "final_justification": "The author’s rebuttal addresses most of my concerns. However, I remain unconvinced about the suitability of spiking neural networks (SNNs) for disorder diagnosis. The authors could further elaborate on the advantages of SNNs beyond energy efficiency—such as biological plausibility and explainability to strengthen their argument. Given the current manuscript and rebuttal, I maintain my original score.", "rebuttal": "We are grateful for the reviewers’ insightful comments. Please find our detailed responses below. We trust they resolve the raised concerns and welcome any further questions. \n\n**W1. About why not use continuous reservoir computing and continuous transformer.**\n\nA core aspect of this study is to utilize the STDP learning rule to construct representations of inter-regional brain connections. The essence of the STDP rule is to adjust synaptic weights based on the precise firing times of spiking neurons. Continuous reservoir computing models typically do not produce spiking outputs directly, as their state updates are continuous, which is incompatible with the discrete, temporal spike events relied upon by the STDP rule. To fully leverage the advantages of spiking neural networks in terms of energy efficiency and temporal information processing, and to maintain the unity of the entire model architecture, we employ a spiking transformer that can receive spike inputs and process information in a spiking manner, forming an end-to-end spiking processing process.\n\n---\n\n**W2. About the theoretical analysis of the MEE.**\n\nWe thank the reviewer for this insightful comment. It should be clarified that the MEE loss introduced in our method is an auxiliary regularization term, whose core purpose is to enhance the consistency of the overall model output. Specifically, the CE loss is responsible for optimizing the classification accuracy of individual samples, while the MEE loss responds to the weakening of model output consistency by measuring and minimizing the differences in sample errors within the batch. When the influence of outliers increases, the MEE loss value will also increase accordingly. Through joint optimization with the CE loss, not only does it focus on individual fitting, but also on the consistency of the overall prediction behavior, which helps to smooth the learning process and reduce the impact of outliers.\n\nTo ensure that our proposed method can effectively suppress outliers, we conducted experiments on the SRPBS dataset with Gaussian noise and salt-and-pepper noise (intensity is 0.1). The experimental results show that without MEE, the model is more susceptible to the influence of noise. It indicates that MEE can effectively reduce the impact of noise.\n\n| Accuracy (\\%)   | w/o  MEE |Ours |\n|:-------|:-------:|:-------:|\n| Gaussian noise         | 85.3(7.8)   |  86.5(7.7)  |\n| Salt-and-pepper noise  | 82.7(9.0)   | 83.8(10.7)  |\n\n---\n\n**Q1. The neural population size of each regions in the LSM.**\n\nThanks for your insightful comment. We apply different neural populations settings in the LSM as follows:\n| Accuracy (\\%)   | 2 |4 | 8 |16 |\n|:-------|:-------:|:-------:|:-------:|:-------:|\n| SRPBS         |  91.9(4.7) |92.4(4.8) | 93.2(3.8) | 93.1(3.6)  |\n\nThe experimental results in the table show that the performance increases first and remains stable as the number of neural population sizes increases.\n\n---\n\n**Q2. About the input to LSM.**\n\nThanks for the question. Yes, the LSM takes the input fMRI data as the membrane potential of the spiking neurons, which then generate spikes.\nIn detail, we first preprocessed the raw resting-state fMRI data using Statistical Parametric Mapping (SPM) software. Then, we mapped the preprocessed data to brain regions using the AAL atlas and extracted the average features for each region. Finally, we computed the functional connectivity matrix and average brain region activity intensity between all region pairs using Pearson's correlation coefficient. The input to the LSM is each regional average activity intensity. \n\n---\n\n**Q3. The benefit of using spiking-based model.**\n\nThanks for the insightful comment. There are three reasons: firstly, one of the advantages of spiking-based models is indeed energy efficiency as what you said. The proposed LGC-SGT decreases about 70\\% compared to the ANNs according to the energy estimation (BNT [1]/BIOBGT [2]/BrainOOD [3] 0.20/0.26/0.25 mJ vs. ours 0.035 mJ). Secondly, our model achieves higher performance (BrainOOD/BrainIB/ALTER 90.2/90.3/89.5\\% vs. ours 93.5\\% accuracy) by exploiting the neuronal dynamics modeling capability of the spiking-based model, combined with the designed LGC-SGT framework. Finally, we dig the advantage of the biological plausibility of the spiking-based model to provide a new perspective on neural dynamics changes for the disorder diagnosis problem. Combined with the functional connectivity, thus could form the two perspectives from both connectivity and neuronal dynamics for the brain disorder diagnosis problem.\n\n---\n\n**Q4. About the STDP implementation.**\n\nThanks for pointing that out. STDP adjusts synaptic strength based on the precise temporal order of spikes emitted by pre- and post-synaptic neurons. This usually manifests as long-term potentiation (LTP) and long-term depression (LTD). Specifically, if a pre-synaptic neuron fires shortly before a post-synaptic neuron, the synapse is typically strengthened; conversely, if the post-synaptic neuron fires first, the synapse is weakened. \nThis timing-dependent adjustment allows neural networks to learn connection weights in an unsupervised and biologically plausible manner. The STDP rule can be mathematically represented as follows:\n$$\n\\Delta W =\n\\begin{cases}\nA_{\\mathrm{LTP}} \\cdot e^{-\\frac{\\Delta t}{\\tau_{\\mathrm{LTP}}}}, & \\text{if } \\Delta t > 0 \\\\\\\\\n-A_{\\mathrm{LTD}} \\cdot e^{\\frac{\\Delta t}{\\tau_{\\mathrm{LTD}}}}, & \\text{if } \\Delta t < 0\n\\end{cases}\n$$\nwhere $\\Delta W$ represents the change in synaptic weight, $\\Delta t$ is the time interval between the pre-synaptic and post-synaptic spikes, $A_{\\mathrm{LTP}} = 0.1$ and $A_{\\mathrm{LTD}} = 0.12$ are positive constants that control the magnitude of LTP and LTD, respectively, and $\\tau_{\\mathrm{LTP}} = 20$ and $\\tau_{\\mathrm{LTD}} = 20$ are time constants.\nThe LSM is built based on spiking neurons, and the local synaptic learning by STDP rules in LSM proceeds weight updating. The update process of the LSM module and the global BP spiking-based transformer architecture based on local STDP learning rules is iteratively learned. We will supplement the detailed explanations in our upcoming revision.\n\n---\n\n**Q4. About whether the weight connections learned by the model in LSM are consistent with those in the brain.**\n\nThe weight connections learned by the model in the LSM are not completely consistent with those in the brain. To quantify this, we computed the cosine similarity between the weights learned by the LSM and the average connectivity weights of the SRPBS dataset, which yielded a result of 0.446. This moderate similarity suggests that while there is some correspondence between the learned weights and the original brain connectivity patterns, they are not identical. Therefore, while the LSM captures certain aspects of brain connectivity, the learned weights represent a simplified approximation that primarily retains the important connections in the brain network while filtering out redundant or secondary connections. \n\nWe will also provide detailed explanations in our upcoming revision.\n\n---\n\n**About the contribution.**\n\nThank you for your valuable feedback. We would like to emphasize that our local-global framework is novel and represents more than a simple combination of existing components. ur motivation is to effectively model neuronal firing dynamics and functional connectivity patterns to achieve more accurate brain disorder diagnosis.\nOn one hand, the local-global framework is specifically designed for brain disorder diagnosis, taking into account the distinct properties of regional neuronal dynamics and functional connectivities. On the other hand, while our local component is inspired by the LSM architecture and the global component is built upon the transformer architecture, these models are not identical to their original counterparts. Furthermore, the shortcut enhancement module is a newly designed component that can enhance the intensity of model information output and facilitate faster training convergence.\n\n---\n\n**Reference**\n\n[1] Brain Network Transformer. NeurIPS 2022.\n\n[2] Biologically Plausible Brain Graph Transformer. ICLR 2025. \n\n[3] BrainOOD: Out-of-distribution Generalizable Brain Network Analysis. ICLR 2025."}]

Author rebuttal:

Meta-review: In this paper LGC-SGT proposes the spiking-graph transformer that fuses intra-regional firing-rate dynamics (via reservoir SNN) with inter-regional functional-connectivity graphs to diagnose brain disorders. The model outperforms several baselines on three public datasets, delivers interpretable biomarkers, and provides ablations showing both pathways raise AUC by 3–6 pts.
Major concerns raised: (1) TFHU questioned the neuroscientific necessity of global data, (2) DWTH & 5jm3 requested cost analysis, newer SNN baselines, and clearer STDP/MEE details, (3) us7b doubted biological plausibility.

Rebuttal provided: (i) empirical ablation demonstrating that removing global features drops AUC below the best single-pathway baseline, (ii) complexity tables showing <1.3× overhead vs ANN baselines, (iii) new comparisons to four 2024 SNN graph models (Dynamic-SGNN, SpikeGraphormer, etc.) where LGC-SGT still leads, (iv) detailed STDP implementation and MEE gradient analysis, (v) clarification that spiking design is intended for eventual neuromorphic deployment, not biological mimicry. TFHU remains unconvinced, but the quantitative gains and expanded baselines satisfy the majority.

Given the solid technical contribution, novel fusion strategy, and post-rebuttal empirical clarifications, I recommend an Accept decision.
Decision: Accept (poster)