Local-Global Coupling Spiking Graph Transformer for Brain Disorders Diagnosis from Two Perspectives

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.

W1. About why not use continuous reservoir computing and continuous transformer.

A 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.

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W2. About the theoretical analysis of the MEE.

We 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.

To 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.

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Q1. The neural population size of each regions in the LSM.

Thanks for your insightful comment. We apply different neural populations settings in the LSM as follows:

The experimental results in the table show that the performance increases first and remains stable as the number of neural population sizes increases.

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Q2. About the input to LSM.

Thanks for the question. Yes, the LSM takes the input fMRI data as the membrane potential of the spiking neurons, which then generate spikes. In 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.

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Q3. The benefit of using spiking-based model.

Thanks 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.

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Q4. About the STDP implementation.

Thanks 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. 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:

$$\Delta W = \begin{cases} A_{\mathrm{LTP}} \cdot e^{-\frac{\Delta t}{\tau_{\mathrm{LTP}}}}, & \text{if } \Delta t > 0 \\\\ -A_{\mathrm{LTD}} \cdot e^{\frac{\Delta t}{\tau_{\mathrm{LTD}}}}, & \text{if } \Delta t < 0 \end{cases}$$

where $\Delta W$ 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. The 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.

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Q4. About whether the weight connections learned by the model in LSM are consistent with those in the brain.

The 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.

We will also provide detailed explanations in our upcoming revision.

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About the contribution.

Thank 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. On 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.

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Reference

[1] Brain Network Transformer. NeurIPS 2022.

[2] Biologically Plausible Brain Graph Transformer. ICLR 2025.

[3] BrainOOD: Out-of-distribution Generalizable Brain Network Analysis. ICLR 2025.

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.

Q1. About the STDP implementation.

We 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:

$$\Delta W = \begin{cases} A_{\mathrm{LTP}} \cdot e^{-\frac{\Delta t}{\tau_{\mathrm{LTP}}}}, & \text{if } \Delta t > 0 \\\\ -A_{\mathrm{LTD}} \cdot e^{\frac{\Delta t}{\tau_{\mathrm{LTD}}}}, & \text{if } \Delta t < 0 \end{cases}$$

where $\Delta W$ 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. During 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.

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Q2.About the choice of hyperparameters.

Thanks for your insightful suggestions. All hyperparameters were determined through grid search in our model. The specific ablation experiments are as follows.

The specific parameter values for the selection of each dataset are as follows.

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Q3. Clarified definition in Eq.10.

Eq. (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. $O_{\mathrm{final}} = O^{l} \cdot SN_{\mathrm{final}}(O^{l}).$

The advantages/disadvantages of mixing features before the spiking layer with binarized features:

Advantages: 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.

Disadvantages: 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.

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Q4. The comparisons with existing approaches.

Thank 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. Despite 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.

We will also provide the above detailed explanations in our upcoming revision.

Reference

[1] SpikeGraphormer: A high-performance graph transformer with spiking graph attention. arXiv preprint arXiv:2403.15480, 2024.

[2] SiGNN: A spike-induced graph neural network for dynamic graph representation learning. Pattern Recognition, 2025.

[3] A graph is worth 1-bit spikes: When graph contrastive learning meets spiking neural networks. ICLR 2024.

[4] Spiking graph neural network on Riemannian manifolds. NeurIPS 2024.

[5] Dynamic spiking graph neural networks. AAAI 2024.

[6] Continuous spiking graph neural networks. arXiv preprint arXiv:2404.01897, 2024.

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.

W1. About the computational cost analysis and discussion of related works.

Thanks 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%.

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W2. About the discrete spiking attention mechanisms.

Thanks 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.

The 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 $\varphi(x)=\frac{1}{2} \tanh \left(3\left(x-0.5\right)\right)+\frac{1}{2}$).

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W3. How shortcut-enhanced output strategy fundamentally resolves the conflict between real-valued intermediate features and binary spikes

Thanks 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.)

The effectiveness of methods beyond this specific SNN architecture:

We also validate the effectiveness of the shortcut-enhanced output strategy on other SNN architectures and other datasets. The 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.

Reference

[1] Brain Network Transformer. NeurIPS 2022.

[2] Biologically Plausible Brain Graph Transformer. ICLR 2025.

[3] BrainOOD: Out-of-distribution Generalizable Brain Network Analysis. ICLR 2025.

[4] Estimating mutual information. Physical Review E, 2004.

[5] Advancing spiking neural networks toward deep residual learning. IEEE transactions on neural networks and learning systems, 2024.

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.

W1. About the integration between intra-regional neuronal firing dynamics and inter-regional connectivity patterns.

We agree that a clear explanation of the integration between local spiking dynamics and global connectivity contributes to improved diagnosis.

From 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.

From 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.

To 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.

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W2. About the baseline methods.

Thanks 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.

Besides, 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.

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W3. About the individual contributions.

We 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.

Reference

[1] Hippocampal contributions to social and cognitive deficits in autism spectrum disorder. Trends in neurosciences, 2021.

[2] Molecular pathways of major depressive disorder converge on the synapse. Molecular Psychiatry, 2023.

[3] Multi-target drugs for Alzheimer's disease. Trends in Pharmacological Sciences, 2024.

[4] Multisensory flicker modulates widespread brain networks and reduces interictal epileptiform discharges. Nature communications, 2024.

[5] Network abnormalities and interneuron dysfunction in Alzheimer disease. Nature Reviews Neuroscience, 2016.

[6] Connectivity-guided intermittent theta burst versus repetitive transcranial magnetic stimulation for treatment-resistant depression: a randomized controlled trial. Nature Medicine, 2024.

[7] Roles of the medial and lateral orbitofrontal cortex in major depression and its treatment. Molecular psychiatry, 2024.

[8] Orbitofrontal cortex-hippocampus potentiation mediates relief for depression: A randomized double-blind trial and TMS-EEG study. Cell Reports Medicine, 2023.

[9] Estimating mutual information. Physical Review E, 2004.

[10] Graph self-supervised learning with application to brain networks analysis. IEEE Journal of Biomedical and Health Informatics, 2023.

[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.

[12] Multi-scale Spatial-Temporal Graph Attention Network for fMRI Brain Disease Classification. IEEE Transactions on Instrumentation and Measurement, 2025.