BrainCGT: A Brain Graph Transformer for Modeling Causal Connectivity in Neurological Disorder Diagnosis

1 Introduction

Brain network analysis is a core paradigm in computational neuroscience for studying neurological and neurodevelopmental disorders [Bullmore and Sporns, 2009]. The brain is modeled as a graph whose nodes represent anatomically or functionally defined regions and whose edges encode statistical or causal interactions. fMRI enables estimation of these graphs from temporally resolved signals and provides a principled basis for analyzing disease-related connectivity disruptions [Smith et al., 2011]. This representation offers a principled framework for analyzing connectivity disruptions associated with disease states. However, hierarchical modular organization and dynamic information exchange challenge conventional models, motivating more expressive approaches for accurate and interpretable diagnosis [Meunier et al., 2010; Kong and Yu, 2014].

∗Corresponding author.

Existing fMRI-based disease-classification models mainly use whole-brain or modular networks. Whole-brain methods build fully connected graphs from atlases such as AAL and Pearson correlation across all regions [Rolls et al., 2020]. These graphs are analyzed using handcrafted graph metrics or learned representations from end-to-end graph models [Li et al., 2021]. However, they treat the brain as homogeneous and miss modular disruptions critical to many disorders. Modular methods use community detection or predefined resting-state networks and combine modules with graph fusion or convolutional models [Thomas Yeo et al., 2011; Liu et al., 2024]. Yet most still rely on undirected functional connectivity and omit directional information flow, even when Graph Transformers are used [Xia et al., 2025; Dong et al., 2024].

Despite this progress, diagnostic graph models usually ignore causal connectivity, which captures directional influence between brain regions [Ji et al., 2023]. Such directionality is central to disorders including Alzheimer's Disease, Parkinson's Disease, and Autism Spectrum Disorder because dysfunction reflects altered causal interactions rather than isolated disconnections. Correlation-based undirected connectivity obscures these relationships, limiting diagnostic accuracy, biological interpretability, and mechanistic insight [Van Den Heuvel and Pol, 2010]. We therefore hypothesize that integrating causal connectivity into modular graph learning improves classification and reveals disorder-specific communication patterns.

To address this limitation we propose BrainCGT 1 , a causal brain graph transformer for directed interactions within and across modular brain networks. BrainCGT estimates asymmetric effective connectivity for seven functional modules using multivariate Granger causality, encodes direction-sensitive topological descriptors, and applies direction-aware attention to model disorder-specific causal interactions. We evaluate BrainCGT on ADNI, PPMI, and ABIDE for binary classification. Results show consistent gains in accuracy, F1 score, and AUC over state-of-the-art undirected graph baselines while improving biological interpretability. These findings demonstrate that explicit causal modeling improves diagnostic performance while enhancing biological interpretability of disease-related brain mechanisms.

1 The source codes are available at: https://github.com/

This paper makes the following key contributions:

1. We propose BrainCGT an end to end framework that integrates causal connectivity into modular brain networks for neurological disorder diagnosis addressing information flow limitations of undirected functional connectivity.
2. We introduce a causal brain graph transformer with direction aware input embeddings and direction biased attention mechanisms that encode node specific causal roles and learn asymmetric directed graph structures.
3. Experimental evaluations on ADNI, PPMI, and ABIDE demonstrate that BrainCGT outperforms state of the art models while identifying interpretable disease altered causal pathways and drivers of dysfunction.

2 RelatedWork

2.1 Brain Network Analysis for Brain Diseases Diagnosis

Brain network analysis provides a quantitative framework for characterizing disease related alterations in large scale functional architecture [Bullmore and Sporns, 2009]. Functional connectivity is modeled as a graph whose nodes represent ROIs and whose edges encode fMRI derived statistical coupling. Classical pipelines build whole brain undirected graphs using atlas parcellation such as AAL and Pearson correlation summarizing static co activation structure [Rolls et al., 2020]. Early studies relied on graph theoretic descriptors and conventional classifiers which overlook nonlinear mesoscale disease related topology. Recent graph learning methods learn representations from FC matrices yet shallow message passing limits long range dependency modeling [Cui et al., 2023; Luo et al., 2025]. This limitation is compounded by whole brain modeling which ignores modular organization and obscures intra and inter module pathological interactions [Meunier et al., 2010].

Modular brain network analysis characterizes neuropathology by explicitly exploiting the brain community structure. These models assume that disease perturbs specific functional modules or the pathways mediating inter modular communication. Community detection partitions whole brain graphs into densely connected subgraphs which define functional modules for hierarchical modeling. Recent

Ahsan-Shehzad/BrainCGT.

modular graph architectures integrate multi scale information using attention mechanisms and capture intra and inter modular dependencies [Pei et al., 2025; Peng et al., 2025]. However these approaches rely predominantly on functional connectivity which produces symmetric undirected graphs reflecting statistical co activation rather than directed signaling [Xu et al., 2026]. Although causal connectivity methods infer directed graphs using techniques such as Granger causality they are typically applied at the whole brain level and neglect modular topology [Zhang et al., 2025; Arab et al., 2025].

2.2 Graph Transformers

Graph Transformer architectures overcome fundamental limitations of message passing Graph Neural Networks by enabling global dependency modeling [Shehzad et al., 2026]. Conventional GNNs rely on local aggregation which restricts receptive fields induces over smoothing and limits long range dependency extraction [Luo et al., 2024]. Graph Transformers address these constraints through self attention that directly models pairwise node interactions within a single layer [Vaswani et al., 2017]. Structural encodings preserve graph topology and guide attention toward meaningful global patterns [Ying et al., 2021]. Recent studies adapt Graph Transformers to brain networks and improve diagnostic performance by capturing global and multiscale dependencies [Alharthi and Alzahrani, 2023; Shehzad et al., 2025a; Shehzad et al., 2025b]. Transformer-based diagnosis has also expanded to multimodal settings including speech-based early Alzheimer's disease detection with hypergraph transformers [Abid et al., 2025]. However connectivity-focused approaches still rely on functional connectivity which obscures directed causal signaling and limits diagnostic precision and interpretability.

3 The Design of BrainCGT

3.1 ProblemFormulation

We pose neurological disorder diagnosis as a supervised graph classification problem on subject-specific causal brain networks. Let D = {(V (s) , y(s) )}Ss=1 denote S subjects where V (s) ∈ RX×Y×Z×T is a 4D fMRI volume and y(s) ∈ Y is the diagnostic label. We learn fθ : G → Y that maps each G (s) to ˆ y(s) by minimizing a classification loss L(fθ(G (s) ), y(s) ). We represent each subject by G (s) = (V, E, A(s) , X (s) ) with shared nodes V and edges E. Stage 1 parcellates V (s) into N ROIs using a modular atlas, yielding X (s) = {x(s) i (t)}Ni=1 and sparse asymmetric A(s) via multivariate Granger causality. Stage 2 uses direction-aware embeddings with intra/intermodule causal attention and hierarchical fusion to produce discriminative graph-level embeddings for classification. Posthoc interpretability quantifies causal attributions at node, edge, and module granularity. Figure 1 illustrates the framework.

3.2 Causal Brain Network Construction

fMRI Preprocessing

Preprocessing produces temporally and spatially standardized 4D fMRI volumes with statistical properties suited to multivariate autoregressive modeling. Each raw scan is Vraw ∈ RX×Y ×Z×T with spatial indices (X, Y, Z) and temporal index T and serves as input for downstreammodeling. In FSL we perform slice-timing correction and MCFLIRT motion correction and normalize to the MNI152 template using affine and non-linear transforms. We apply Gaussian smoothing with full width at half maximum of 6 mm to improve signalto-noise ratio. We regress white matter and cerebrospinal fluid signals plus six motion parameters then band-pass filter within 0.01 ≤ f ≤ 0.1 Hz. To enforce covariance stationarity we apply voxel-wise detrending and first-order differencing and harmonize multi-site datasets with ComBat. The resulting volume is Vpre ∈ RX×Y ×Z×T .

Modular Parcellation

We construct region-level representations by parcellating each preprocessed fMRI volume into anatomically defined ROIs and assigning each ROI to a functional module. We use the Brainnetome Atlas with N = 246 cortical and subcortical regions [Fan et al., 2016]. For each ROI ri we compute the regional BOLD time series xi(t) by voxel averaging,

where Vi denotes the voxel set for ri. We then assign each ROI to one of M = 7 Yeo networks [Thomas Yeo et al., 2011] via Module(i) ∈ {1, . . . ,M}. This yields the modular multivariate series X = {xi(t)}Ni=1 that supports subsequent causal inference and hierarchical transformer modeling.

Causal Connectivity Estimation

We estimate directed functional connectivity to construct subject-specific causal brain graphs. From V ∈ RX×Y ×Z×T we extract regional BOLD series {xi(t)}Ni=1 and group ROIs into functional modules [Smith et al., 2011]. For each module pair (m, n) we stack signals into Xmn(t) ∈ Rd with d = |Rm ∪ Rn|. We fit a VAR(p) model for Xmn(t) with coefficients W(mn) k ∈ Rd×d :

We select p by Bayesian Information Criterion and model residuals ϵ(t) as white noise. For each ordered pair (i, j) we test H0 : β(k) ij = 0 ∀k using an F-statistic Fij. We apply false discovery rate correction across all directed pairs and retain xi→xj when corrected p < α. For retained edges we scale influences by min-max normalization and set Aij = 0 otherwise:

The resulting sparse asymmetric A ∈ RN×N defines G = (V, E, A, X ) for the Causal Brain Graph Transformer.

3.3 Causal Brain Graph Transformer Direction-Aware Input Embedding

The input embedding stage fuses regional activity, causal topology, and anatomical position into node vectors. Given G = (V, E,A,X), |V| = N, A ∈ RN×N stores Grangercausal weights, and X = {xi(t)}Ni=1 stores BOLD signals. For each region ri, we apply PCA to xi(t) ∈ RT and retain ai ∈ R. We summarize directed influence using weighted in-degree and out-degree centralities,

We concatenate fi = [ai, din i , dout i , pi] ∈ R3+dp and project using h(0) i =Wefi +be. Stacking {h(0) i }Ni=1 yields H(0) ∈ RN×D for causal attention encoding.

Causal Self-Attention Encoder

We model localized causal interactions using intra-module causal self-attention within each functional module. Module m comprises ROIs Mm ⊆ V from the Yeo2011 parcellation and restricts attention to Mm. Head-specific matrices Wq,Wk,Wv ∈ Rda×D learn feature subspaces across attention heads for causal attention. At layer l we compute query key and value projections for nodes i, j ∈ Mm:

We score directed pairs with e(l) ij to explicitly gate attention by causality:

We define N(i) as intra-module neighbors with nonzero Aij and set α(l) ij = softmaxj∈N(i)(e(l) ij ) to enforce sparse directed message passing. For each head h we aggregate ∑j∈N(i) α(l,h) ij v(h) j and concatenate all heads to form the next embedding. We map the concatenation with Wo ∈ R(Hda)×D to obtain h(l+1) i in RD at layer l + 1:

Residual connections and layer normalization stabilize training and output Hintra ∈ RN×D with module-specific directed dependencies.

Causal Cross-Attention Encoder

To model interactions between functional modules, we introduce a cross-attention mechanism that enables ROIs in one module to aggregate causally-relevant features from ROIs in another. Given a pair of modules (Mm,Mn), where Mm is the target and Mn is the source, we compute attention scores from nodes in Mm to nodes in Mn using a gated mechanism similar to intra-module attention. For each node i ∈ Mm and each node j ∈ Mn, we compute:

The attention score is then calculated as:

where Aij is the inter-module edge weight. The normalized attention coefficient is:

We compute the updated inter-module feature for node i as:

We repeat this process across all ordered module pairs and aggregate the outputs. The resulting set of node embeddings Hinter ∈ RN×D captures cross-network information transfer modulated by causal connectivity.

Hierarchical Adaptive Fusion and Classification

We fuse intra- and inter-modular node representations using gated concatenation and attention pooling for graph-level prediction. For each node i we concatenate both streams to form zi ∈ R2D and retain both components. We compute a dynamic gate gi ∈ R2D with a sigmoid gated MLP to reweight concatenated channels:

The gate performs dimension-wise modulation for each node to produce fused embeddings:

We score each fused node for global attention pooling using si as follows:

We normalize scores across nodes with softmax and compute an attention-weighted graph embedding:

An MLP with ReLU maps hgraph to logits and a softmax yields class probabilities.

Causal Interpretability

To enable post-hoc explanation of model predictions, we adapt the GNNExplainer framework for directed, modular graphs. Given an input graph G and the predicted class ˆ y, we learn a continuous mask M ∈ RN×N over the adjacency matrix to identify the most influential edges and nodes. We formulate the optimization objective as:

where ˜ G is a perturbed version of G sampled under mask M, and λ is a sparsity regularization hyperparameter. We interpret the learned mask to produce edge-level, node-level, and module-level attribution scores. These scores highlight specific causal pathways, source nodes, and network-level disruptions that drive individual-level classifications, providing neuroscientific interpretability and potential biomarkers for clinical analysis. The pseudocode of BrainCGT is given in Algorithm 1.

4 Experimental Results

4.1 Datasets

We evaluate BrainCGT on three multi-site cohorts (see Table 1):

Algorithm 1 BrainCGT Algorithm.

• Input: Raw fMRI volume Vraw ∈ RX×Y ×Z×T Output: Predicted diagnostic label ˆ y 1: procedure BRAINCGT(Vraw) 2: /* Causal Brain Network Construction */ 3: Vpre ← Preprocess(Vraw) 4: {xi(t)}Ni=1 ←ModularParcellation(Vpre) 5: A←GrangerCausalityEstimation({xi(t)}Ni=1 ) 6: X ← {xi(t)}Ni=1 7: G ←BuildGraph(V,X,A) 8: /* Causal Brain Graph Transformer */ 9: H(0) ←DirectionAwareInputEmbedding(G) 10: Initialize model parameters θ 11: for e = 1 to E do 12: Hintra ← CausalSelfAttentionEncoder(H(0) , A) 13: Hinter ← CausalCrossAttentionEncoder(Hintra, A) 14: Hfused ← HierarchicalFusion(Hintra, Hinter) 15: ˆ y ← MLPClassifier(Hfused) 16: Compute loss Lcls(ˆ y, y) 17: Update parameters θ via backpropagation 18: end for 19: /* Causal Interpretability */ 20: CausalAttributionMaps ←GNNExplainer(G, ˆ y) 21: return ˆ y 22: end procedure
• ADNI [Mueller et al., 2005]: Controlled-access Alzheimer cohort. We use resting-state fMRI to build causal graphs and classify CN vs AD. It includes 426 subjects age 50-100, 227/199 male/female, CN n=280, and AD n=146. We drop sessions missing fMRI or metadata.
• PPMI [Marek et al., 2011]: Controlled-access Parkinson cohort. We use resting-state fMRI for causal graphs and classify Control vs PD. It includes 324 subjects age 4085, 194/130 male/female, Control n=94, PD n=230. We remove scans failing quality control.
• ABIDE [Martino et al., 2014]: Open multi-site autism cohort. We use resting-state fMRI for causal graphs and classify Control vs ASD. It includes 1,118 subjects age 8-40, 957/161 male/female, Control n=581, ASD n=537. We apply stratified sampling for site balance [Marzi et al., 2024].

4.2 Baselines

We compare against four baseline families under identical preprocessing and train/val/test splits.

• Conventional machine learning: We use SVM, random forests, and a shallow MLP on handcrafted graph descriptors. We extract degree, betweenness, clustering, assortativity, and modularity, standardize within folds, and tune by stratified grid search.
• Conventional graph learning: We evaluate GIN [Xu et al., 2019], GAT [Velickovic et al., 2018], and Graphormer [Ying et al., 2021] on directed A with ROI summaries and in/out-degree indicators. We train in PyTorch Geometric with Adam, cosine decay, and early stopping, and avoid feature selection.
• Functional connectivity models: We benchmark BrainGB [Cui et al., 2023], KDGCN [Luo et al., 2025], ALTER [Yu et al., 2024], CAGT [Pei et al., 2025], and BioBGT [Peng et al., 2025] using public releases. We estimate undirected connectivity from the same fMRI data and tune hyperparameters on validation only.
• Causal connectivity models: We include CaLLTiF [Arab et al., 2025], BrainGB with Granger causality [Zhang et al., 2025], and STDCDAE [Xu et al., 2026]. We follow each pipeline for directed connectivity estimation and keep metrics and stopping criteria identical.

Implementation Details

BrainCGT includes two modules for causal graph construction and transformer-based classification. We preprocess fMRI with nibabel, nilearn and nipype then parcellate and denoise. Multivariate Granger causality produces asymmetric adjacency matrices with module partitions and direction-aware node features. We implement the transformer in PyTorch Geometric with direction-biased attention and degree-informed embeddings. We use 5-fold stratified subject-level splits for ADNI, PPMI and ABIDE and train each dataset separately. We optimize cross-entropy with AdamW using learning rate 1×10-4 -3×10-4 , weight decay 1×10-4 and batch size 16. We train up to 200 epochs with dropout 0.2 and early stopping with patience 20 and gradient clipping.

Computational Complexity

We analyze BrainCGT complexity to quantify scalability and bottlenecks. Causal construction dominates time: modulewise VAR fitting costs O(TN 2p+N 3 p) and inter-module tests cost O(TEinterp). The transformer costs O(HDE +HND) per layer for sparse attention plus O(DN) pooling and O(D2 ) classification. Total time is O(TN 2p+N 3p+LHDE) and the dense worst case is O(LHDN 2 ). Space is O(E +ND + LHD2 +N 2 p) from sparse graphs, node embeddings, parameters, VAR coefficients, and attention buffers O(HE). Here N denotes ROIs, T time points, E edges, H heads, D hidden size, L layers, and p lag order.

4.3 Performance of BrainCGT

We evaluate BrainCGT on ADNI, PPMI, and ABIDE and summarize results in Table 2. ADNI shows balanced performance with Accuracy 75.13 ± 4.15%, F1 72.55 ± 4.72%, and AUC 75.81 ± 1.38%. PPMI attains high Accuracy 84.46 ± 2.24% but lower F1 64.92±2.39% and AUC 67.56±3.47%, indicating threshold miscalibration under class imbalance. ABIDE remains robust with Accuracy 81.62 ± 1.57% and AUC 80.94±1.59%, while F1 67.46±3.21% reflects cohort heterogeneity and site effects. Small Accuracy and AUC deviations indicate stable training and generalizable causality-aware representations.

4.4 Comparison with Baseline Methods

We compare BrainCGT with conventional ML, generic graph learning, functional connectivity, and causal connectivity baselines in Table 2. Against handcrafted pipelines, BrainCGT improves Accuracy, F1, and AUC by 11.20-21.79 points across ADNI, PPMI, and ABIDE. Against GIN, GAT, and Graphormer, gains reach 4.61-16.60 in Accuracy, 8.64-12.41 in F1, and 3.47-10.87 in AUC. Relative to correlation-based models, BrainCGT improves by 2.19-7.87 Accuracy points and 0.95-2.91 AUC points across cohorts. BrainCGT preserves edge asymmetry and disentangles intra-module and inter-module effects during attention-based encoding. These margins indicate that directed edges and module-aware attention capture cross-network dependencies that correlationbased connectivity can obscure. Compared with causal baselines, BrainCGT usually leads in F1 and AUC, although STDCDAE leads Accuracy on PPMI by 1.51. Overall, hierarchical causal gating and adaptive fusion in BrainCGT yield robust separability under imbalance and site variability without sacrificing calibration.

4.5 Ablation Study

We perform single-factor ablations to measure the contribution of each BrainCGT component to diagnostic accuracy. Table 3 summarizes all results. Each variant removes one component: fMRI preprocessing, modular parcellation (Yeo-7), causal connectivity, direction-aware embeddings, causal selfattention, or causal cross-attention. All other stages remain unchanged. For fairness across configurations, we recompute graphs and retrain every model from scratch with identical data splits, hyperparameters and random seeds. Removing fMRI preprocessing produces the largest accuracy drops on ADNI -14.0%, PPMI -10.7% and ABIDE -10.4%. This confirms the central role of signal conditioning for stable effective connectivity estimation. Removing causal connectivity and causal self-attention also reduces accuracy, with maximum drops of -9.5% and -8.0%. These reductions indicate the importance of directed interactions and direction-specific gating. Removing modular parcellation or causal cross-attention yields moderate degradation and reflects weaker structural priors and limited inter-module integration. Direction-aware embeddings produce smaller but consistent losses. Overall, causal constraints and signal-level preprocessing dominate BrainCGT performance.

4.6 Parameter Analysis

We analyze BrainCGT sensitivity to causal prior strength and modular granularity through the gate scaling factor γ and the number of functional modules M. We sweep γ in {0.00, 0.25, 0.50, 1.00, 1.10, 1.20, 1.50, 2.00} and M in {6, 7, 9, 12, 17} while holding all other settings fixed. Models are trained on ADNI, PPMI, and ABIDE using identical cross-validation folds, and performance is evaluated using held-out accuracy and F1-score. As shown in Figure 2, performance exhibits a concave dependence on γ with optima near γ ≈ 1, specifically (1.1, 1.2, 1.0) for ADNI, PPMI, and ABIDE. Eliminating causal bias at γ = 0 causes large accuracy drops of 12.6%, 13.8%, and 10.4%, with corresponding F1-score reductions up to 20.0%. Over-injection at γ = 2.0 also degrades performance. In Figure 3, varying M yields a U-shaped response with dataset-specific optima (7,7,9). Both under-segmentation and over-segmentation reduce accuracy, confirming the need for balanced mesoscale organization. This behavior is consistent across datasets and indicates stable hyperparameter sensitivity.

4.7 Interpretability Analysis

We evaluate BrainCGT interpretability on ADNI PPMI and ABIDE to assess whether diagnostic decisions rely on biologically grounded directed connectivity [Li et al., 2021]. We adapt GNNExplainer to the directed modular graphs used by BrainCGT and optimize a continuous adjacency mask that balances fidelity and sparsity [Lundberg and Lee, 2017]. Masks are aggregated across nodes and modules and projected to the anatomical parcellation to produce cohort-level causal maps shown in Figure 4. AD maps reveal reduced hippocampal and posterior cingulate outflow and weaker posterior to anterior DMN drive together with increased frontal influence, reflecting medial temporal and posterior DMN degeneration and compensatory executive recruitment [Dai et al., 2019]. PD maps show reduced basal ganglia to motor cortex signaling with elevated thalamic and prefrontal drive, consistent with breakdown of dopaminergic motor loops and increased reliance on top down control [Delgado-Alvarado et al., 2023]. ASD maps show stronger sensory to association signaling and weaker prefrontal regulation along with reduced medial prefrontal temporoparietal and amygdalar interactions. These directed alterations support mechanistic interpretation beyond undirected FC and highlight disorder-specific disruptions in bottom up and top down signaling [Hao et al., 2024; Xu et al., 2026].

5 Conclusion

This paper addresses limitations of neurological disorder diagnosis models based on undirected FC. We propose BrainCGT, a graph transformer that infers modular effective connectivity and integrates it end to end. Direction-aware embeddings and direction-biased attention capture asymmetric causal information flow associated with neuropathological alterations. Evaluation on ADNI, PPMI, and ABIDE shows superior diagnostic accuracy over state-of-the-art FC-based methods. Future work will extend BrainCGT to dynamic and multiscale effective connectivity. Overall, modeling modular effective connectivity yields a more robust and mechanistically informative biomarker than undirected approaches.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 62576073, 62376051, and 62576075.