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Graph convolutional deep learning has emerged as a promising method to explore the functional organization of the human brain in neuroscience research. This paper presents a novel framework that utilizes the gated graph transformer (GGT) model to predict individuals’ cognitive ability based on functional connectivity (FC) derived from fMRI. Our framework incorporates prior spatial knowledge and uses a random-walk diffusion strategy that captures the intricate structural and functional relationships between different brain regions. Specifically, our approach employs learnable structural and positional encodings (LSPE) in conjunction with a gating mechanism to efficiently disentangle the learning of positional encoding (PE) and graph embeddings. Additionally, we utilize the attention mechanism to derive multi-view node feature embeddings and dynamically distribute propagation weights between each node and its neighbors, which facilitates the identification of significant biomarkers from functional brain networks and thus enhances the interpretability of the findings. To evaluate our proposed model in cognitive ability prediction, we conduct experiments on two large-scale brain imaging datasets: the Philadelphia Neurodevelopmental Cohort (PNC) and the Human Connectome Project (HCP). The results show that our approach not only outperforms existing methods in prediction accuracy but also provides superior explainability, which can be used to identify important FCs underlying cognitive behaviors.