Functional connectivity (FC) analysis, a valuable tool for computer-aided brain disorder diagnosis, traditionally relies on atlas-based parcellation. However, issues relating to selection bias and a lack of regard for subject specificity can arise as a result of such parcellations. Addressing this, we propose ABFR-KAN, a transformer-based classification network that incorporates novel advanced brain function representation components with the power of Kolmogorov-Arnold Networks (KANs) to mitigate structural bias, improve anatomical conformity, and enhance the reliability of FC estimation. Extensive experiments on the ABIDE I dataset, including cross-site evaluation and ablation studies across varying model backbones and KAN configurations, demonstrate that ABFR-KAN consistently outperforms state-of-the-art baselines for autism spectrum distorder (ASD) classification. Our code is available at https://github.com/tbwa233/ABFR-KAN.

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