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Mild cognitive impairment (MCI), as a transitional state between normal cognition and Alzheimer\'s disease (AD), is crucial for taking preventive interventions in order to slow down AD progression. Given the high relevance of brain atrophy and the neurodegeneration process of AD, we propose a novel mesh-based pooling module, RegionPool, to investigate the morphological changes in brain shape regionally. We then present a geometric deep learning framework with the RegionPool and graph attention convolutions to perform binary classification on MCI subtypes (EMCI/LMCI). Our model does not require feature engineering and relies only on the relevant geometric information of T1-weighted magnetic resonance imaging (MRI) signals. Our evaluation reveals the state-of-the-art classification capabilities of our network and shows that current empirically derived MCI subtypes cannot identify heterogeneous patterns of cortical atrophy at the MCI stage. The class activation maps (CAMs) generated from the correct predictions provide additional visual evidence for our model\'s decisions and are consistent with the atrophy patterns reported by the relevant literature.
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