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Abstract Gradient mapping is an important technique to summarize high dimensional biological features as low dimensional manifold representations in exploring brain structure-function relationships at various levels of the cerebral cortex. While recent studies have characterized the major gradients of functional connectivity in several brain structures using this technique, very few have systematically examined the correspondence of such gradients across structures under a common systems-level framework. Using resting-state functional magnetic resonance imaging, here we show that the organizing principles of the isocortex, and those of the cerebellum and hippocampus in relation to the isocortex, can be described using two common functional gradients. We suggest that the similarity in functional connectivity gradients across these structures can be meaningfully interpreted within a common computational framework based on the principles of predictive processing. The present results, and the specific hypotheses that they suggest, represent an important step toward an integrative account of brain function.