Comparative and reproducible three-dimension functional spaces in primate cortical connectomes

Intrinsic activity or spontaneous oscillations are believed to be essential for the brain to maintain flexible, adaptive, and responsive cognition to both internal and external demands. However, a functional space remains elusive for understanding this inside-out organization in the primate cortex. Here, we leverage comparative fMRI analysis to identify three conserved and reproducible functional connectivity gradients as three axes of manifold (FMA), which span a low-dimensional organizational space of wakeful primate connectomes. In humans, the primary FMA covers a sensorimotor-to-transmodal gradient that supports signal detection for allostatic anticipation. The second FMA mirrors a representation-to-modulation gradient that integrates attention and performance monitoring to compute prediction errors. The third FMA profiles a self-to-goal gradient that links salience processing and episodic memory to update brain prediction by weighting errors and contextual relevance. Marmosets exhibit a homologous tripartite structure, suggesting evolutionary conservation of predictive coding motifs, albeit with speciesspecific topological variations. These findings unify predictive coding, allostasis, and intrinsic activity into a signal-error-salience predictive modeling framework, where sensory integration, error computation, and salience modulation interact to optimize adaptive responses. By bridging neurocomputational theory with empirical connectomics, this work establishes a cross-species blueprint of brain organization, offering experimental evidence or insights into conserved mechanisms of free-energy principles and dark-energy explorations. These FMAs highlight how evolution refines neural architectures while preserving core computational principles, paving the way for mechanistic studies of predictive dysfunction and evolutionary drivers of primate brain complexity.