Neuroscience research indicates that the interaction among different functional regions of the brain plays a crucial role in driving various cognitive tasks. Existing studies have primarily focused on constructing either local or global functional connectivity maps within the brain, often lacking an adaptive approach to fuse functional brain regions and explore latent relationships between localization during different cognitive tasks. This paper introduces a novel approach called the Local-Ascending-Global Learning Strategy (LAG) to uncover higher-level latent topological patterns among functional brain regions. The strategy initiates from the local connectivity of individual brain functional regions and develops a K-Level Self-Adaptive Ascending Network (SALK) to dynamically capture strong connectivity patterns among brain regions during different cognitive tasks. Through the step-by-step fusion of brain regions, this approach captures higher-level latent patterns, shedding light on the progressively adaptive fusion of various brain functional regions under different cognitive tasks. Notably, this study represents the first exploration of higher-level latent patterns through progressively adaptive fusion of diverse brain functional regions under different cognitive tasks. The proposed LAG strategy is validated using datasets related to fatigue (SEED-VIG), emotion (SEED-IV), and motor imagery (BCI_C_IV_2a). The results demonstrate the generalizability of LAG, achieving satisfactory outcomes in independent-subject experiments across all three datasets. This suggests that LAG effectively characterizes higher-level latent patterns associated with different cognitive tasks, presenting a novel approach to understanding brain patterns in varying cognitive contexts.