Understanding how the brain's complex nonlinear dynamics give rise to adaptive cognition and behavior is a central challenge in neuroscience. These dynamics exhibit scale-free and multifractal properties, influencing the reconfiguration of neural networks. However, conventional neuroimaging models are constrained by linear and stationary assumptions, limiting their ability to capture these processes. Transformer-based architectures, known for capturing long-range dependencies, align well with the brain's hierarchical and temporal organization. We introduce Multi-Band Brain Net (MBBN), a transformer-based framework that models frequency-specific spatiotemporal brain dynamics from fMRI by integrating scale-free network principles with frequency-resolved multi-band self-attention. Trained on three large-scale neuroimaging cohorts (UK Biobank, ABCD, ABIDE) totaling 45,951 individuals, MBBN reveals previously undetectable frequency-dependent network interactions, shedding light on connectivity disruptions in psychiatric conditions (ADHD, ASD, depression). This validation shows robust generalizability and highlights core neural principles conserved across populations. MBBN achieves up to 30.59% higher predictive accuracy than state-of-the-art methods, demonstrating the advantage of frequency-informed spatiotemporal modeling in capturing latent neural computations. MBBN's interpretability uncovers novel frequency-specific biomarkers for neurodevelopmental disorders, providing insights into the hierarchical organization of brain function. By offering an interpretable framework for spatiotemporal learning, MBBN provides insights into how neural computations underpin cognitive function and psychiatric vulnerability, with implications for brain decoding, cognitive neuroscience, and precision psychiatry.