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This lecture explores the integration of brain connectivity knowledge to decode and interpret brain activity using graph signal processing and spectral residual networks. It discusses the application of graph theory in modeling brain structure and function, leveraging graph spectral analysis and graph signal processing. The talk presents ongoing works that use functional connectivity graphs to define spectral convolution operators in deep residual networks for task decoding. It also analyzes brain activity with high-density EEG using graph signal processing to estimate coupling and decoupling of electrophysiological activity on a structural connectivity graph. The ultimate goal is to enhance the understanding of brain complexity through connectivity-informed analysis of brain activity.