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Many studies in neuroscience have focused on interpreting brain activity using functional connectivity (FC). The most widely used approach for measuring FC is based on linear correlation (e.g., the Pearson correlation), where the temporal cofluctuations between functional brain regions are computed. However, such approaches ignore nonlinear dependencies among regions that might carry distinctive information across groups of subjects. In this study, we offer a deep learning-based approach that also captures nonlinear temporal relationships between brain networks. Our approach consists of two main parts: an encoder that learns domainspecific embeddings of time courses estimated from independent component analysis (ICA) and a similarity metric that measures the similarities between the embeddings. We call such similarities as nonlinear functional relationships between networks. Our findings on a large dataset (including above 11k normal control subjects) suggest that male subjects exhibit stronger nonlinear network-network relationships than female subjects in most cases. Furthermore, we observe that, unlike FC, our approach could capture some intra-network relationships, especially between cognitive control and visual networks, which are significantly different between males and females, suggesting that our approach can provide a complementary interpretation of the functional brain activity to FC. 

Resting-state functional magnetic resonance imaging (rsfMRI) has become a widely used approach for detecting subtle differences in functional brain fluctuations in various studies of the healthy and disordered brain. Such studies are often based on temporal functional connectivity (i.e., the correlation between time courses derived from regions or networks within the fMRI data). While being successful for a number of tasks, temporal connectivity does not fully leverage the available spatial information. In this research study, we present a new perspective on spatial functional connectivity, which involves learning patterns of spatial coupling among brain networks by utilizing recent advances in deep learning as well as the contrastive learning framework. We show that we can learn domain-specific mappings of brain networks that can, in turn, be used to characterize differences between schizophrenia patients and control. Furthermore, we show that the coupling of intradomain networks in the controls is stronger than in patients suffering from the disorder. We also evaluate the coupling among networks of different domains and find various patterns of stronger or weaker coupling among certain domains, which provide additional insights about the brain.