Geometry-Guided Generative Representation for Functional Brain Graphs

In network neuroscience, functional brain systems are often characterized using separate yet related graph-theoretic or spectral descriptors, overlooking how these properties covary and partially overlap across individuals and conditions. We anticipate that dense, weighted functional connectivity graphs lie on a low-dimensional latent geometry along which both topological and spectral structures vary smoothly at the population level. Although graph-based deep learning offers a powerful framework for modeling these brain connectomes, supervised approaches are constrained by the limited availability of labeled data. Existing unsupervised graph representation methods also typically focus on node-level embeddings, which are limited in capturing compact graph-level representations that preserve information from dense functional connectomes. To address these gaps, we learn compact brain graph representations using a graph transformer autoencoder, where domain-specific, aligned functional gradient geometry provides an inductive bias to guide learning. Despite being trained in a fully unsupervised manner, our approach meaningfully separates cognitive states and enables decoding of visual stimuli, with performance further improved by incorporating neural dynamics. In parallel, to enable generation of synthetic brain graphs, we fit a diffusion model to the learned latent representation and decode samples back to dense connectomes.

Brain systems can be studied through a connection map of how strongly each brain region's activity synchronously rises and falls with every other region. Such maps are large and densely interconnected, and studies usually describe their organization through different measures, some indexing how regions form communities and others how they vary along smooth large-scale axes. Although these are different views of the same connectivity, they are often studied separately, missing how they fit together. Methods that learn from hand-labeled scans are also limited, as such labels are scarce and noisy in brain studies. We built a model that, without any task or diagnosis labels, learns to compress each dense connection map into a compact representation and rebuild the original map from it. We guide this learning using functional gradients, a compact coordinate system that captures the brain's dominant organizational geometry. Although no labels are provided, the compressed representations can distinguish mental states and viewed stimuli, improving further when neural activity over time is included; they also reveal how task-related shifts in brain organization relate to cognition, and can generate realistic synthetic connection maps.