Neurospectrum: A Geometric and Topological Deep Learning Framework for Uncovering Spatiotemporal Signatures in Neural Activity
Dhananjay Bhaskar, Yanlei Zhang, Jessica L. Moore, Feng Gao, Bastian Rieck, Guy Wolf, Firas A. Khasawneh, Elizabeth Munch, Jack Adam Noah, Helen Pushkarskaya, Christopher Pittenger, Valentina Greco, Smita Krishnaswamy · bioRxiv (Cold Spring Harbor Laboratory) · 2023
, a framework that encodes neural activity as latent trajectories shaped by spatial and temporal structure. At each timepoint, signals are represented on a graph capturing spatial relationships, with a learnable attention mechanism highlighting important regions. These are embedded using graph wavelets and passed through a manifold-regularized autoencoder that preserves temporal geometry. The resulting latent trajectory is summarized using a principled set of descriptors - including curvature, path signatures, persistent homology, and recurrent networks -that capture multiscale geometric, topological, and dynamical features. These features drive downstream prediction in a modular, interpretable, and end-to-end trainable framework. We evaluate Neurospectrum on simulated and experimental datasets. It tracks phase synchronization in Kuramoto simulations, reconstructs visual stimuli from calcium imaging, and identifies biomarkers of obsessive-compulsive disorder in fMRI. Across tasks, Neurospectrum uncovers meaningful neural dynamics and outperforms traditional analysis methods.