Neurospectrum: A Geometric and Topological Deep Learning Framework for Uncovering Spatiotemporal Signatures in Neural Activity

Dhananjay Bhaskar, Yanlei Zhang, Jessica Moore, Feng Gao, Bastian Rieck, Guy Wolf, Firas Khasawneh, Elizabeth Munch, J. Adam Noah, Helen Pushkarskaya, Christopher Pittenger, Valentina Greco, Smita Krishnaswamy

Abstract: h3>Abstract</h3> <p>Neural signals are high-dimensional, noisy, and dynamic, making it challenging to extract interpretable features linked to behavior or disease. We introduce <i>Neurospectrum</i>, 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.</p><p>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.</p>

External IDs:doi:10.1101/2023.03.22.533807