Regensburg 2025 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 7: Focus Session: Self-Regulating and Learning Systems: from Neural to Social Networks
SOE 7.9: Talk
Wednesday, March 19, 2025, 12:15–12:30, H45
Employing normalizing flows to examine neural manifold characteristics and curvatures — •Peter Bouss1,2, Sandra Nestler3, Kirsten Fischer1,2, Claudia Merger4, Alexandre René2,5, and Moritz Helias1,2 — 1IAS-6, Forschungszentrum Jülich, Germany — 2RWTH Aachen University, Germany — 3Technion, Haifa, Israel — 4SISSA, Trieste, Italy — 5University of Ottawa, Canada
Despite the vast number of active neurons, neuronal population activity supposedly lies on low-dimensional manifolds (Gallego et al., 2017). To learn the statistics of neural activity, we use Normalizing Flows (NFs) (Dinh et al., 2014). These neural networks are trained to estimate the probability distribution by learning an invertible map to a latent distribution.
We adjust NF’s training objectives to distinguish between relevant and noise dimensions, by using a nested dropout procedure in the latent space (Bekasov & Murray, 2020). An approximation of the network for each mixture component as a quadratic mapping enables us to calculate the Riemannian curvature tensors of the neural manifold. We focus mainly on the directions in the tangent space, in which the sectional curvature shows local extrema.
Finally, we apply the method to electrophysiological recordings of the visual cortex in macaques (Chen et al., 2022). We show that manifolds deviate significantly from being flat. Analyzing the curvature of the manifolds yields insights into the regimes where neuron groups interact in a non-linear manner.
Keywords: Manifolds; Curvature; Normalizing Flows; Dimensionality Reduction