A normalizing flow with a mixture-of-Gaussians latent space and a quadratic post-hoc approximation yields higher-order correlations and curvature estimates for neural manifolds in macaque visual cortex.
Ordering Dimensions with Nested Dropout Normalizing Flows
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abstract
The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided compact representations by fitting flows constrained to manifolds, but hasn't defined a density off that manifold. In this work we consider flows with full support in data space, but with ordered latent variables. Like in PCA, the leading latent dimensions define a sequence of manifolds that lie close to the data. We note a trade-off between the flow likelihood and the quality of the ordering, depending on the parameterization of the flow.
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Characterizing Neural Manifolds' Properties and Curvatures using Normalizing Flows
A normalizing flow with a mixture-of-Gaussians latent space and a quadratic post-hoc approximation yields higher-order correlations and curvature estimates for neural manifolds in macaque visual cortex.