10 papers
Kähler landscapes for complex neural network descents and guarantees including a search and destroy of the Calabi-Yau manifold
Andrew Gracyk
We study landscapes for complex-parameterized networks. Our approach is motivated with an information-theoretic manifold perspective of the parameter and via classical optimization…
Inexact calculus of variations on the hyperspherical tangent bundle with connections to the attention mechanism
Andrew Gracyk
We offer a theoretical mathematical background through Lagrangian optimization on the unit hyperspherical manifold and its tangential structure. Our methods can be categorized as i…
Complex normalizing flows can almost be information Kähler-Ricci flows
Andrew Gracyk
We develop interconnections between the complex normalizing flow for data drawn from Borel probability measures on the twofold realification of the complex manifold and a nonlinear…
Geometric flow regularization in latent spaces for smooth dynamics with the efficient variations of curvature
Andrew Gracyk
We design strategies in nonlinear geometric analysis to temper the effects of adversarial learning for sufficiently smooth data of numerical method-type dynamics in encoder-decoder…
Variational autoencoders with latent high-dimensional steady geometric flows for dynamics
Andrew Gracyk
We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs wit…
Ricci flow regularization in latent spaces for the forward learning of partial differential equations
Andrew Gracyk
We present a manifold-based machine learning encoder-decoder method for learning dynamics in time, notably partial differential equations (PDEs), in which the manifold latent space…