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Found 14 papers, 3 papers with code
Neural Contractive Dynamical Systems
Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions.
On the curvature of the loss landscape
In this work, we consider the loss landscape as an embedded Riemannian manifold and show that the differential geometric properties of the manifold can be used when analyzing the generalization abilities of a deep net.
Reactive Motion Generation on Learned Riemannian Manifolds
We argue that Riemannian manifolds may be learned via human demonstrations in which geodesics are natural motion skills.
On the Impact of Stable Ranks in Deep Nets
A recent line of work has established intriguing connections between the generalization/compression properties of a deep neural network (DNN) model and the so-called layer weights' stable ranks.
Pulling back information geometry
Latent space geometry has shown itself to provide a rich and rigorous framework for interacting with the latent variables of deep generative models.
Learning Riemannian Manifolds for Geodesic Motion Skills
For robots to work alongside humans and perform in unstructured environments, they must learn new motion skills and adapt them to unseen situations on the fly.
A prior-based approximate latent Riemannian metric
In this work we propose a surrogate conformal Riemannian metric in the latent space of a generative model that is simple, efficient and robust.
Bayesian Quadrature on Riemannian Data Manifolds
Riemannian manifolds provide a principled way to model nonlinear geometric structure inherent in data.
Geometrically Enriched Latent Spaces
A common assumption in generative models is that the generator immerses the latent space into a Euclidean ambient space.
Variational Autoencoders with Riemannian Brownian Motion Priors
Variational Autoencoders (VAEs) represent the given data in a low-dimensional latent space, which is generally assumed to be Euclidean.
Fast and Robust Shortest Paths on Manifolds Learned from Data
We propose a fast, simple and robust algorithm for computing shortest paths and distances on Riemannian manifolds learned from data.
Geodesic Clustering in Deep Generative Models
Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data.
Latent Space Oddity: on the Curvature of Deep Generative Models
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space.
A Locally Adaptive Normal Distribution
The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric.
