Related papers: Reactive Motion Generation on Learned Riemannian M…

Human motion generation involves creating natural sequences of human body poses, widely used in gaming, virtual reality, and human-computer interaction. It aims to produce lifelike virtual characters with realistic movements, enhancing…

Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Traditional imitation learning provides a set of methods and algorithms to learn a reward function or policy from expert demonstrations. Learning from demonstration has been shown to be advantageous for navigation tasks as it allows for…

Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with…

Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, constitute the first step to understand semi-Riemannian Geometry.…

Generating robot motion for multiple tasks in dynamic environments is challenging, requiring an algorithm to respond reactively while accounting for complex nonlinear relationships between tasks. In this paper, we develop a novel policy…

We introduce the Riemannian Motion Policy (RMP), a new mathematical object for modular motion generation. An RMP is a second-order dynamical system (acceleration field or motion policy) coupled with a corresponding Riemannian metric. The…

Humanoid motion control has witnessed significant breakthroughs in recent years, with deep reinforcement learning (RL) emerging as a primary catalyst for achieving complex, human-like behaviors. However, the high dimensionality and…

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…

Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to…

In robotics motion is often described from an external perspective, i.e., we give information on the obstacle motion in a mathematical manner with respect to a specific (often inertial) reference frame. In the current work, we propose to…

Riemannian manifolds have been widely employed for video representations in visual classification tasks including video-based face recognition. The success mainly derives from learning a discriminant Riemannian metric which encodes the…

Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…

Neural samplers such as variational autoencoders (VAEs) or generative adversarial networks (GANs) approximate distributions by transforming samples from a simple random source---the latent space---to samples from a more complex distribution…

Human-like motion generation for robots often draws inspiration from biomechanical studies, which often categorize complex human motions into hierarchical taxonomies. While these taxonomies provide rich structural information about how…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in a general metric space without linear structure. In such settings the classical additive error…