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In this paper, we propose RiemannianFlow, a deep generative model that allows robots to learn complex and stable skills evolving on Riemannian manifolds. Examples of Riemannian data in robotics include stiffness (symmetric and positive…

In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…

Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…

Fluid deformation controls myriad processes in random flows including mixing and dispersion, stress development in complex fluids, colloid transport and deposition, droplet breakup and emulsification, fluid-structure interaction, chemical…

Recent advances in decentralized deep learning algorithms have demonstrated cutting-edge performance on various tasks with large pre-trained models. However, a pivotal prerequisite for achieving this level of competitiveness is the…

We consider the problem of decentralized deep learning where multiple agents collaborate to learn from a distributed dataset. While there exist several decentralized deep learning approaches, the majority consider a central parameter-server…

We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…

Stochastic Gradient Descent (SGD) has been the method of choice for learning large-scale non-convex models. While a general analysis of when SGD works has been elusive, there has been a lot of recent progress in understanding the…

Discrete diffusion has recently emerged as a promising paradigm in discrete data modeling. However, existing methods typically rely on a fixed rate transition matrix during training, which not only limits the expressiveness of latent…

We propose an efficient protocol for decentralized training of deep neural networks from distributed data sources. The proposed protocol allows to handle different phases of model training equally well and to quickly adapt to concept…

This paper develops an unified framework to study finite-sample convergence guarantees of a large class of value-based asynchronous reinforcement learning (RL) algorithms. We do this by first reformulating the RL algorithms as…

This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning…

The classical (overdamped) Langevin dynamics provide a natural algorithm for sampling from its invariant measure, which uniquely minimizes an energy functional over the space of probability measures, and which concentrates around the…

The key idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we…

Our work is motivated by a desire to study the theoretical underpinning for the convergence of stochastic gradient type algorithms widely used for non-convex learning tasks such as training of neural networks. The key insight, already…

While Learned Data Compression (LDC) has achieved superior compression ratios, balancing precise probability modeling with system efficiency remains challenging. Crucially, uniform single-stream architectures struggle to simultaneously…

Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system,…

We study propagation of dissipative structures in inhomogeneous media with a focus on pinning and depinning transitions. We model spatial complexity in the medium as generated by dynamical systems. We are thus able to capture transitions…