Related papers: InvKA: Gait Recognition via Invertible Koopman Aut…

We study the metastability properties of a simple prototypical bistable system using the formalism of the Koopman operator. Instead of studying noise-induced transitions by following the trajectories of the system, we track them by studying…

Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine learning. Existing work provides limited analysis or it depends on local theories, such as fixed-point analysis. In contrast, we propose to analyze…

This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. We defined conditions for discovering new invariant subspaces in the state space of a dynamical system starting from an…

The Koopman and Perron Frobenius transport operators are fundamentally changing how we approach dynamical systems, providing linear representations for even strongly nonlinear dynamics. Although there is tremendous potential benefit of such…

The current state-of-the-art in quadruped locomotion is able to produce a variety of complex motions. These methods either rely on switching between a discrete set of skills or learn a distribution across gaits using complex black-box…

This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman…

Decisions in automated logistic systems can be improved based on knowledge of real-time state of individual parts and also environmental factors. These knowledge can be obtained through travel time of edges by individual robots which…

Real-world time series are characterized by intrinsic non-stationarity that poses a principal challenge for deep forecasting models. While previous models suffer from complicated series variations induced by changing temporal distribution,…

Koopman operator describes evolution of observables in the phase space, which could be used to extract characteristic dynamical features of a nonlinear system. Here, we show that it is possible to carry out interesting symbolic partitions…

Complex eigenspectra of transfer and Koopman operators describe rotational motion in dynamical systems. A particularly relevant situation in applications is when the rotation speed depends on the state-space position of the dynamics. We…

Gait recognition offers a non-intrusive biometric solution by identifying individuals through their walking patterns. Although discriminative models have achieved notable success in this domain, the full potential of generative models…

This work introduces a novel and adaptable architecture designed for real-time occupancy forecasting that outperforms existing state-of-the-art models on the Waymo Open Motion Dataset in Soft IOU. The proposed model uses recursive latent…

Gait recognition from motion capture data, as a pattern classification discipline, can be improved by the use of machine learning. This paper contributes to the state-of-the-art with a statistical approach for extracting robust gait…

A method is presented for accelerating inference in transformer language models by exploiting the low effective rank of the token activation manifold at each layer. The method decomposes each activation vector into a subspace component and…

A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…

System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…

This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We…

Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman…

The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a…

Finite-dimensional approximations of the Koopman operator rely critically on identifying nearly invariant subspaces. This invariance proximity can be rigorously quantified via the principal angles between a candidate subspace and its image…