相关论文: Information Shapes Koopman Representation

We propose deep Koopman-layered models with learnable parameters in the form of Toeplitz matrices for analyzing the transition of the dynamics of time-series data. The proposed model has both theoretical solidness and flexibility. By virtue…

Koopman operator recently gained increasing attention in the control systems community for its abilities to bridge linear and nonlinear systems. Data driven Koopman operator approximations have established themselves as key enablers for…

Learned representations at the level of characters, sub-words, words and sentences, have each contributed to advances in understanding different NLP tasks and linguistic phenomena. However, learning textual embeddings is costly as they are…

An information-theoretic framework is introduced to analyze last-layer embedding, focusing on learned representations for regression tasks. We define representation-rate and derive limits on the reliability with which input-output…

The constituents of a complex system exchange information to function properly. Their signalling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange…

We address the question of characterizing and finding optimal representations for supervised learning. Traditionally, this question has been tackled using the Information Bottleneck, which compresses the inputs while retaining information…

Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…

Inference capabilities of machine learning (ML) systems skyrocketed in recent years, now playing a pivotal role in various aspect of society. The goal in statistical learning is to use data to obtain simple algorithms for predicting a…

In this paper, we propose a unified information theoretic framework for learning-motivated methods aimed at odometry estimation, a crucial component of many robotics and vision tasks such as navigation and virtual reality where relative…

Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…

In recent years, self-supervised learning has played a pivotal role in advancing machine learning by allowing models to acquire meaningful representations from unlabeled data. An intriguing research avenue involves developing…

Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that…

Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to…

In this paper we propose a novel approach to compute the Koopman operator from sparse time series data. In recent years there has been considerable interests in operator theoretic methods for data-driven analysis of dynamical systems.…

Information Bottlenecks (IBs) learn representations that generalize to unseen data by information compression. However, existing IBs are practically unable to guarantee generalization in real-world scenarios due to the vacuous…

This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in…

Low-dimensional representations of underdamped systems often provide insightful grasps and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most…

The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…

The system frequency is a critical measure of power system stability and understanding, and modeling it are key to ensure reliable power system operations. Koopman-based autoencoders are effective at approximating complex nonlinear data…

We introduce a unified framework that combines nonlinear dynamics, perceptual psychophysics and high frequency haptic rendering to enhance realism in surgical simulation. The interaction of the surgical device with soft tissue is elevated…