相关论文: Residual Koopman Spectral Profiling for Predicting…

This paper addresses the problem of nonlinear state estimation for dynamical systems whose governing equations are approximated through Koopman operator liftings. While Koopman-based predictors have demonstrated broad approximation…

In spite of their huge success, transformer models remain difficult to scale in depth. In this work, we develop a unified signal propagation theory and provide formulae that govern the moments of the forward and backward signal through the…

Estimating how often an ML model will fail at deployment scale is central to pre-deployment safety assessment, but a feasible evaluation set is rarely large enough to observe the failures that matter. Jones et al. (2025) address this by…

Large transformer models trained on diverse datasets have shown a remarkable ability to learn in-context, achieving high few-shot performance on tasks they were not explicitly trained to solve. In this paper, we study the in-context…

We propose Koopman Spectral Wasserstein Gradient Descent (KSWGD), a particle-based generative modeling framework that learns the Langevin generator via Koopman theory and integrates it with Wasserstein gradient descent. Our key insight is…

In a critical software system, the testers have to spend an enormous amount of time and effort to maintain the software due to the continuous occurrence of defects. Among such defects, some severe defects may adversely affect the software.…

We consider the inverse problem of reconstructing the optical parameters for stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains multiple scales characterized by the magnitude of a…

In this paper, we consider the design of data-driven predictive controllers for nonlinear systems from input-output data via linear-in-control input Koopman lifted models. Instead of identifying and simulating a Koopman model to predict…

Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness…

Many spectral CT applications require accurate material decomposition. Existing material decomposition algorithms are often susceptible to significant noise magnification or, in the case of one-step model-based approaches, hampered by slow…

We analyze the stability of recurrent networks, specifically, reservoir computing models during training by evaluating the eigenvalue spectra of the reservoir dynamics. To circumvent the instability arising in examining a closed loop…

The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with…

Multispectral pedestrian detection has attracted increasing attention from the research community due to its crucial competence for many around-the-clock applications (e.g., video surveillance and autonomous driving), especially under…

This study investigates the performance of robust anomaly detection models in industrial inspection, focusing particularly on their ability to handle noisy data. We propose to leverage the adaptation ability of meta learning approaches to…

We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…

Pre-trained model assessment for transfer learning aims to identify the optimal candidate for the downstream tasks from a model hub, without the need of time-consuming fine-tuning. Existing advanced works mainly focus on analyzing the…

Training instabilities in deep networks - loss spikes, oscillatory convergence, and gradient pathologies - are empirically prevalent but lack a rigorous operator-theoretic explanation. We show that the linearized update operators for…

In many classification problems a classifier should be robust to small variations in the input vector. This is a desired property not only for particular transformations, such as translation and rotation in image classification problems,…

This paper tackles the data-driven approximation of unknown dynamical systems using Koopman-operator methods. Given a dictionary of functions, these methods approximate the projection of the action of the operator on the finite-dimensional…

Noise is ubiquitous in data used to train large language models, but it is not well understood whether these models are able to correctly generalize to inputs generated without noise. Here, we study noise-robust learning: are transformers…