Related papers: A Note on Kernel Methods for Multiscale Systems wi…
We propose a novel deterministic sampling method to approximate a target distribution $\rho^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD). By employing the general \emph{energetic variational…
Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress…
We theoretically study divergent fluctuations of dynamical events at non-ergodic transitions. We first focus on the finding that a non-ergodic transition can be described as a saddle connection bifurcation of an order parameter for a time…
We observe a novel 'multiple-descent' phenomenon during the training process of LSTM, in which the test loss goes through long cycles of up and down trend multiple times after the model is overtrained. By carrying out asymptotic stability…
Fine-tuning LLMs on narrowly harmful datasets can lead to behavior that is broadly misaligned with respect to human values. To understand when and how this emergent misalignment occurs, we develop a comprehensive framework for detecting and…
The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…
We propose MMD-OPT: a sample-efficient approach for minimizing the risk of collision under arbitrary prediction distribution of the dynamic obstacles. MMD-OPT is based on embedding distribution in Reproducing Kernel Hilbert Space (RKHS) and…
Accurate quantification of uncertainty is crucial for real-world applications of machine learning. However, modern deep neural networks still produce unreliable predictive uncertainty, often yielding over-confident predictions. In this…
Conditional Maximum Mean Discrepancy (CMMD) can capture the discrepancy between conditional distributions by drawing support from nonlinear kernel functions, thus it has been successfully used for pattern classification. However, CMMD does…
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the…
We develop novel clustering algorithms for functional data when the number of clusters $K$ is unknown and also when it is prefixed. These algorithms are developed based on the Maximum Mean Discrepancy (MMD) measure between two sets of…
Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of…
Detection of critical slowing down (CSD) is the dominant avenue for anticipating critical transitions from noisy time-series data. Most commonly, changes in variance and lag-1 autocorrelation [AC(1)] are used as CSD indicators. However,…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
We study the statistical mechanics of binary systems under gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems, in the microcanonical and canonical ensembles, we…
We present a selective sampling method designed to accelerate the training of deep neural networks. To this end, we introduce a novel measurement, the minimal margin score (MMS), which measures the minimal amount of displacement an input…
Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem based on importance sampling, cloning, and spectral…
A key element in transfer learning is representation learning; if representations can be developed that expose the relevant factors underlying the data, then new tasks and domains can be learned readily based on mappings of these salient…
Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantization. Formally, we seek a weighted mixture of Dirac measures…
Process Monitoring involves tracking a system's behaviors, evaluating the current state of the system, and discovering interesting events that require immediate actions. In this paper, we consider monitoring temporal system state sequences…