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Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Quantum dynamics that explore an unexpectedly small fraction of Hilbert space is inherently interesting. Integrable systems, quantum scars, MBL, hidden tensor structures, and systems with gauge symmetries are examples. Beyond dimension and…

Weak identification arises in many statistical problems when key variables exhibit weak correlations-for example, when instrumental variables correlate weakly with treatment, or when proxy variables correlate weakly with unmeasured…

In many engineering systems, proper predictive maintenance and operational control are essential to increase efficiency and reliability while reducing maintenance costs. However, one of the major challenges is that many sensors are used for…

Entanglement is a ubiquitous feature of low temperature systems and believed to be highly relevant for the dynamics of condensed matter properties and quantum computation even at higher temperatures. The experimental certification of this…

The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements cannot be viewed as revealing pre-existing properties of…

In quantum mechanics, observation actively shapes the system, paralleling the statistical notion of Missing Not At Random (MNAR). This study introduces a unified framework for \textbf{robust causal directionality inference} in quantum…

Previously, we showed that computational mechanic's causal states -- predictively-equivalent trajectory classes for a stochastic dynamical system -- can be cast into a reproducing kernel Hilbert space. The result is a widely-applicable…

Behavioural metrics have been shown to be an effective mechanism for constructing representations in reinforcement learning. We present a novel perspective on behavioural metrics for Markov decision processes via the use of positive…

Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…

Highly directional mmWave/THz links require rapid beam alignment, yet exhaustive codebook sweeps incur prohibitive training overhead. This letter proposes a sensing-assisted adaptive probing policy that maps multimodal sensing…

In this report, we study the reduced conditional dynamics of a quantum system in the case of indirect quantum measurement. The detectors microscopic part (pointer) interacts with the measured system (target) and the environment, which…

We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral…

We study the problem of solving a linear sensing system when the observations are unlabeled. Specifically we seek a solution to a linear system of equations y = Ax when the order of the observations in the vector y is unknown. Focusing on…

This paper investigates context stickiness in in-context learning (ICL), a phenomenon where earlier examples in a prompt interfere with a transformer's ability to adapt to later tasks. Using synthetic regression tasks over linear and…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

We explore the power of spatial context as a self-supervisory signal for learning visual representations. In particular, we propose spatial context networks that learn to predict a representation of one image patch from another image patch,…

We uncover a local order parameter for measurement-induced phase transitions: the average entropy of a single reference qubit initially entangled with the system. Using this order parameter, we identify scalable probes of…

Safe control for dynamical systems is critical, yet the presence of unknown dynamics poses significant challenges. In this paper, we present a learning-based control approach for tracking control of a class of high-order systems, operating…

Contextuality is a foundational phenomenon underlying key differences between quantum theory and classical realistic descriptions of the world. Here we propose an experimental test which is capable of revealing contextuality in all qutrit…