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An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continu- ously coupled.…
A wide range of (multivariate) temporal (1D) and spatial (2D) data analysis tasks, such as grouping vehicle sensor trajectories, can be formulated as clustering with given metric constraints. Existing metric-constrained clustering…
Although Chain-of-Thought (CoT) has achieved remarkable success in enhancing the reasoning ability of large language models (LLMs), the mechanism of CoT remains a ``black box''. Even if the correct answers can frequently be obtained,…
We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective…
Multivariate time series (MTS) analysis prevails in real-world applications such as finance, climate science and healthcare. The various self-attention mechanisms, the backbone of the state-of-the-art Transformer-based models, efficiently…
We discuss the treatment, in an effective field theory, of multi-particle correlations within a "large" system. We show that the act of coarse-graining necessarily introduces violations of unitarity in the evolution of states where the…
This work improves the existing central limit theorems (CLTs) for geometric functionals of Gibbs processes in three aspects. First, we derive a CLT for weakly stabilizing functionals, thereby improving on the previously used assumption of…
Determining whether a given state can be transformed into a target state using free operations is one of the fundamental questions in the study of resources theories. Free operations in resource theories can be enhanced by allowing for a…
Training large language models to predict beyond their training context lengths has drawn much attention in recent years, yet the principles driving such behavior of length generalization remain underexplored. We propose a new theoretical…
This paper presents a closed-form notion of controllability and observability for systems with communication delays, actuation delays, and locality constraints. The formulation reduces to classical notions of controllability and…
Aiming at the problems of computational inefficiency and insufficient interpretability faced by large models in complex tasks such as multi-round reasoning and multi-modal collaboration, this study proposes a three-layer collaboration…
In this letter, we develop a mode-coupling theory for a class of nonlinear Langevin equations with multiplicative noise using a field theoretic formalism. These equations are simplified models of realistic colloidal suspensions. We prove…
The Central Limit Theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently, the calculation of the probability distribution function (PDF) of the magnetization…
We extend the 2 dimensional Causal Dynamical Triangulation (CDT) model from the usual model of closed string to the one of open-closed string. The matrix-vector model describing the loop gas model is modified so as to possess the nature of…
We study the quadratically regularized optimal transport (QOT) problem for quadratic cost and compactly supported marginals $\mu$ and $\nu$. It has been empirically observed that the optimal coupling $\pi_\epsilon$ for the QOT problem has…
Adapted or causal transport theory aims to extend classical optimal transport from probability measures to stochastic processes. On a technical level, the novelty is to restrict to couplings which are bicausal, i.e. satisfy a property which…
Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in…
The ubiquitous effects of the environment on quantum-mechanical systems generally cause temporally correlated fluctuations. This particularly holds for systems of interest for quantum computation where such effects lead to correlated…
Machine Learning explainability techniques have been proposed as a means of `explaining' or interrogating a model in order to understand why a particular decision or prediction has been made. Such an ability is especially important at a…
The strong-coupling perturbation theory (SCPT) for correlated electron systems is extended to the case of full Coulomb interaction. The Coulomb mechanism of the orbital polarization is discussed and attention is paid to the importance of…