Tootfinder

Information-theoretic analysis of complex eigenmodes across avoided crossings in open microcavities
Kyu-won Park, soojoon-Lee, Kabgyun Jeong
https://arxiv.org/abs/2509.19827 ht…

Information-theoretic analysis of complex eigenmodes across avoided crossings in open microcavities
Avoided crossings (ACs) are hallmark signatures of mode interaction in quantum and wave systems. Open microcavities whose resonances are naturally described as quasi-normal modes (QNMs) with complex eigenfrequencies offer a convenient platform to observe how openness and loss reorganize modal structure. We introduce a compact \emph{quadrature space} framework that represents a complex QNM by probability weights on its real and imaginary quadratures, and we apply Shannon-type measures to these d…

Learning Linear Regression with Low-Rank Tasks in-Context
Kaito Takanami, Takashi Takahashi, Yoshiyuki Kabashima
https://arxiv.org/abs/2510.04548 https://a…

Learning Linear Regression with Low-Rank Tasks in-Context
In-context learning (ICL) is a key building block of modern large language models, yet its theoretical mechanisms remain poorly understood. It is particularly mysterious how ICL operates in real-world applications where tasks have a common structure. In this work, we address this problem by analyzing a linear attention model trained on low-rank regression tasks. Within this setting, we precisely characterize the distribution of predictions and the generalization error in the high-dimensional li…

Optimization of Base-n Radix Sort for Skewed Datasets
Atharv Pandey, Lakshmanan Kuppusamy
https://arxiv.org/abs/2509.19021 https://arxiv.org/pdf/2509.19021…

Going with the Flow: Solving for Symmetry-Driven PDE dynamics with Physics-informed Neural Networks
Michail Kavousanakis, Gianluca Fabiani, Anastasia Georgiou, Constantinos Siettos, Panagiotis Kevrekidis, Ioannis Kevrekidis
https://arxiv.org/abs/2509.15963

Going with the Flow: Solving for Symmetry-Driven PDE dynamics with Physics-informed Neural Networks
In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dynamically factoring out continuous symmetries such as translation and scaling. This is achieved through the use of time-dependent transformations -- what can be viewed as dynamic pinning conditions -- that render the symmetry-invariant solution stationary or slowly varying in rescaled coordinates. The transformation pr…