Related papers: Analytic Models for the Evolution of Semilocal Str…

Evolving data streams induce joint nonstationarity in continual semantic segmentation, where semantic classes, input distributions, and supervision availability change simultaneously over time. This setting reflects practical structured…

Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A…

The charge-velocity-dependent one-scale model is an extension of the canonical velocity-dependent one-scale model which explicitly incorporates additional degrees of freedom on the string worldsheet, such as arbitrary currents and charges,…

We propose an extended local-world evolving network model including a triad formation step. In the process of network evolution, random fluctuation in the number of new edges is involved. We derive analytical expressions for degree…

This paper presents a statistically sound method for measuring the accuracy with which a probabilistic model reflects the growth of a network, and a method for optimising parameters in such a model. The technique is data-driven, and can be…

Recently, significant progress has been made on semantic segmentation. However, the success of supervised semantic segmentation typically relies on a large amount of labelled data, which is time-consuming and costly to obtain. Inspired by…

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…

Automation of machine learning model development is increasingly becoming an established research area. While automated model selection and automated data pre-processing have been studied in depth, there is, however, a gap concerning…

Semiparametric language models (LMs) have shown promise in continuously learning from new text data by combining a parameterized neural LM with a growable non-parametric memory for memorizing new content. However, conventional…

Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…

I use a combination of state-of-the-art numerical simulations and analytic modelling to discuss the scaling properties of cosmic defect networks, including superstrings. Particular attention is given to the role of extra degrees of freedom…

The paper explores the challenges of regression analysis in evolving data streams, an area that remains relatively underexplored compared to classification. We propose a standardized evaluation process for regression and prediction interval…

Understanding training dynamics and feature evolution is crucial for the mechanistic interpretability of large language models (LLMs). Although sparse autoencoders (SAEs) have been used to identify features within LLMs, a clear picture of…

As Large Language Models (LLMs) move from curated training sets into open-ended real-world environments, a fundamental limitation emerges: static training cannot keep pace with continual deployment environment change. Scaling training-time…

A locally iterative learning (LIL) rule is adapted to a model of the associative memory based on the evolving recurrent-type neural networks composed of growing neurons. There exist extremely different scale parameters of time, the…

Lecture notes from 2008 CMI/ETH Summer School on Evolution Equations. These notes are an informal introduction to the applications of microlocal methods in the study of linear evolution equations and spectral theory. Calculi of…

We present an extension of the velocity-dependent one-scale model for cosmic string evolution, which is suitable for describing the evolution of local and global monopole networks. We discuss the key dynamical features that need to be…

We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…

A classical measure of string comparison is given by the longest common subsequence (LCS) problem on a pair of strings. We consider its generalisation, called the semi-local LCS problem, which arises naturally in many string-related…

We use the Velocity-dependent One Scale Model for topological defect evolution to explore and classify the possible scaling solutions for string networks with time-varying tension, in cosmological and non-cosmological settings and under two…