Related papers: Growth Functions, Rates and Classes of String-Base…
Accelerating large language model pre-training is a critical issue in present research. In this paper, we focus on speeding up pre-training by progressively growing from a small Transformer structure to a large one. There are two main…
Introduced about thirty years ago in the field of Data Compression, the Burrows-Wheeler Transform (BWT) is a string transformation that, besides being a booster of the performance of memoryless compressors, plays a fundamental role in the…
String diagrams are a powerful and intuitive graphical syntax, originated in the study of symmetric monoidal categories. In the last few years, they have found application in the modelling of various computational structures, in fields as…
String Quantum Gravity is motivated and introduced. Advances in the study of the classical and quantum string dynamics in curved spacetime are reported: 1-New Classes of Exact Multistring solutions in curved spacetimes. 2-Mass spectrum of…
In a recent paper, Krapivsky and Redner (Phys. Rev. E, 71 (2005) 036118) proposed a new growing network model with new nodes being attached to a randomly selected node, as well to all ancestors of the target node. The model leads to a…
We introduce the notion of composite growth function and provide examples that illustrate the primary properties of these growth functions. There are provided examples of Mealy automata that have composite non-monotonic growth functions of…
We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main…
Among their many uses, growth processes (probabilistic amplification), were used for constructing reliable networks from unreliable components, and deriving complexity bounds of various classes of functions. Hence, determining the initial…
We define the Cayley graph and its growth function for multivalued groups. We prove that if we change a finite set of generators of multivalued group, or change the starting point, we get an equivalent growth function. We prove that if we…
Mathematical methods of analysis of data and of predicting growth are discussed. The starting point is the analysis of the growth rates, which can be expressed as a function of time or as a function of the size of the growing entity.…
We develop an approach to efficiently grow neural networks, within which parameterization and optimization strategies are designed by considering their effects on the training dynamics. Unlike existing growing methods, which follow simple…
A novel mechanism to produce a cosmic network of fundamental superstrings based on a time-varying string tension has been recently proposed. It has been found that fundamental superstrings can grow in a kinating background driven by the…
Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar…
Random matrix products arise in many science and engineering problems. An efficient evaluation of its growth rate is of great interest to researchers in diverse fields. In the current paper, we reformulate this problem with a generating…
Among the wide variety of evolutionary computing models, Finite State Machines (FSMs) have several attractions for fundamental research. They are easy to understand in concept and can be visualised clearly in simple cases. They have a ready…
In highly repetitive strings, like collections of genomes from the same species, distinct measures of repetition all grow sublinearly in the length of the text, and indexes targeted to such strings typically depend only on one of these…
This review provides an introduction to two dimensional growth processes. Although it covers a variety processes such as diffusion limited aggregation, it is mostly devoted to a detailed presentation of stochastic Schramm-Loewner evolutions…
While increasingly large models have revolutionized much of the machine learning landscape, training even mid-sized networks for Reinforcement Learning (RL) is still proving to be a struggle. This, however, severely limits the complexity of…
Artificial Intelligence has looked into biological systems as a source of inspiration. Although there are many aspects of the brain yet to be discovered, neuroscience has found evidence that the connections between neurons continuously grow…
We present a study of dynamical scaling and domain growth in a non potential system that models Rayleigh-Benard convection in a rotating cell. In d=1, dynamical scaling holds, but the non potential terms modify the characteristic growth law…