Hasil untuk "Law"

J. Kaplan, Sam McCandlish, T. Henighan et al.

We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven orders of magnitude. Other architectural details such as network width or depth have minimal effects within a wide range. Simple equations govern the dependence of overfitting on model/dataset size and the dependence of training speed on model size. These relationships allow us to determine the optimal allocation of a fixed compute budget. Larger models are significantly more sample-efficient, such that optimally compute-efficient training involves training very large models on a relatively modest amount of data and stopping significantly before convergence.

Immanuel Kant, Edited BY Jens Timmermann English, M. Gregor

Erik P. Verlinde

Starting from first principles and general assumptions we present a heuristic argument that shows that Newton’s law of gravitation naturally arises in a theory in which space emerges through a holographic scenario. Gravity is identified with an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton’s law of inertia needs to be explained. The equivalence principle auggests that it is actually the law of inertia whose origin is entropic.

Z. Bai, J. Silverstein

F. Digham, Mohamed-Slim Alouini, M. Simon

L. Godden

S. D. Groot, P. Mazur

C. Hang, T. Lee, W. K. Ho

Adaptive control is the attempt to " redesign " the controller while online, by looking at its performance and changing its dynamic in an automatic way. Adaptive control is that feedback law that looks at the process and the performance of the controller and reshapes the controller closed loop behavior autonomously. Plant Adaptation Procedure Controller u(t) y(t) y(t) u(t) Figure 1. Adaptive Control as Feedback Law Adaptive Control is made by combining 1. online parameter estimator based on current measurements and control actions 2. control law, that recalculates the controller based on those parameters There are two main modalities of adaptive control. We discussed them below. In this case, the estimated parameters refer to the plant, and the controller is designed based on those parameters. For example, an energy consumption coefficient is estimated; a linearized version of the plant is produced, which is then used in a pole placement method to calculate the gains of the final controller. The main problem is to make sure that the controller behaves well in cases when the estimation of the plant is not good, like for example, during transients. In principle, the indirect method is applicable to all types of plants.

J. Turkevich, P. C. Stevenson, J. Hillier

P. C. Paris, F. Erdogan

S. Peltzman

R. Ball, Scott Keating, Christian Leuz et al.

L. A. Amaral, Antonio Scala, M. Barthelemy et al.

We study the statistical properties of a variety of diverse real-world networks. We present evidence of the occurrence of three classes of small-world networks: (a) scale-free networks, characterized by a vertex connectivity distribution that decays as a power law; (b) broad-scale networks, characterized by a connectivity distribution that has a power law regime followed by a sharp cutoff; and (c) single-scale networks, characterized by a connectivity distribution with a fast decaying tail. Moreover, we note for the classes of broad-scale and single-scale networks that there are constraints limiting the addition of new links. Our results suggest that the nature of such constraints may be the controlling factor for the emergence of different classes of networks.

R. Deegan, O. Bakajin, T. Dupont et al.

Z. Bauman

A. Barabási, R. Albert, Hawoong Jeong

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-field method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-field method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling.

R. Ball, Ashok Robin, J. Wu

S. Kauffman

N. Frijda

Zijian Yao

This study proposes a systematic policy framework that leverages special tax measures to steer stakeholder behavior toward urban cultural heritage conservation. Integrating comparative policy analysis, microeconomic modeling, systematic policy framework construction and case studies from China, we design a synergistic system of tax incentives and disincentives across income, consumption, and property taxes. The framework is contextualized within China’s forthcoming Cultural Heritage Conservation Law and demonstrates how fiscal instruments can align individual economic rationality with collective conservation goals. A three-stage decision model – grounded in Multi-Criteria Decision Analysis (MCDA) – is introduced to assess the suitability, necessity, and balancing of tax interventions. Based on the analysis of secondary sources and policy documents, empirical case studies in Suzhou and Tianshui are used to illustrate the framework’s efficacy and limitations. The findings offer a transferable model for sustainable urban governance, with relevance for rapidly urbanizing regions globally.