Despite the developed solutions rely on a series of approximations, they precisely capture all the scaling laws associated with the problem. Zones of applicability of these limiting solutions are calculated, and their dependence on the problem parameters is investigated....
作者首先引入Neural Scaling Laws (神经标度律/神经缩放定律),即 深度学习的误差随着训练集大小、模型大小或两者的幂数而下降。 尽管在这一规律的推动下,深度学习的性能在近年来实现了突飞猛进的发展。 但是从另一个角度看,这种幂律缩放也导致了巨量的资源消耗,包括数据收集、计算以及能源消耗等各个方面。 而且按照幂...
(fBm)ina,niteintervalwithabsorbingboundariesateachend.AnalyticalargumentsareusedtosuggestasimplescalinglawfortheMFPTandnumericalexperimentsareperformedtoverifyitsaccuracy.ThesameapproachisusedtoderiveascalinglawforfBmwithapower-lawclock(fBm-plc).TheMFPTscalinglawsareemployedtodevelopscalinglawsforthe,nite-size...
What is the Power Law? Thepower law(also called the scaling law) states that a relative change in one quantity results in a proportional relative change in another. The simplest example of the law in action is a square; if you double the length of a side (say, from 2 to 4 inches) ...
The power law (in which the power is usually a fraction) characterizing the degree of flux deviation from the critical value is referred to as the “scaling law” (or “scaling”). From:Studies in Interface Science,2001 Also in subject areas: ...
Scaling laws of laboratory experiments are very important in shedding light on the behavior of similar real systems. The importance of this concept in petroleum engineering is the fact that oil recovery from reservoir matrix blocks, for example, can be predicted from experimental tests conducted on ...
Metrics Abstract Power-law scaling, a central concept in critical phenomena, is found to be useful in deep learning, where optimized test errors on handwritten digit examples converge as a power-law to zero with database size. For rapid decision making with one training epoch, each example is...
Neural scaling laws are observed in a range of domains, to date with no clear understanding of why they occur. Recent theories suggest that loss power laws arise from Zipf's law, a power law observed in domains like natural language. One theory suggests that language scaling laws emerge when...
Any geodesic entering this horizon inevitably progresses toward the singularity at the center of the black hole, where conventional physical laws break down [1]. Consequently, no radiation can escape from within a black hole. From a classical perspective, the mass of a black hole can be ...
Correlations and scaling laws in human mobility. PLoS ONE 9, e84954; 10.1371/journal.pone.0084954 (2014). Article CAS ADS Google Scholar Cohen, J. Statistical Power Analysis for the Behavioral Sciences. 2nd edn (Routledge, 1988). Ross, S. M. Stochastic Processes. 2nd edn (Wiley, New ...