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...
We have mentioned a number of times that one indicator of fractal random processes is an inverse power law, and that such laws come in two flavors, spectra and probability densities. The inverse power-law spectrum, or equivalently the correlation function, indicates the existence of long-term ...
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) then the area will quadrup...
(fBm)ina,niteintervalwithabsorbingboundariesateachend.AnalyticalargumentsareusedtosuggestasimplescalinglawfortheMFPTandnumericalexperimentsareperformedtoverifyitsaccuracy.ThesameapproachisusedtoderiveascalinglawforfBmwithapower-lawclock(fBm-plc).TheMFPTscalinglawsareemployedtodevelopscalinglawsforthe,nite-size...
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: ...
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...
A power law (PL), also known as a scaling law, is the form taken by a remarkable number of regularities or ‘laws’ in economics, and is a relation of the type Y = kXα, where Y and X are variables of interest, α is called the power law exponent,...
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 presented only ...
These various scaling velocities generated from the scaling laws suggested by several authors will be used in combination with our scaling law such that it covers most of the possible scenarios of imbibition processes. 2.2. Injection velocity In case of forced imbibition, the magnitude of the inject...
A power law is the form taken by a remarkable number of regularities in economics, and is a relation of the type Y = kX α , where Y and X are variables of interest, α is called the power law exponent, and k is a constant. Man