In mathematics, a smooth maximum of an indexed family x1, ..., xn of numbers is a smooth approximation to the maximum function max ( x 1 , … , x n ) ...

it often needs to be approximated by a smooth function that is close to the maximum of the set. A smooth maximum, for example, g(x1, x2, …, xn) = log(...

"softmax" may be misleading. Softmax is not a smooth maximum (that is, a smooth approximation to the maximum function). The term "softmax" is also used for...

RealSoftMax or multivariable softplus) function is a smooth maximum – a smooth approximation to the maximum function, mainly used by machine learning algorithms...

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed...

"Smooth Operator" is a song by English band Sade from their debut studio album, Diamond Life (1984), and was co-written by Sade and Ray St. John. It was...

Solar maximum is the regular period of greatest solar activity during the Sun's 11-year solar cycle. During solar maximum, large numbers of sunspots appear...

address these issues, Joel Horowitz proposed a variant, called the smoothed maximum score estimator. When modelling discrete choice problems, it is assumed...

maximum or minimum. The log semiring has applications in mathematical optimization, since it replaces the non-smooth maximum and minimum by a smooth operation...

linear subtraction. The LogSumExp function is a smooth maximum: a smooth approximation to the maximum function. The following properties hold for M f...

thermal maximum (PETM), alternatively ”Eocene thermal maximum 1 (ETM1)“ and formerly known as the "Initial Eocene" or “Late Paleocene thermal maximum", was...

{\displaystyle H_{4}(2,4)} converges to 65536 in 2863311767 steps, the maximum depth of recursion is 65534. The computation according to the rules {r6...

The smooth newt, European newt, northern smooth newt or common newt (Lissotriton vulgaris) is a species of newt. It is widespread in Europe and parts...

8–102 metres, usually around rocks. Males can reach a maximum total length of 15 centimetres. The smooth alligatorfish is preyed upon by the Pacific halibut...

skeletal muscle, the contractions of smooth and cardiac muscles are myogenic (meaning that they are initiated by the smooth or heart muscle cells themselves...

body when viewed head on. The smooth trunkfish has an angular body sheathed in plate-like scales, growing to a maximum length of 47 centimetres (19 in)...

next to the great hammerhead, the smooth hammerhead typically measures 2.5–3.5 m (8.2–11.5 ft) long, with a maximum recorded length and weight of 5 m...

origin, the function −x2−y2 certainly has a maximum. Let M denote an open subset of Euclidean space. If a smooth function u : M → R {\displaystyle u:M\to...

speeds for the aircraft at its maximum weight. The yellow band is the range in which the aircraft may be operated in smooth air, and then only with caution...

their usual maximum size is 150 cm. They commonly grow to 100–120 cm with a birth length around 35 cm. The reproduction of commons smooth-hounds is viviparous...

minimum smoothed sunspot number of 2.2,[failed verification] and ended in December 2019. Activity was minimal until early 2010. It reached its maximum in April...

in April 2020 (± 6 months), and the number of sunspots reaching a (smoothed) maximum of 115 in July 2025 (± 8 months). This prediction is in line with...

rock at depths from near the surface to 8 metres (26 ft). It can reach a maximum length of 2.9 centimetres (1.1 in) SL. This species is currently the only...

Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function...

The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge about a system is the one...

saddle point since it is neither a relative maximum nor relative minimum, but it does not have a relative maximum or relative minimum in the y {\displaystyle...

developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced...

In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior...

that Maximum Force was superior to most games in that style, including Area 51. In particular, they praised the sound effects and the smoothly animated...

Peter Li and Shing-Tung Yau discovered a new method for applying the maximum principle to control the solutions of the heat equation. Their results...