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The name "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 the closely related LogSumExp function, which is a smooth maximum. For this reason, some prefer the more accurate term "softargmax", though the term "softmax" is conventional in ...
In many cases, a single family approximates both: maximum as the parameter goes to positive infinity, minimum as the parameter goes to negative infinity; in symbols, as and as . The term can also be used loosely for a specific smooth function that behaves similarly to a maximum, without necessarily being part of a ...
The LogSumExp (LSE) (also called RealSoftMax [1] or multivariable softplus) function is a smooth maximum – a smooth approximation to the maximum function, mainly used by machine learning algorithms. [2] It is defined as the logarithm of the sum of the exponentials of the arguments:
def ternary_search (f, left, right, absolute_precision)-> float: """Find maximum of unimodal function f() within [left, right]. To find the minimum, reverse the if/else statement or reverse the comparison. """ while abs (right-left) >= absolute_precision: left_third = left + (right-left) / 3 right_third = right-(right-left) / 3 if f (left_third) < f (right_third): left = left_third else: right ...
In mathematical analysis, the maximum and minimum [a] of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum , [ b ] they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function.
In mathematics, the arguments of the maxima (abbreviated arg max or argmax) and arguments of the minima (abbreviated arg min or argmin) are the input points at which a function output value is maximized and minimized, respectively. [note 1] While the arguments are defined over the domain of a function, the output is part of its codomain.
STL also has utility functions for manipulating another random-access container as a binary max-heap. The Boost libraries also have an implementation in the library heap. Python's heapq module implements a binary min-heap on top of a list. Java's library contains a PriorityQueue class, which implements a min-priority-queue as a binary heap.
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval, it will find that extremum, while for an interval containing multiple extrema (possibly including the interval boundaries), it will converge to one of them.