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Therefore, compilers will attempt to transform the first form into the second; this type of optimization is known as map fusion and is the functional analog of loop fusion. [2] Map functions can be and often are defined in terms of a fold such as foldr, which means one can do a map-fold fusion: foldr f z . map g is equivalent to foldr (f .
Neural operators directly learn operators between function spaces; they can receive input functions, and the output function can be evaluated at any discretization. [ 1 ] The primary application of neural operators is in learning surrogate maps for the solution operators of partial differential equations (PDEs), [ 1 ] which are critical tools ...
In the sense that a GTM explicitly requires a smooth and continuous mapping from the input space to the map space, it is topology preserving. However, in a practical sense, this measure of topological preservation is lacking. [31] The growing self-organizing map (GSOM) is a growing variant of the self-organizing map. The GSOM was developed to ...
In computer science, zipping is a function which maps a tuple of sequences into a sequence of tuples. This name zip derives from the action of a zipper in that it interleaves two formerly disjoint sequences.
MapReduce is a programming model and an associated implementation for processing and generating big data sets with a parallel and distributed algorithm on a cluster. [1] [2] [3]A MapReduce program is composed of a map procedure, which performs filtering and sorting (such as sorting students by first name into queues, one queue for each name), and a reduce method, which performs a summary ...
In Python, functions are first-class objects that can be created and passed around dynamically. Python's limited support for anonymous functions is the lambda construct. An example is the anonymous function which squares its input, called with the argument of 5:
Note that the parameters to cons must be flipped, because the element to add is now the right hand parameter of the combining function. Another easy result to see from this vantage-point is to write the higher-order map function in terms of foldr, by composing the function to act on the elements with cons, as:
In mathematics higher-order functions are also termed operators or functionals. The differential operator in calculus is a common example, since it maps a function to its derivative, also a function. Higher-order functions should not be confused with other uses of the word "functor" throughout mathematics, see Functor (disambiguation).