### Recognition of Generalized Patterns by a Differential Polynomial Neural Network

#### Abstract

A lot of problems involve unknown data relations, identification of which can serve as a generalization of their qualities. Relative values of variables are applied in this case, and not the absolute values, which can better make use of data properties in a wide range of the validity. This resembles more to the functionality of the brain, which seems to generalize relations of variables too, than a common pattern classification. Differential polynomial neural network is a new type of neural network designed by the author, which constructs and approximates an unknown differential equation of dependent variables using special type of root multi-parametric polynomials. It creates fractional partial differential terms, describing mutual derivative changes of some variables, likewise the differential equation does. Particular polynomials catch relations of given combinations of input variables. This type of identification is not based on a whole-pattern similarity, but only to the learned hidden generalized relations of variables.

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