On Machine Learning Knowledge Representation In The Form Of Partially Unitary Operator. Knowledge Generalizing Operator

Abstract

A new form of ML knowledge representation with high generalization power is developed and implemented numerically. Initial IN attributes and OUT class label are transformed into the corresponding Hilbert spaces by considering localized wavefunctions. A partially unitary operator optimally converting a state from IN Hilbert space into OUT Hilbert space is then built from an optimization problem of transferring maximal possible probability from IN to OUT, this leads to the formulation of a new algebraic problem. Constructed Knowledge Generalizing Operator U can be considered as a IN to OUT quantum channel; it is a partially unitary rectangular matrix of the dimension dim(OUT) dim(IN) transforming operators as A^OUT=U A^IN U^. Whereas only operator U projections squared are observable OUT|U|IN^2 (probabilities), the fundamental equation is formulated for the operator U itself. This is the reason of high generalizing power of the approach; the situation is the same as for the Schr\"odinger equation: we can only measure ^2, but the equation is written for itself.

Tasks

Reproductions