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

• URL: http://arxiv.org/abs/2212.14810v1
• Date: Thu, 22 Dec 2022 06:29:27 GMT
• Title: On Machine Learning Knowledge Representation In The Form Of Partially Unitary Operator. Knowledge Generalizing Operator
• Authors: Vladislav Gennadievich Malyshkin
• Abstract summary: A new form of ML knowledge representation with high generalization power is developed and implemented numerically. $mathcalU$ can be considered as a $mathitIN$ to $mathitOUT$ quantum channel.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A new form of ML knowledge representation with high generalization power is developed and implemented numerically. Initial $\mathit{IN}$ attributes and $\mathit{OUT}$ class label are transformed into the corresponding Hilbert spaces by considering localized wavefunctions. A partially unitary operator optimally converting a state from $\mathit{IN}$ Hilbert space into $\mathit{OUT}$ Hilbert space is then built from an optimization problem of transferring maximal possible probability from $\mathit{IN}$ to $\mathit{OUT}$, this leads to the formulation of a new algebraic problem. Constructed Knowledge Generalizing Operator $\mathcal{U}$ can be considered as a $\mathit{IN}$ to $\mathit{OUT}$ quantum channel; it is a partially unitary rectangular matrix of the dimension $\mathrm{dim}(\mathit{OUT}) \times \mathrm{dim}(\mathit{IN})$ transforming operators as $A^{\mathit{OUT}}=\mathcal{U} A^{\mathit{IN}} \mathcal{U}^{\dagger}$. Whereas only operator $\mathcal{U}$ projections squared are observable $\left\langle\mathit{OUT}|\mathcal{U}|\mathit{IN}\right\rangle^2$ (probabilities), the fundamental equation is formulated for the operator $\mathcal{U}$ itself. This is the reason of high generalizing power of the approach; the situation is the same as for the Schr\"{o}dinger equation: we can only measure $\psi^2$, but the equation is written for $\psi$ itself.

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