论文标题
在机器学习知识表示的形式中，部分统一操作员的形式。知识概括操作员
On Machine Learning Knowledge Representation In The Form Of Partially Unitary Operator. Knowledge Generalizing Operator
论文作者
论文摘要
具有高概括能力的新形式的ML知识表示形式将开发和实现数值。初始$ \ mathit {in} $属性和$ \ mathit {out} $ class标签通过考虑局部波形函数转换为相应的希尔伯特空格。 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.构建的知识概括运算符$ \ Mathcal {u} $可以被视为$ \ Mathit {in} $ to $ \ Mathit {out} $ Quantum Channel;它是尺寸$ \ mathrm {dim}（\ Mathit {out}）\ times \ times \ Mathrm {dim}（\ Mathit {in}）$转换运算符作为$ a^{\ Mathit {\ Mathit} = \ Mathcal {in Int { \ Mathcal {U}^{\ Dagger} $。虽然只有运算符$ \ MATHCAL {u} $投影是可以观察到的$ \ left \ langle \ langle \ mathit {out} | \ Mathcal {u} | \ Mathit {in} \ right \ rangle^2 $（概率），但基础方程是为operator $ $ $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ math。这就是该方法高概括力量的原因。情况与Schrödinger方程相同：我们只能测量$ψ^2 $，但是该方程是为$ψ$本身编写的。
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 Schrödinger equation: we can only measure $ψ^2$, but the equation is written for $ψ$ itself.
