SVM/SVR Kernels as Quantum Propagators
This work addresses a theoretical gap in machine learning for physics applications, but it is incremental as it builds on existing kernel and quantum theory.
The paper tackled the problem of linking SVM kernel functions to quantum propagators, establishing a mathematical equivalence and showing that kernels corresponding to Green's functions improve SVM predictive accuracy in physical systems, with numerical experiments confirming significant gains.
We establish a mathematical equivalence between Support Vector Machine (SVM) kernel functions and quantum propagators represented by time-dependent Green's functions, which has remained largely unexplored. We demonstrate that many common SVM kernels correspond naturally to Green's functions via operator inversion theory. The sigmoid kernel does not always satisfy Mercer's theorem, and therefore the corresponding Green's function may also fail to perform optimally. We further introduce a Kernel Polynomial Method (KPM) for designing customized kernels that align with Green's functions. Our numerical experiments confirm that employing positive-semidefinite kernels that correspond to Green's functions significantly improves predictive accuracy of SVM models in physical systems.