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SVM/SVR Kernels as Quantum Propagators

Created by
  • Haebom

Author

Nan-Hong Kuo, Renata Wong

Outline

This paper establishes a mathematical equivalence between the kernel function of a support vector machine (SVM) and a quantum propagator expressed as a time-varying Green's function. We show that many common SVM kernels correspond naturally to the Green's function via operator inverse theory. Since the sigmoid kernel does not always satisfy Mercer's theorem, its corresponding Green's function may not perform optimally. This paper presents the Kernel Polynomial Method (KPM) for designing a kernel that corresponds to the Green's function. Numerical experiments demonstrate that using a positive semi-definite kernel corresponding to the Green's function significantly improves the predictive accuracy of SVM models in physical systems.

Takeaways, Limitations

Takeaways: By demonstrating the mathematical equivalence between the SVM kernel and the quantum propagator, we present a new possibility for applying quantum mechanics theory to machine learning. KPM enables the design of customized kernels based on the Green's function, which is expected to improve the predictive performance of SVM models. We present a practical method for improving the predictive accuracy of SVM models in physical systems.
Limitations: Some kernels, such as the sigmoid kernel, do not satisfy Mercer's theorem, which may result in suboptimal Green's function performance. Further research is needed to determine the generalizability of kernel design using KPM and its applicability to various systems. Analysis of the computational cost and efficiency of the proposed method is lacking.
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