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arXiv · 2204.04582

Real order total variation with applications to the loss functions in learning schemes

Pan Liu·Xin Yang Lu·Kunlun He
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Abstract

Loss function are an essential part in modern data-driven approach, such as bi-level training scheme and machine learnings. In this paper we propose a loss function consisting of a $r$-order (an)-isotropic total variation semi-norms $TV^r$, $r\in \mathbb{R}^+$, defined via the Riemann-Liouville (R-L) fractional derivative. We focus on studying key theoretical properties, such as the lower semi-continuity and compactness with respect to both the function and the order of derivative $r$, of such loss functions.

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Pan Liu, Xin Yang Lu, Kunlun He. 2022-04-10. Real order total variation with applications to the loss functions in learning schemes. https://arxiv.org/abs/2204.04582

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