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

Loss functions are an essential part in modern data-driven approaches, 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 ∈ ℝ + , defined via the Riemann–Liouville (RL) 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. [ABSTRACT FROM AUTHOR]