Differential Equation Units: Learning Functional Forms of Activation Functions from Data

From path functions to differential forms

Differential privacy for functions and functional data

Differential privacy is a framework for privately releasing summaries of a database. Previous work has focused mainly on methods for which the output is a finite dimensional vector, or an element of some discrete set. We develop methods for releasing functions while preserving differential privacy. Specifically, we show that adding an appropriate Gaussian process to the function of interest yie...

Learning activation functions from data using cubic spline interpolation

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which i...

Functional Coding of Differential Forms

Algebraic computations in differential geometry have usually a strong “analytic” side, and symbolic formula crunching is heavily used, even if at the end, the user needs only numbers, or graphic visualization. We show how to implement in a simple way the domain of differential forms with the p-vector algebra, Hodge “star” operator, and the differentiation. There is no explicit symbolic manipula...

The Pullback Equation for Differential Forms