  A supervised learning problem is to find a function in a hypothesis function
space given values on isolated data points. Inspired by the frequency principle
in neural networks, we propose a Fourier-domain variational formulation for
supervised learning problem. This formulation circumvents the difficulty of
imposing the constraints of given values on isolated data points in continuum
modelling. Under a necessary and sufficient condition within our unified
framework, we establish the well-posedness of the Fourier-domain variational
problem, by showing a critical exponent depending on the data dimension. In
practice, a neural network can be a convenient way to implement our
formulation, which automatically satisfies the well-posedness condition.
