论文标题
傅里叶域变化表述及其适应性的监督学习
Fourier-domain Variational Formulation and Its Well-posedness for Supervised Learning
论文作者
论文摘要
监督的学习问题是在孤立的数据点上给定值的假设功能空间中找到一个函数。受神经网络中的频率原理的启发，我们提出了一种傅立叶域变异表述，以解决监督的学习问题。该公式规定了在连续建模中施加给定值的约束的困难。在我们统一框架内的必要条件下，我们通过根据数据维度显示关键指数来确定傅立叶域变化问题的良好性。在实践中，神经网络可以是实施我们的配方的便捷方法，该方法会自动满足适应性良好的条件。
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.
