Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework that, under mild assumptions, allows the exact enforcement of constraints on parameterized sets of functions such as DNNs. Instead of imposing "soft'' constraints via additional terms in the loss, we restrict (a subset of) the DNN parameters to a submanifold on which the constraints are satisfied exactly throughout the entire training procedure. We focus on constraints that are outside the scope of equivariant networks used in Geometric Deep Learning. As a major example of the framework, we restrict filters of a Convolutional Neural Network (CNN) to be wavelets, and apply these wavelet networks to the task of contour prediction in the medical domain.

翻译：深度神经网络（DNNs）因其能够有效逼近大规模函数类而被广泛应用。然而，这种灵活性使得对DNNs施加严格约束成为一个开放性问题。本文提出一个框架，在温和假设条件下，允许对参数化函数集（如DNNs）精确施加约束。我们并非通过在损失函数中添加额外项来施加“软约束”，而是将DNN参数（的子集）限制在一个子流形上，使得整个训练过程中约束得到精确满足。我们重点关注超出几何深度学习中等变网络范畴的约束。作为该框架的一个主要示例，我们将卷积神经网络（CNN）的滤波器限制为小波，并将这些小波网络应用于医学领域的轮廓预测任务。